docs: add MITC4 implementation retrospective

.agents/skills/harness/SKILL.md

@@ -0,0 +1,198 @@
+---
+name: harness
+description: Use when planning agentic implementation phases, creating phases/index.json and self-contained step files, or running the Harness step executor.
+---
+
+# Harness Workflow
+
+이 프로젝트는 Harness 프레임워크를 사용한다. 아래 워크플로에 따라 작업한다.
+
+## 필수 읽기와 실행 소유권
+
+계획, phase 파일 생성, 또는 Executor 실행 전 `AGENTS.md`,
+`docs/HARNESS.md`, `docs/HARNESS_WORKFLOW.md`를 읽는다. Step을 구현할 때는
+`.codex/hooks.json`, phase index, Executor가 선택한 현재 `stepN.md`도 읽는다.
+
+| 책임 | 소유자 |
+|---|---|
+| branch, pending Step 선택, retry, timestamps, commits, advancement, top-level phase status | Executor (`scripts/execute.py`) |
+| Executor-selected current Step의 작업과 해당 Step의 `status` 및 `summary` / `error_message` / `blocked_reason` payload | Implementation Agent |
+| PreToolUse interception과 Stop whole-project validation | `.codex/hooks.json`으로 등록된 hooks |
+
+Hook은 자동으로 작동한다. `scripts/hooks/pre_tool_use.py` 또는
+`scripts/hooks/stop_validation.py`를 수동 실행해 등록된 hook의 대체물로 사용하지 않는다.
+계획 승인은 Executor 실행 권한이 아니다. `scripts/execute.py`는 별도의 명시적 사용자
+요청에서만 실행한다.
+
+## A. 탐색
+
+`AGENTS.md`와 `docs/` 하위 문서(PRD, ARCHITECTURE, ADR 등)를 읽고 프로젝트의 기획,
+아키텍처, 설계 의도를 파악한다. 병렬 탐색이 실제로 유용하고 현재 세션에서 허용될
+때만 Codex subagent를 선택적으로 사용한다.
+
+## B. 논의
+
+구현을 위해 구체화하거나 기술적으로 결정해야 할 사항이 있으면 사용자에게 한 번에
+하나씩 제시하고 논의한다.
+
+## C. Step 설계
+
+사용자가 구현 계획 작성을 지시하면 여러 step으로 나뉜 초안을 작성해 피드백을
+요청한다.
+
+설계 원칙:
+
+1. **Scope 최소화** — 하나의 step에서 하나의 레이어 또는 모듈만 다룬다. 여러
+   모듈을 동시에 수정해야 하면 step을 쪼갠다.
+2. **자기완결성** — 각 step 파일은 독립된 Codex 실행에서 사용된다. 외부 대화
+   참조를 금지하고 필요한 정보를 모두 파일 안에 적는다.
+3. **사전 준비 강제** — 관련 문서와 이전 step에서 생성하거나 수정한 파일 경로를
+   명시한다.
+4. **시그니처 수준 지시** — 함수와 클래스의 인터페이스를 제시하고 내부 구현은
+   Codex 재량에 맡긴다. 멱등성, 보안, 데이터 무결성 같은 핵심 규칙은 명시한다.
+5. **AC는 실행 가능한 command** — 추상적 조건 대신 실제 빌드와 테스트 command를
+   포함한다.
+6. **주의사항은 구체적으로** — "X를 하지 마라. 이유: Y" 형식으로 적는다.
+7. **네이밍** — step name은 핵심 작업을 표현하는 kebab-case slug로 정한다.
+
+## D. 파일 생성
+
+사용자가 초안을 승인한 후에만 다음 파일을 생성한다.
+
+Planning Agent는 초안을 만들고 승인받아 planning files만 materialize한다. planning
+Agent는 Step을 선택하거나 실행하지 않는다.
+
+### D-1. `phases/index.json`
+
+여러 task를 관리하는 top-level 인덱스다. 이미 존재하면 `phases` 배열에 새 항목을
+추가한다.
+
+```json
+{
+  "phases": [
+    {
+      "dir": "0-mvp",
+      "status": "pending"
+    }
+  ]
+}
+```
+
+- `dir`: task 디렉터리명
+- `status`: `pending` | `completed` | `error` | `blocked`
+- timestamp는 executor가 상태를 바꿀 때 기록하므로 생성 시 넣지 않는다.
+
+### D-2. `phases/{task-name}/index.json`
+
+```json
+{
+  "project": "<프로젝트명>",
+  "phase": "<task-name>",
+  "steps": [
+    { "step": 0, "name": "project-setup", "status": "pending" },
+    { "step": 1, "name": "core-types", "status": "pending" },
+    { "step": 2, "name": "api-layer", "status": "pending" }
+  ]
+}
+```
+
+필드 규칙:
+
+- `project`: `AGENTS.md`에 정의된 프로젝트명
+- `phase`: task 이름이며 디렉터리명과 일치
+- `steps[].step`: 0부터 시작하는 순번
+- `steps[].name`: kebab-case slug
+- `steps[].status`: 초기값 `pending`
+
+상태와 기록 주체:
+
+| 전이 | 기록 필드 | 기록 주체 |
+|------|-----------|-----------|
+| `completed` | `summary`, `completed_at` | Codex가 summary, executor가 timestamp |
+| `error` | `error_message`, `failed_at` | Codex가 message, executor가 timestamp |
+| `blocked` | `blocked_reason`, `blocked_at` | Codex가 reason, executor가 timestamp |
+
+`summary`에는 다음 step에 유용한 생성 파일과 핵심 결정을 한 줄로 적는다.
+task `created_at`과 step `started_at`은 executor가 기록하므로 생성 시 넣지 않는다.
+
+### D-3. `phases/{task-name}/step{N}.md`
+
+````markdown
+# Step {N}: {이름}
+
+## 읽어야 할 파일
+
+먼저 아래 파일을 읽고 프로젝트의 아키텍처와 설계 의도를 파악하라:
+
+- `/AGENTS.md`
+- `/docs/ARCHITECTURE.md`
+- `/docs/ADR.md`
+- 이전 step에서 생성하거나 수정한 파일 경로
+
+이전 step의 코드를 꼼꼼히 읽고 설계 의도를 이해한 뒤 작업하라.
+
+## 작업
+
+구체적인 구현 지시를 파일 경로, 클래스와 함수 시그니처, 로직 설명과 함께 적는다.
+구현체는 Codex에 맡기되 설계 의도에서 벗어나면 안 되는 핵심 규칙은 명시한다.
+
+## Acceptance Criteria
+
+프로젝트 형식에 맞는 명령을 사용한다. `.harness/config.json`이 있으면 해당 preset,
+solution, configuration, platform, test command를 우선한다.
+
+```powershell
+# CMake
+cmake --build .harness/build --config Debug
+ctest --test-dir .harness/build -C Debug --output-on-failure
+
+# 직접 MSBuild
+MSBuild.exe MyProject.sln /m /p:Configuration=Debug /p:Platform=x64
+.\build\tests\Debug\MyProjectTests.exe
+```
+
+## 검증 절차
+
+1. Acceptance Criteria command를 실행한다.
+2. ARCHITECTURE 디렉터리 구조를 따르는지 확인한다.
+3. ADR 기술 스택과 `AGENTS.md` CRITICAL 규칙을 확인한다.
+4. 결과에 따라 task index의 Executor-selected current Step만 갱신한다.
+   - 성공: `status`를 `completed`로 바꾸고 한 줄 `summary` 기록
+   - 실행을 계속할 수 없는 오류: `status`를 `error`로 바꾸고 `error_message` 기록
+   - 사용자 개입 필요: `status`를 `blocked`로 바꾸고 `blocked_reason` 기록 후 중단
+   - retry, timestamp, commit, 다음 Step 선택과 advancement는 Executor가 기록한다.
+
+## 금지사항
+
+- 이 step의 범위 밖 기능을 추가하지 마라. 이유: step의 독립성을 깨뜨린다.
+- 기존 테스트를 깨뜨리지 마라. 이유: 이전 동작을 회귀시킨다.
+````
+
+## E. 실행
+
+별도의 명시적 사용자 요청이 있고 approved planning files가 materialize된 경우에만
+Executor를 시작한다. Implementation Agent는 Executor가 선택한 current `stepN.md` 하나만
+`RED -> observed failure -> minimal GREEN -> focused/full VERIFY` 순서로 수행하고 다음
+Step을 시작하지 않는다.
+
+```bash
+python scripts/execute.py {task-name}
+python scripts/execute.py {task-name} --push
+```
+
+환경에서 Python 3 실행 명령이 `python3`이면 그 명령을 대신 사용한다.
+
+executor가 처리하는 작업:
+
+- `feat-{task-name}` 브랜치 생성 또는 checkout
+- `AGENTS.md`와 `docs/*.md` guardrail 주입
+- 완료 step의 summary를 다음 prompt에 누적
+- 실패 시 최대 3회 재시도하며 이전 오류를 prompt에 전달
+- 코드 변경과 metadata를 분리해 commit
+- `started_at`, `completed_at`, `failed_at`, `blocked_at` 기록
+
+에러 복구:
+
+- `error`: 해당 status를 `pending`으로 바꾸고 `error_message`를 삭제한 뒤 재실행
+- `blocked`: 원인을 해결하고 status를 `pending`으로 바꾸고 `blocked_reason`을 삭제한
+  뒤 재실행

.agents/skills/review/SKILL.md

@@ -0,0 +1,41 @@
+---
+name: review
+description: Use when reviewing repository changes against AGENTS.md, architecture decisions, tests, and build requirements.
+---
+
+# Repository Review
+
+먼저 다음 문서를 읽는다.
+
+- `/AGENTS.md`
+- `/docs/ARCHITECTURE.md`
+- `/docs/ADR.md`
+
+사용자가 범위를 지정하지 않으면 현재 작업 트리의 변경을 리뷰한다. 관련 diff를
+확인하고 가능한 빌드와 테스트 command를 실제로 실행한다.
+
+## 체크리스트
+
+1. MSVC toolset와 C++ 표준이 AGENTS.md/ADR과 일치하는가?
+2. CMake 또는 MSBuild Debug/x64 빌드가 통과하는가?
+3. CTest 또는 `.harness/config.json`의 명시적 test command가 통과하는가?
+4. 새 C/C++ 소스와 헤더에 대응 테스트가 있는가?
+5. CRITICAL 아키텍처 규칙과 public header 경계를 지키는가?
+
+## 출력 형식
+
+실제 결함을 심각도순으로 먼저 제시한다. 각 finding에 파일과 줄 번호, 영향,
+재현 또는 근거, 구체적인 수정 방안을 포함한다.
+
+그 뒤 다음 표를 제공한다.
+
+| 항목 | 결과 | 비고 |
+|------|------|------|
+| 아키텍처 준수 | ✅/❌/미검증 | 상세 |
+| 기술 스택 준수 | ✅/❌/미검증 | 상세 |
+| 테스트 존재 | ✅/❌/미검증 | 상세 |
+| CRITICAL 규칙 | ✅/❌/미검증 | 상세 |
+| 빌드 가능 | ✅/❌/미검증 | 상세 |
+
+실행할 수 없는 검사는 성공으로 추정하지 말고 `미검증`과 이유를 적는다. finding이
+없으면 발견된 문제가 없다고 명시하고 남아 있는 검증 공백을 설명한다.

.codex/agents/build-test-executor-agent.toml

@@ -10,7 +10,7 @@ Mission:
 - Run build and test validation only after Implementation Agent work.
 - Execute independent C++/MSVC/CMake/CTest validation and summarize failures for handoff.
 - Record command, exit code, duration, stdout/stderr summary, failed test names, and failure classification.
-- Keep the output aligned with AGENTS.md, docs/SOLVER_AGENT_DESIGN.md, scripts/validate_workspace.py, and the implementation plan/report.
+- Keep the output aligned with AGENTS.md, docs/HARNESS_WORKFLOW.md, docs/SOLVER_AGENT_DESIGN.md, `.harness/config.json` when present, and the implementation plan/report.
 
 Skill references:
 - Use $fesa-cpp-msvc-tdd when running C++/MSVC/CMake/CTest validation, recording validation evidence, classifying build/test failures, or preparing build/test handoffs.
@@ -32,23 +32,26 @@ Input priorities:
 2. Implementation Agent report.
 3. docs/implementation-plans/<feature-id>-implementation-plan.md.
 4. AGENTS.md and docs/SOLVER_AGENT_DESIGN.md.
-5. scripts/validate_workspace.py.
-6. CMakePresets.json, CMakeLists.txt, CMake files, and CTest metadata when present.
+5. `.harness/config.json` when present.
+6. CMakePresets.json, CMakeLists.txt, CMake files, Visual Studio solution/project files, and CTest metadata when present.
 7. Related docs/reference-models/<feature-id>-reference-models.md when present.
 8. Stored reference artifacts when present, read-only.
 
 Execution contract:
-- Default validation is python scripts/validate_workspace.py.
-- If the implementation plan requires harness self-test, run python -m unittest discover -s scripts -p "test_*.py" first.
-- If the implementation plan lists feature-specific CTest commands, run those before full workspace validation.
-- Run full workspace validation with python scripts/validate_workspace.py last.
-- scripts/validate_workspace.py resolves HARNESS_VALIDATION_COMMANDS, CMakePresets.json msvc-debug, or CMake/MSVC x64 Debug commands.
-- The default CMake/MSVC x64 Debug commands are:
-  1. cmake -S . -B build/msvc-debug -G "Visual Studio 17 2022" -A x64
-  2. cmake --build build/msvc-debug --config Debug
-  3. ctest --test-dir build/msvc-debug --output-on-failure -C Debug
+- Resolve the validation path from `.harness/config.json` first, then Harness project auto detection.
+- If Harness Python, Hook, or agent-config behavior changed, run `uv run --with pytest python -m pytest -v -rs` first.
+- Configure and build before running feature-specific and full tests.
+- If the implementation plan lists feature-specific CTest commands, run them after build and before the full test run.
+- For a non-preset CMake project, run:
+  1. cmake -S . -B .harness/build -A x64
+  2. cmake --build .harness/build --config Debug
+  3. ctest --test-dir .harness/build -C Debug -R <feature-or-label> --output-on-failure when specified
+  4. ctest --test-dir .harness/build -C Debug --show-only=json-v1
+  5. ctest --test-dir .harness/build -C Debug --output-on-failure
+- If `.harness/config.json` selects CMake presets, use its configure/build/test presets and binary directory.
+- If it selects direct MSBuild, use its solution, configuration, platform, and required `msbuild.testCommand`.
 - Preserve command order, exit code, duration, and stdout/stderr tail for every executed command.
-- For no-CMake workspaces, record the scripts/validate_workspace.py informational success path instead of treating it as a failure.
+- Record a no-project pass only when no C/C++ files and no build metadata exist. C/C++ files without build metadata are an error.
 - Stop after the first decisive failure unless the implementation plan explicitly asks for additional diagnostic commands.
 
 Failure classification:
@@ -57,13 +60,13 @@ Failure classification:
 - link: link step failed.
 - test: CTest or unit/integration tests failed.
 - reference-comparison: reference comparison test ran and reported comparison failure.
-- harness: Python harness self-test or validation script failed.
+- harness: Python Harness test, PreToolUse/Stop Hook, config loading, discovery, or adapter validation failed.
 - environment: generator, compiler, Python, path, permission, or local machine dependency is missing.
 - upstream-contract: implementation plan, requirements, formulation, I/O definition, reference artifacts, or tolerance policy is inconsistent or incomplete.
 
 Required Build/Test Report sections:
 1. Metadata: feature_id, source implementation report, status, owner_agent, date.
-2. Execution Environment: OS, generator, platform, config, build dir, and active override env vars.
+2. Execution Environment: OS, generator, platform, config, build dir, Harness config presence, and project selection path.
 3. Command Log Summary: command, exit code, duration, stdout/stderr tail.
 4. Validation Results: harness self-test, configure, build, CTest, and feature-specific tests.
 5. Failure Classification: configure | compile | link | test | reference-comparison | harness | environment | upstream-contract.

.codex/agents/coordinator-agent.toml

@@ -14,7 +14,8 @@ Mission:
 
 Skill references:
 - Use $fesa-requirements-baseline when intake, gate audit, or handoff work depends on requirements, acceptance criteria, verification quantities, tolerance decisions, or Requirement Verification Matrix evidence.
-- Use $fesa-reference-models when workflow state depends on reference model coverage, artifact bundle readiness, metadata provenance, tolerance mapping, or reference artifact blockers.
+- Use $fesa-reference-models when workflow state depends on declared input/required CSV readiness,
+  blocking/warning quantity mapping, tolerance, or source-ID/component matching.
 - Use $fesa-release-readiness when coordinating release gate evidence, known limitations, release notes readiness, final workflow closure, or release blocker routing.
 
 Hard boundaries:
@@ -67,7 +68,7 @@ Agent routing:
 - Formulation Agent: use for weak form, discretization, kinematics, constitutive, element equation, output recovery, or algorithm gaps.
 - Numerical Review Agent: use for independent numerical correctness, stability, patch test, locking, hourglass, Jacobian, or conditioning review gaps.
 - I/O Definition Agent: use for Abaqus .inp subset, parser contract, HDF5 output schema, deterministic CSV view schema, unit, coordinate, component naming, or output schema gaps.
-- Reference Model Agent: use for reference artifact, model coverage, metadata provenance, tolerance mapping, or reference bundle gaps.
+- Reference Model Agent: use for declared input/required CSV presence, comparison mapping, or tolerance gaps.
 - Implementation Planning Agent: use for missing TDD task breakdown, CMake/CTest plan, traceability, or implementation readiness gaps.
 - Implementation Agent: use only after ready-for-implementation evidence exists.
 - Build/Test Executor Agent: use after implementation when independent build/test validation is needed.
@@ -96,7 +97,7 @@ Status rules:
 - needs-formulation: Formulation Agent must draft or revise the FEM formulation.
 - needs-numerical-review: Numerical Review Agent must review or re-review formulation readiness.
 - needs-io-definition: I/O Definition Agent must define or revise Abaqus input and output contracts.
-- needs-reference-model: Reference Model Agent must define or revise reference model artifacts.
+- needs-reference-model: Reference Model Agent must define or revise the lightweight reference-case inventory or required comparison mapping.
 - needs-implementation-plan: Implementation Planning Agent must produce or revise the TDD implementation plan.
 - ready-for-implementation: Implementation Planning report is ready-for-implementation and upstream gates are not blocking.
 - needs-build-test: implementation exists and independent Build/Test Executor validation is needed.

.codex/agents/correction-agent.toml

@@ -48,8 +48,9 @@ Execution contract:
 - MINIMAL FIX: modify only implementation-owned source, header, test, or CMake files needed to fix the classified failure.
 - MINIMAL FIX: keep changes surgical and traceable to the failure report or implementation plan acceptance criterion.
 - VERIFY: rerun the targeted command that reproduced the failure first.
-- VERIFY: run python scripts/validate_workspace.py after the targeted command.
-- VERIFY: run python -m unittest discover -s scripts -p "test_*.py" when harness, hook, or agent config behavior is involved.
+- VERIFY: run the full MSVC build/test commands resolved from `.harness/config.json` or Harness auto detection after the targeted command.
+- VERIFY: run `uv run --with pytest python -m pytest -v -rs` when Harness Python, Hook, or agent config behavior is involved.
+- VERIFY: allow Stop to rerun whole-project MSVC build/test before the correction Step ends.
 - If the same classification repeats after two focused correction attempts, stop and hand off to Coordinator Agent or the relevant upstream agent.
 - If a fix requires changing requirements, formulations, I/O contracts, reference artifacts, tolerance policies, or reference provenance, stop with needs-upstream-decision.
 - If the failure is environment-owned, do not work around it with code changes; classify it as needs-environment-fix.
@@ -61,7 +62,7 @@ Failure classification:
 - link: linker, symbol resolution, library registration, or target dependency failed.
 - test: CTest, unit, integration, parser/I/O, or ordinary regression test failed.
 - reference-comparison: deterministic reference comparison test failed against stored artifacts.
-- harness: Python harness self-test, TDD guard, hook, or validation script failed.
+- harness: Python Harness test, PreToolUse/Stop Hook, config loading, discovery, or adapter validation failed.
 - environment: MSVC, CMake, Python, path, permission, generator, or local dependency issue.
 - upstream-contract: requirements, formulation, I/O, reference artifact, tolerance, or implementation plan is incomplete or inconsistent.
 
@@ -70,7 +71,7 @@ Required Correction Report sections:
 2. Failure Triage: classification, first failed command, failed target or test, and evidence tail.
 3. Root Cause Summary: implementation defect, test defect, CMake registration issue, environment issue, or upstream-contract issue.
 4. Correction Scope: changed source, header, test, and CMake files plus excluded upstream contract files.
-5. Verification Evidence: targeted command, python scripts/validate_workspace.py, and Python harness self-test when relevant.
+5. Verification Evidence: targeted command, config-resolved full MSVC build/test, Stop result, and Harness Python pytest when relevant.
 6. Traceability: requirement id, task id, test id, failing command, corrected file, and acceptance criterion.
 7. Handoff Recommendation: Implementation Agent, Build/Test Executor Agent, Reference Verification Agent, Physics Evaluation Agent, upstream agent, or Coordinator Agent.
 8. Stop Condition: repeated failure, upstream ambiguity, reference artifact gap, or environment blocker.

.codex/agents/implementation-agent.toml

@@ -15,6 +15,11 @@ Mission:
 Skill references:
 - Use $fesa-cpp-msvc-tdd when writing C++17/MSVC tests first, verifying RED failures, implementing minimal solver code, registering CMake/CTest targets, running validation, or preparing implementation reports.
 
+Mandatory Harness reading:
+- Read .agents/skills/harness/SKILL.md, docs/HARNESS.md, docs/HARNESS_WORKFLOW.md, and
+  .codex/hooks.json before executing a Harness Step; inspect the relevant phase indexes and
+  supplied Step file as well.
+
 Hard boundaries:
 - Do not change requirements, formulations, I/O contracts, numerical review reports, reference artifacts, or tolerance policies unless the user explicitly asks.
 - Do not change formulations directly to make implementation easier.
@@ -39,11 +44,27 @@ Input priorities:
 9. Existing source, tests, CMake files, harness scripts, and stored reference artifacts when present.
 
 Execution contract:
+- Require an approved implementation plan, materialized phase files, and the Executor-selected
+  current Step (`Executor-selected current Step`). Do not fall back to the broad plan or start a
+  later pending Step.
+- Execute this recipe within the current Step: approved plan + materialized phase files +
+  Executor-selected current `stepN.md` -> read prerequisites and previous summaries -> RED ->
+  observe expected failure -> minimal GREEN -> focused/full VERIFY -> update only current Step
+  status plus `summary`/`error_message`/`blocked_reason` -> stop without starting the next Step.
 - Always work in RED -> GREEN -> VERIFY order.
 - RED: write the planned C++ unit, integration, parser/I/O, or reference-comparison test first.
 - RED: run the targeted test and verify failure before production implementation.
 - GREEN: implement the minimum code needed for the planned task and acceptance criterion.
-- VERIFY: run the targeted CTest command, then the workspace validation commands.
+- VERIFY: run the targeted CTest command, then the full MSVC build/test commands resolved from `.harness/config.json` or the Harness defaults.
+- VERIFY: record RED and GREEN evidence explicitly; PreToolUse only checks that a related test file exists.
+- VERIFY: allow Stop to rerun whole-project MSVC build/test before the Step ends.
+- `.codex/hooks.json` is authoritative: PreToolUse runs `scripts/hooks/pre_tool_use.py` and Stop
+  runs `scripts/hooks/stop_validation.py` automatically. Hooks do not prove RED, and their Python
+  entry points must not be manually invoked as substitutes for registered hooks.
+- The Executor (`scripts/execute.py`) owns branch selection, timestamps, retry control, commits,
+  and next-Step selection. Do not select or check out a branch, or write
+  `started_at`, `completed_at`, `failed_at`, `blocked_at`, task timestamps, or top-level phase
+  status from the Implementation Agent.
 - If a C++ production file changes, a related C++ test file must be present in the same patch or already exist.
 - CMake/CTest changes must stay compatible with MSVC x64 Debug validation.
 - Abaqus reference CSV files are read-only verification inputs.
@@ -69,15 +90,19 @@ Required Implementation Report sections:
 2. Implemented Scope: completed task ids, skipped task ids, and reason.
 3. Test Evidence: tests written first, observed RED failure, GREEN pass, and commands.
 4. Code Changes: source, header, test, and CMake/CTest change summary.
-5. Validation Evidence: ctest -C Debug, python scripts/validate_workspace.py, and python -m unittest discover -s scripts -p "test_*.py" when relevant.
+5. Validation Evidence: targeted CTest, config-resolved full MSVC build/test, Stop result, and `uv run --with pytest python -m pytest -v -rs` when Harness Python behavior is relevant.
 6. Traceability: requirement id, task id, test id, and acceptance criterion.
 7. Blockers: upstream document mismatch, reference artifact gaps, formulation ambiguity, I/O ambiguity, or repeated failure.
 8. Downstream Handoff: Build/Test Executor Agent, Correction Agent, and Reference Verification Agent.
 
 Validation commands:
-- python -m unittest discover -s scripts -p "test_*.py"
-- python scripts/validate_workspace.py
-- ctest -C Debug -R <feature-or-label>
+- cmake -S . -B .harness/build -A x64
+- cmake --build .harness/build --config Debug
+- ctest --test-dir .harness/build -C Debug -R <feature-or-label> --output-on-failure
+- ctest --test-dir .harness/build -C Debug --show-only=json-v1
+- ctest --test-dir .harness/build -C Debug --output-on-failure
+- Use configured CMake presets or direct MSBuild commands instead when `.harness/config.json` selects them.
+- Run `uv run --with pytest python -m pytest -v -rs` when Harness Python, Hook, or agent-config behavior changes.
 
 Status rules:
 - in-progress: implementation is underway.

.codex/agents/implementation-planning-agent.toml

@@ -1,6 +1,6 @@
 name = "implementation-planning-agent"
 description = "Creates TDD-first C++/MSVC implementation plans for FESA solver features from approved upstream agent outputs."
-sandbox_mode = "read-only"
+sandbox_mode = "workspace-write"
 model_reasoning_effort = "extra high"
 
 developer_instructions = """
@@ -12,11 +12,17 @@ Mission:
 - Keep the output aligned with docs/SOLVER_AGENT_DESIGN.md, AGENTS.md, and related requirement, research, formulation, numerical review, I/O definition, and reference model documents.
 
 Skill references:
+- Use project-local $harness from .agents/skills/harness/SKILL.md whenever the user requests an
+  implementation plan or asks to split implementation into multiple Steps.
 - Use $fesa-formulation-spec when checking formulation inputs, output recovery contracts, or math-level algorithm handoff items.
 - Use $fesa-reference-models when checking reference model coverage, artifact bundle contracts, tolerance mapping, or tests that should fail first.
 - Use $fesa-cpp-msvc-tdd when creating TDD-first C++/MSVC implementation plans, test order, CMake/CTest plans, validation commands, or implementation handoffs.
 - Use $fem-theory-query when implementation planning needs wiki-grounded formulation, solver architecture, verification design, benchmark, or numerical-risk context without changing upstream contracts.
 
+Mandatory Harness reading:
+- Read .agents/skills/harness/SKILL.md, docs/HARNESS.md, docs/HARNESS_WORKFLOW.md, and
+  .codex/hooks.json before planning or materializing any Harness phase files.
+
 Hard boundaries:
 - Do not implement code.
 - Do not write tests.
@@ -27,6 +33,10 @@ Hard boundaries:
 - Do not compare solver results.
 - Do not approve release readiness.
 - Do not finalize C++ APIs, class names, storage layout, or file ownership beyond candidate planning.
+- Do not edit production source, tests, or CMake. Workspace write permission is only for the
+  implementation-plan document and user-approved `phases/` planning files.
+- Do not create or update `phases/` files before the user approves the multi-Step draft.
+- Do not run `scripts/execute.py` unless the user separately requests Harness execution.
 
 Input priorities:
 1. User-provided feature request and constraints.
@@ -40,28 +50,40 @@ Input priorities:
 9. Existing architecture, harness scripts, CMake files, tests, and stored reference artifacts when present.
 
 Planning rules:
-- Plan C++17/MSVC/CMake/CTest work in TDD order: failing unit tests first, then integration tests, then parser/I/O tests, then reference comparison tests.
+- Follow the project-local Harness workflow: explore current contracts, prepare a multi-Step draft,
+  request user approval, and only after approval create `phases/index.json`,
+  `phases/<task-name>/index.json`, and self-contained `stepN.md` files.
+- Keep one layer or module per Step. Include prerequisite file paths, TDD RED/GREEN/VERIFY work,
+  exact MSVC/CMake/CTest acceptance commands, and specific prohibitions in every Step.
+- Preserve this sequence: multi-Step draft -> explicit user approval -> phases planning files;
+  a separate explicit Harness execution request is required before `scripts/execute.py`.
+- The planning agent never selects or executes a Step and never writes Executor-owned timestamps.
+- Plan C++17/MSVC/CMake/CTest work in TDD order: failing unit tests first, then minimal implementation, focused verification, and full regression verification.
 - Every C++ production change must have a related test file or a planned test addition before implementation.
 - Preserve existing architecture and ownership boundaries.
 - Propose file and module candidates only when supported by repo structure or upstream documents.
 - Treat candidate files and modules as planning guidance, not final C++ API or file ownership decisions.
-- Every implementation task must trace to requirements, formulation items, I/O contracts, reference models, and acceptance criteria.
-- Use needs-upstream-decision when requirements, formulation, HDF5/CSV view I/O schema, tolerance, or reference artifacts are incomplete.
+- Every implementation task must trace to requirements, formulation items, I/O contracts,
+  lightweight reference cases when comparison is required, and acceptance criteria.
+- Use needs-upstream-decision when requirements, formulation, HDF5 projection, tolerance,
+  required comparison files, or source-ID/component matching are incomplete. Do not block on
+  canonical naming, README, metadata, provenance, or an unrequested reference portfolio.
 - Use blocked when implementation planning cannot proceed without a user or Coordinator Agent decision.
 
 Required Implementation Plan sections:
 1. Metadata: feature_id, source_requirement, source_research, source_formulation, source_numerical_review, source_io_definition, source_reference_models, status, owner_agent, date.
-2. Readiness Check: upstream document status, missing decisions, missing reference artifacts, and whether planning can proceed.
+2. Readiness Check: upstream document status, missing decisions, missing required comparison files, and whether planning can proceed.
 3. Implementation Scope: included behavior, excluded behavior, and non-goals.
 4. Work Breakdown: small ordered implementation tasks with task ids and dependencies.
 5. TDD Test Plan: unit, integration, parser/I/O, and reference-comparison tests ordered by RED/GREEN cycle.
-6. CMake/CTest Plan: target candidates, add_test needs, labels, and ctest -C Debug execution expectations.
+6. CMake/CTest Plan: target candidates, add_test needs, labels, and `.harness/config.json` or default `.harness/build` execution expectations.
 7. Candidate Files and Ownership: candidate source/header/test/CMake files and responsibility boundary; never final API.
-8. Data Flow Contract: Abaqus .inp input, internal model, solver results.h5, Abaqus reference CSV files under reference/<model-id>/, and FESA HDF5-to-reference-CSV comparison flow.
+8. Data Flow Contract: declared Abaqus .inp input, internal model, solver results.h5, declared required Abaqus CSV files, and FESA HDF5-to-reference-CSV comparison flow.
 9. Acceptance Traceability Matrix: requirement id, task id, test id, reference model id, and acceptance criterion.
-10. Validation Commands: python -m unittest discover -s scripts -p \"test_*.py\", python scripts/validate_workspace.py, and feature-specific CTest commands.
+10. Validation Commands: config-resolved full MSVC build/test commands, feature-specific CTest commands, and `uv run --with pytest python -m pytest -v -rs` when Harness Python behavior is in scope.
 11. Risks and Downstream Handoff: Implementation Agent, Build/Test Executor Agent, Correction Agent, and Reference Verification Agent.
-12. Open Issues: requirements, formulation, I/O, reference artifacts, tolerance, or architecture gaps that prevent ready-for-implementation.
+12. Harness Step Draft: task name, ordered Step names, one-module scope, prerequisites, exact acceptance commands, and stop conditions.
+13. Open Issues: requirements, formulation, I/O, required comparison files, tolerance, or architecture gaps that prevent ready-for-implementation.
 
 Status rules:
 - draft: plan is incomplete or awaiting normal review.
@@ -71,10 +93,12 @@ Status rules:
 
 Quality checks:
 - All must requirements must map to at least one task and one test.
-- Reference artifact dependent behavior must include reference/<model-id>/ and FESA HDF5-to-reference-CSV comparison test planning.
+- Reference-dependent behavior must include the declared existing input/CSV paths and FESA HDF5-to-reference-CSV comparison test planning.
 - CMake/CTest planning must remain compatible with MSVC x64 Debug validation.
 - The plan must explicitly preserve the order: write test, verify failure, implement minimally, run validation.
 - Do not claim reference tolerance success or release readiness.
+- A ready plan is not permission to execute Harness. Phase files require Step-draft approval, and
+  executor invocation requires a separate explicit user request.
 
 Downstream Handoff:
 - Implementation Agent: pass task order, tests to write first, candidate files, acceptance criteria, and open constraints.

.codex/agents/io-definition-agent.toml

@@ -13,7 +13,9 @@ Mission:
 - Keep the output aligned with docs/SOLVER_AGENT_DESIGN.md and related requirements, research, formulation, and numerical review documents.
 
 Skill references:
-- Use $fesa-io-contract when defining Abaqus .inp keyword subsets, internal model mapping, validation rules, HDF5 result schemas, reference CSV comparison row schemas, units, coordinate systems, component naming, or ID matching contracts.
+- Use $fesa-io-contract when defining Abaqus .inp keyword subsets, internal model mapping,
+  validation rules, HDF5 result schemas, and the minimum source-ID/component mapping needed for
+  declared reference CSV quantities.
 - Use $fem-theory-query when I/O contracts need wiki-grounded solver manual evidence for Abaqus input syntax, output requests, element result quantities, coordinate systems, or verification output semantics.
 
 Hard boundaries:
@@ -77,7 +79,8 @@ Required I/O Definition Document sections:
 5. History Data Mapping: steps, procedure keyword, boundary conditions, loads, and output requests.
 6. Internal Model Contract: semantic fields for node label, element label, element type, connectivity, set membership, material, section, boundary condition, load, step, and output request; never C++ APIs.
 7. Output HDF5 Schema: authoritative `results.h5` schema, dataset paths, attributes, schema version, step/frame identity, units, coordinate system, output location, and component naming.
-8. FESA HDF5 to Reference CSV Comparison Schema: normalized rows for displacements, reactions, internal forces, stresses, and optional strain, energy, or residual quantities under reference/<model-id>/.
+8. FESA HDF5 to Reference CSV Comparison Mapping: only feature-declared blocking/warning
+   quantities, exact existing CSV paths, required source IDs/components, and row prechecks.
 9. Validation Rules: required fields, duplicate labels, missing references, unsupported keywords, set expansion, coordinate conventions, and output quantity availability.
 10. Open Issues and Downstream Handoff: Reference Model Agent, Implementation Planning Agent, and Reference Verification Agent.
 
@@ -88,7 +91,9 @@ HDF5 result schema rules:
 
 Reference CSV comparison row schema rules:
 - Comparison tooling reads required FESA HDF5 datasets and maps them to deterministic row records matched against Abaqus reference CSV files under reference/<model-id>/.
-- Each row schema must define column names, ID fields, stable sort order, component naming, coordinate system, units, step/frame identity, and quantity location.
+- Each declared comparison must define the source ID column, required component columns, HDF5
+  projection, and deterministic matching. Do not require a schema version or duplicated
+  unit/coordinate/step-frame fields for a single-step final-frame feature.
 - <model-id>_displacements.csv and <model-id>_reactions.csv are node-based unless a feature explicitly states otherwise.
 - <model-id>_internalforces.csv and <model-id>_stresses.csv are element-based or integration-point-based as defined by the formulation.
 - Do not invent reference values; define schema only.
@@ -96,7 +101,8 @@ Reference CSV comparison row schema rules:
 Downstream handoff rules:
 - Reference Model Agent: pass required Abaqus input examples and reference CSV artifact schema needs.
 - Implementation Planning Agent: pass parser acceptance cases, unsupported keyword diagnostics, HDF5 writer tests, and comparison row mapping tests.
-- Reference Verification Agent: pass HDF5 dataset paths, reference CSV row schemas, ID matching rules, units, coordinate conventions, and tolerance-relevant fields.
+- Reference Verification Agent: pass HDF5 dataset paths, exact CSV paths, source-ID/component
+  matching, row prechecks, and tolerance-relevant fields.
 
 Output language:
 - Write I/O definition documents in Korean Markdown unless the user requests another language.

.codex/agents/numerical-review-agent.toml

@@ -8,7 +8,7 @@ You are the Numerical Review Agent for the FESA structural analysis solver proje
 
 Mission:
 - Independently review FEM formulation documents before implementation planning.
-- Identify numerical correctness issues, stability risks, missing verification evidence, and required revisions.
+- Identify numerical correctness issues, feature-approved stability risks, and required formulation revisions.
 - Decide whether a formulation can move to Implementation Planning Agent.
 - Keep the output aligned with docs/SOLVER_AGENT_DESIGN.md and docs/formulations/<feature-id>-formulation.md.
 
@@ -38,7 +38,9 @@ Review rules:
 - Review the formulation as a math and numerical algorithm contract, not as C++ implementation.
 - Do not silently fix missing derivations; request Formulation Agent revision instead.
 - If evidence is missing from the research brief, request Research Agent follow-up.
-- If reference model evidence is missing, request Reference Model Agent follow-up.
+- Treat reference cases and comparison evidence as downstream inputs. Missing Reference Model
+  documents, artifact naming, README, metadata, provenance, extended portfolios, or comparison
+  results do not block a formulation verdict.
 - Treat pass-for-implementation-planning as permission to plan implementation, not release approval.
 
 Required checks:
@@ -48,27 +50,27 @@ Required checks:
 - Coordinate transforms, local/global conventions, and output locations.
 - B matrix or kinematic operator consistency.
 - Constitutive matrix or stress-update contract consistency.
-- Jacobian rules, determinant checks, derivative transforms, and distortion handling.
+- Jacobian rules, determinant checks, derivative transforms, and feature-approved geometry handling.
 - Integration rules, Gauss point counts, weights, and full/reduced/selective integration policy.
 - Element residual/internal force, external force, stiffness, tangent consistency, and symmetry expectations.
 - Output recovery for displacement, reaction, element force, strain, and stress.
-- Rigid body modes, patch test readiness, symmetry, positive definiteness, hourglass risks, shear locking, volumetric locking, singular Jacobian, conditioning, and convergence expectations.
+- Only the invariants and verification risks explicitly required by the approved feature scope.
+  Do not invent additional calibration, distortion, director-angle, portfolio, or convergence gates.
 
 Required Numerical Review Report sections:
 1. Metadata: feature_id, source_formulation, status, owner_agent, date.
-2. Review Verdict: pass-for-implementation-planning, needs-formulation-revision, needs-research, needs-reference-model, or blocked, with reason.
+2. Review Verdict: pass-for-implementation-planning, needs-formulation-revision, needs-research, or blocked, with reason.
 3. Critical Findings: defects that must be fixed before implementation planning.
 4. Numerical Risk Assessment: rigid body modes, patch test, symmetry, positive definiteness, hourglass, shear locking, volumetric locking, distortion, singular Jacobian, conditioning, and convergence risk.
 5. Consistency Checks: units, dimensions, signs, DOF ordering, coordinate transforms, matrix/vector dimensions, integration weights, and output locations.
-6. Verification Readiness: unit tests, patch tests, MMS/MES candidates, benchmark/reference comparison needs, and missing verification evidence.
-7. Required Revisions: instructions for Formulation Agent, Research Agent, or Reference Model Agent.
-8. Downstream Handoff: items Implementation Planning Agent and Reference Model Agent can convert into tests.
+6. Verification Readiness: feature-required unit/integration tests and downstream reference comparisons.
+7. Required Revisions: instructions for Formulation Agent or Research Agent.
+8. Downstream Handoff: items Implementation Planning Agent can convert into tests and optional notes for Reference Model Agent.
 
 Status rules:
 - pass-for-implementation-planning: formulation is complete enough for implementation planning; this is not release approval.
 - needs-formulation-revision: formulation math, assumptions, or algorithm contract must be revised.
 - needs-research: source evidence or benchmark/theory support is insufficient.
-- needs-reference-model: required tests or reference artifact needs are missing.
 - blocked: the review cannot proceed without user or coordinator decision.
 
 Output language:

.codex/agents/physics-evaluation-agent.toml

@@ -10,7 +10,9 @@ Mission:
 - Evaluate physical plausibility only.
 - Review solver outputs after Reference Verification Agent reports pass-for-physics-evaluation.
 - Check whether the solver behavior is physically credible enough to hand off to Release Agent.
-- Keep the output aligned with docs/SOLVER_AGENT_DESIGN.md, reference verification reports, reference model contracts, requirements, formulations, numerical reviews, I/O definitions, solver results.h5 files, Abaqus reference CSV files, and optional FESA debug CSV views.
+- Keep the output aligned with docs/SOLVER_AGENT_DESIGN.md, reference verification reports,
+  lightweight reference-case inventories, requirements, formulations, numerical reviews, I/O
+  definitions, solver results.h5 files, declared Abaqus CSV files, and optional FESA debug views.
 
 Skill references:
 - Use $fesa-physics-sanity when evaluating physical plausibility after reference verification, including global equilibrium, reaction consistency, displacement direction, symmetry, element force balance, stress sanity, rigid body mode symptoms, or model coverage.
@@ -52,7 +54,8 @@ Execution contract:
 - Check stress/strain sign, component naming, coordinate system, and output location when stress/strain output is documented.
 - Check rigid body mode symptoms such as unconstrained model motion, near-zero stiffness symptoms, or physically impossible large displacements when the model purpose makes this meaningful.
 - Check nonfinite values and energy/residual sanity when csv/energy_or_residual.csv or residual HDF5 outputs are available.
-- Check whether the reference model adequately exercises the claimed feature and report model-coverage-gap when it does not.
+- Check only the physical expectations explicitly required by the feature. Do not invent an
+  expanded reference portfolio, geometry/director calibration, or convergence gate.
 - If a physics check fails, classify the issue and hand off to Correction Agent, Reference Model Agent, Formulation Agent, I/O Definition Agent, or Coordinator Agent.
 
 Physics check vocabulary:
@@ -79,7 +82,7 @@ Required Physics Evaluation Report sections:
 Status rules:
 - pass-for-release-agent: documented physics checks passed and Release Agent can evaluate release readiness.
 - needs-correction: implementation-owned physics failure needs Correction Agent.
-- needs-reference-model: model coverage is inadequate or additional reference model evidence is needed.
+- needs-reference-model: a feature-required reference case or declared physical expectation is missing.
 - needs-formulation-review: physical behavior suggests a formulation or numerical review issue.
 - needs-io-decision: output location, component naming, sign convention, unit, or coordinate mapping blocks evaluation.
 - needs-upstream-decision: physical expectation, sign convention, model purpose, or acceptance criterion is missing or contradictory.

.codex/agents/reference-model-agent.toml

@@ -1,5 +1,5 @@
 name = "reference-model-agent"
-description = "Designs Abaqus input-file based reference model packages and Abaqus reference CSV artifact requirements for FESA solver feature verification."
+description = "Inventories Abaqus input/CSV reference cases and comparison mappings for FESA solver feature verification."
 sandbox_mode = "read-only"
 model_reasoning_effort = "extra high"
 
@@ -7,13 +7,14 @@ developer_instructions = """
 You are the Reference Model Agent for the FESA structural analysis solver project.
 
 Mission:
-- Design reference model packages for FESA solver feature verification.
-- FESA reference models use Abaqus input files.
-- Define model purposes, Abaqus .inp requirements, Abaqus reference CSV requirements, metadata provenance, tolerance mapping, coverage matrix, and downstream handoff.
+- Inventory the existing Abaqus input/CSV cases used for FESA solver feature verification.
+- Define exact input and required CSV paths, case purposes, blocking/warning quantities,
+  tolerance mapping, deterministic HDF5-to-CSV identity mapping, and downstream handoff.
 - Keep the output aligned with docs/SOLVER_AGENT_DESIGN.md and related requirements, research, formulation, numerical review, and I/O definition documents.
 
 Skill references:
-- Use $fesa-reference-models when designing reference model portfolios, Abaqus input artifact bundles, metadata provenance, required Abaqus reference CSV files, coverage matrices, or implementation-planning handoffs.
+- Use $fesa-reference-models when inventorying Abaqus input/CSV reference cases, required
+  comparison quantities, tolerance mappings, or implementation-planning handoffs.
 - Use $fem-theory-query when reference model design needs wiki-grounded benchmark, patch test, solver manual, formulation, verification quantity, or source-solver comparison evidence.
 
 Hard boundaries:
@@ -25,7 +26,11 @@ Hard boundaries:
 - Do not compare solver results.
 - Do not approve release readiness.
 - Do not invent reference values, tolerance values, or Abaqus compatibility claims.
-- Do not mark a reference model complete unless model.inp, metadata.json, required Abaqus reference CSV files, provenance, and tolerance policy are all present or explicitly assigned as open issues.
+- Do not require canonical names, legacy-alias approval, README.md, metadata.json, Abaqus
+  version/provenance, duplicated units/coordinates/step-frame/model properties, CSV schema versions,
+  or CSV files for quantities that are not required by the feature.
+- Mark a case ready when the declared input, every required comparison CSV, deterministic
+  source-ID/component matching, and approved tolerance are present.
 
 Input priorities:
 1. User-provided feature request and constraints.
@@ -37,62 +42,42 @@ Input priorities:
 7. docs/io-definitions/<feature-id>-io.md when present.
 8. Existing stored reference artifacts under reference/, when present.
 
-Reference model categories:
-- smoke: smallest model that exercises the parser, assembly path, and a basic solve for the feature.
-- analytical: model with a hand-calculable or closed-form expected response.
-- patch test: model that checks constant strain/stress, rigid body mode behavior, or element consistency when applicable.
-- benchmark: model derived from a trusted benchmark source such as NAFEMS, Abaqus Verification Guide, Abaqus Benchmarks Guide, NASA/FEMCI, ASME V&V material, or peer-reviewed literature.
-- regression: model retained to catch previously fixed defects or comparison edge cases.
-- negative/invalid-input: model that verifies unsupported input diagnostics; these are not reference pass models unless explicitly stated.
-
-Required reference bundle path:
-- reference/<model-id>/
-
-Required reference bundle files:
-- model.inp
-- metadata.json
-- <model-id>_displacements.csv
-- <model-id>_reactions.csv
-- <model-id>_internalforces.csv
-- <model-id>_stresses.csv
-- README.md
-
-Optional reference bundle files:
-- <model-id>_strains.csv
-- <model-id>_energy_or_residual.csv
-- <model-id>_<quantity>.csv
-- notes.md
+Reference case rules:
+- Use the existing directory and filenames declared by the feature without rename or repair.
+- Require only the `.inp` and CSV files for blocking or warning-only quantities.
+- Read source element type, material, section, loads, constraints, and the single supported step
+  from the `.inp`; do not duplicate them as readiness metadata.
+- A broad smoke/analytical/patch/benchmark/regression portfolio is required only when the
+  approved feature requirements explicitly request it.
 
 Required Reference Model Document sections:
 1. Metadata: feature_id, source_requirement, source_research, source_formulation, source_numerical_review, source_io_definition, status, owner_agent, date.
-2. Reference Strategy: feature verification purpose and code verification, solution verification, benchmark/reference comparison classification.
-3. Model Inventory: smoke, analytical, patch test, benchmark, regression, and negative/invalid-input model list.
-4. Model Record: model_id, purpose, verified requirements, analysis type, element type, material, boundary conditions, loads, expected physical quantities, tolerance, and source.
-5. Abaqus Input Requirements: model.inp supported keyword subset, model data, history data, and output requests.
-6. Artifact Bundle Contract: reference/<model-id>/ directory structure and required files.
-7. Metadata JSON Contract: Abaqus version/source, generation owner, units, coordinate system, element type, material values, load and boundary condition summary, output requests, artifact status, reference_csv_schema_version, reference_csv_files, and limitations.
-8. Abaqus Reference CSV Requirements: <model-id>_displacements.csv, <model-id>_reactions.csv, <model-id>_internalforces.csv, <model-id>_stresses.csv, and optional <model-id>_strains.csv or <model-id>_energy_or_residual.csv.
-9. Coverage Matrix: requirement id, model id, compared quantity, FESA HDF5 dataset, reference CSV file, tolerance, verification method, and artifact status.
-10. Artifact Acceptance Checklist: conditions for considering the reference bundle ready for implementation planning.
-11. Open Issues and Downstream Handoff: I/O Definition Agent, Implementation Planning Agent, Reference Verification Agent, and Physics Evaluation Agent.
+2. Reference Strategy: feature-required blocking and warning-only comparisons.
+3. Reference Case Inventory: case id, purpose, exact input path, exact required CSV paths, and status.
+4. Comparison Mapping: FESA HDF5 dataset, source identity, components, CSV columns, and row prechecks.
+5. Tolerance Mapping: exact upstream tolerance and blocking/warning behavior.
+6. Readiness Checklist: required files readable, required IDs/components unique and finite, and tolerance fixed.
+7. Open Issues and Downstream Handoff: I/O Definition Agent, Implementation Planning Agent, Reference Verification Agent, and Physics Evaluation Agent.
 
 Abaqus input rules to preserve in model planning:
 - FESA input uses Abaqus .inp files but supports only the feature-specific keyword subset defined by I/O Definition Agent.
 - model.inp must stay inside the supported keyword subset unless unsupported keywords are explicitly tracked as open issues.
 - Separate model data from history data conceptually.
-- Output requests must be sufficient to populate required Abaqus reference CSV files.
-- Node and element labels, set names, coordinate system, units, step/frame identity, output locations, and component naming must be traceable into FESA HDF5 datasets and reference CSV row schemas.
+- Required source IDs and comparison components must be traceable between FESA HDF5 and the
+  declared CSV. A single supported step/final frame needs no duplicated CSV step/frame fields.
 
 Artifact readiness rules:
 - status must be draft, needs-user-decision, needs-reference-artifacts, ready-for-implementation-planning, or blocked.
-- Use needs-reference-artifacts when required Abaqus reference CSV files or metadata provenance are missing.
-- Use needs-user-decision for unknown tolerance, units, model source, or unsupported keyword policy.
-- Do not claim ready-for-implementation-planning unless required artifacts, provenance, tolerance, and coverage matrix are complete.
+- Use needs-reference-artifacts only when the declared input or a required comparison CSV is missing.
+- Use needs-user-decision when a blocking/warning quantity, source-ID/component mapping, tolerance,
+  or unsupported keyword policy is unknown.
+- Do not claim ready-for-implementation-planning unless required files, matching, and tolerance are complete.
 
 Downstream handoff rules:
 - I/O Definition Agent: request supported keyword changes, output request clarifications, FESA HDF5 schema clarifications, and reference CSV row schema clarifications.
 - Implementation Planning Agent: pass tests that should fail before implementation, model order, and acceptance criteria.
-- Reference Verification Agent: pass FESA HDF5 dataset paths, reference CSV schemas, ID matching rules, units, coordinate conventions, output locations, and tolerance mapping.
+- Reference Verification Agent: pass exact input/CSV paths, FESA HDF5 dataset paths,
+  source-ID/component matching, row prechecks, and tolerance mapping.
 - Physics Evaluation Agent: pass equilibrium, symmetry, displacement direction, stress location, rigid body mode, and load path sanity checks.
 
 Output language:

.codex/agents/reference-verification-agent.toml

@@ -10,11 +10,12 @@ Mission:
 - Run reference verification only.
 - Compare generated FESA solver `results.h5` against Abaqus reference CSV files.
 - Reference CSV files are created by solving the same Abaqus `.inp` model outside the agent workflow; they are not derived from FESA HDF5.
-- Report tolerance-based verification outcomes for displacements, reactions, internal forces, stresses, and approved optional quantities.
+- Report tolerance-based outcomes only for feature-declared blocking and warning-only quantities.
 - Keep the output aligned with docs/SOLVER_AGENT_DESIGN.md, reference model contracts, I/O definitions, build/test reports, implementation reports, generated solver HDF5 outputs, and stored reference/<model-id>/ artifacts.
 
 Skill references:
-- Use $fesa-reference-comparison when comparing generated solver HDF5 results with Abaqus reference CSV files, checking schema, units, ID matching, tolerance metrics, or reference verification status.
+- Use $fesa-reference-comparison when comparing generated solver HDF5 results with declared
+  Abaqus reference CSV files, checking source-ID/component matching, tolerance metrics, or status.
 - Use $fesa-io-contract when comparison is blocked by Abaqus input scope, FESA HDF5 schema, reference CSV row schema, units, coordinate system, output location, component naming, or ID matching ambiguity.
 
 Hard boundaries:
@@ -25,11 +26,11 @@ Hard boundaries:
 - Do not change tolerance policies.
 - Do not run Abaqus, Nastran, or any reference solver.
 - Do not generate or modify Abaqus reference CSV files.
-- Do not modify model.inp, metadata.json, <model-id>_displacements.csv, <model-id>_reactions.csv, <model-id>_internalforces.csv, <model-id>_stresses.csv, or any stored reference artifact.
+- Do not modify any declared input, reference CSV, or other stored reference artifact.
 - Do not approve release readiness.
 - Do not approve physics validation success.
 - Do not produce the final release checklist.
-- Do not invent tolerance, schema, unit, coordinate system, output location, or reference provenance values.
+- Do not invent tolerance, source-ID/component matching, or required quantity values.
 
 Input priorities:
 1. User-provided reference verification request and constraints.
@@ -38,17 +39,20 @@ Input priorities:
 4. docs/io-definitions/<feature-id>-io.md.
 5. Implementation Agent report and docs/implementation-plans/<feature-id>-implementation-plan.md.
 6. Generated solver result HDF5, normally `results.h5`, from the implemented solver or feature-specific comparison command.
-7. Stored reference/<model-id>/ artifacts, including metadata.json and Abaqus reference CSV files.
+7. Declared stored reference input and required Abaqus reference CSV files.
 8. Related requirements, formulations, numerical review reports, and research docs as read-only contracts.
 
 Execution contract:
 - Always work in ARTIFACT CHECK -> COMPARE -> CLASSIFY -> REPORT order.
-- ARTIFACT CHECK: verify metadata.json, model.inp, generated solver results.h5, reference/<model-id>/<model-id>_displacements.csv, reference/<model-id>/<model-id>_reactions.csv, reference/<model-id>/<model-id>_internalforces.csv, reference/<model-id>/<model-id>_stresses.csv, reference CSV schema version, FESA HDF5 schema version, units, coordinate system, step/frame identity, node/element ID matching rule, output location, component naming, and tolerance policy.
+- ARTIFACT CHECK: verify the declared input, generated solver results.h5, every CSV required by the
+  feature, required source IDs/components, row uniqueness/finite values, HDF5 dataset projection,
+  and tolerance policy. Do not require canonical names, README, metadata, provenance, duplicated
+  unit/coordinate/step-frame fields, or a reference CSV schema version.
 - ARTIFACT CHECK: if solver output path or comparison command is missing, stop with needs-solver-results.
-- ARTIFACT CHECK: if required reference artifacts or provenance are missing, stop with needs-reference-artifacts.
-- ARTIFACT CHECK: if tolerance, schema, units, coordinate system, output location, ID matching rule, or zero-reference relative scale policy is missing, stop with needs-upstream-decision.
+- ARTIFACT CHECK: if the declared input or required comparison CSV is missing, stop with needs-reference-artifacts.
+- ARTIFACT CHECK: if tolerance, HDF5 projection, source-ID/component matching, or zero-reference scale policy is missing, stop with needs-upstream-decision.
 - COMPARE: read FESA HDF5 datasets and compare normalized rows directly against Abaqus reference CSV rows.
-- COMPARE: compare displacement, reaction, internal force, stress, and approved optional quantities only when upstream contracts require them.
+- COMPARE: compare only the blocking and warning-only quantities declared upstream.
 - COMPARE: comparison tooling may materialize FESA debug CSV views from results.h5 for debugging or review only.
 - COMPARE: use upstream tolerance policies exactly as specified. Do not adjust tolerances to force a pass.
 - COMPARE: report max absolute error, max relative error, RMS error, norm error when applicable, worst id, worst component, row counts, missing rows, extra rows, and pass/fail per quantity.
@@ -56,9 +60,8 @@ Execution contract:
 - REPORT: write or propose a Korean Markdown reference comparison report and hand off to the correct downstream agent.
 
 Comparison rules:
-- Nodal displacements and reactions can be compared only when node id, DOF/component, coordinate system, units, and step/frame identity match.
-- Internal forces can be compared only when element id, output location, component naming, units, and step/frame identity match.
-- Stresses and strains can be compared only when element id, integration point or recovery location, component naming, coordinate system, units, and step/frame identity match.
+- Compare rows by the feature-declared source identity and component. Never match by row order alone.
+- Reject missing, extra, duplicate, or nonfinite required rows before numeric comparison.
 - FESA `results.h5` is the authoritative solver output.
 - Abaqus reference CSV files are the authoritative reference result artifacts.
 - FESA debug CSV views are derived review artifacts only. Do not treat FESA debug CSV views as authoritative solver output or reference artifacts.
@@ -66,9 +69,9 @@ Comparison rules:
 
 Required Reference Verification Report sections:
 1. Metadata: feature_id, source docs and reports, status, owner_agent, date.
-2. Artifact Inventory: reference model dir, model.inp path, metadata path, required reference CSV readiness, solver results.h5 path, optional solver debug CSV view readiness, and metadata provenance.
-3. Comparison Contract: HDF5 schema version, reference CSV schema version, ID matching rules, units, coordinate system, output location, component naming, tolerance source.
-4. Quantity Results: displacement, reaction, internal force, stress, and optional quantity row counts, max absolute error, max relative error, RMS error, norm error, worst id/component, pass/fail.
+2. Artifact Inventory: declared input path, required CSV paths, solver results.h5 path, and optional solver debug CSV view.
+3. Comparison Contract: HDF5 dataset, source-ID/component matching, row prechecks, tolerance source, and blocking/warning behavior.
+4. Quantity Results: every declared quantity's row counts, max absolute error, max relative error, RMS error, norm error, worst id/component, and pass/fail or warning.
 5. Failure Classification: missing-reference-artifact | missing-solver-output | schema-mismatch | id-mismatch | unit-or-coordinate-mismatch | tolerance-failure | nonfinite-result | upstream-contract | environment.
 6. Handoff Recommendation: Correction Agent, Reference Model Agent, I/O Definition Agent, Physics Evaluation Agent, or Coordinator Agent.
 7. No-Change Assertion: source, test, CMake, reference artifacts, and tolerance policies were not modified.
@@ -77,9 +80,9 @@ Required Reference Verification Report sections:
 Status rules:
 - pass-for-physics-evaluation: all required reference comparisons pass and Physics Evaluation Agent is next.
 - needs-correction: implementation-owned solver result mismatch or nonfinite result needs Correction Agent.
-- needs-reference-artifacts: required Abaqus reference CSV or provenance is missing.
+- needs-reference-artifacts: the declared input or a required Abaqus reference CSV is missing.
 - needs-solver-results: generated solver results.h5 or feature-specific comparison command is missing.
-- needs-upstream-decision: schema, tolerance, units, coordinate system, output location, or ID matching policy is missing or contradictory.
+- needs-upstream-decision: tolerance, HDF5 projection, required quantity, or source-ID/component matching is missing or contradictory.
 - blocked: no safe progress is possible without user or Coordinator Agent decision.
 
 Quality gate:

.codex/agents/release-agent.toml

@@ -52,7 +52,8 @@ Execution contract:
 - GATE AUDIT: require Physics Evaluation status pass-for-release-agent.
 - GATE AUDIT: if any required report is missing, stale, contradictory, or failed, stop with the appropriate needs-* status.
 - TRACEABILITY CHECK: confirm every must requirement traces to acceptance criteria, implementation or test evidence, reference model evidence, and release scope.
-- TRACEABILITY CHECK: record deferred requirements, unresolved defects, accepted risks, unsupported Abaqus keywords, and incomplete reference artifacts as release limitations or blockers.
+- TRACEABILITY CHECK: record deferred requirements, unresolved defects, accepted risks,
+  unsupported Abaqus keywords, and missing feature-required comparison files as limitations or blockers.
 - RELEASE DOCUMENTATION: prepare a Korean Markdown release checklist, known limitations, and Release Notes Draft.
 - RELEASE DOCUMENTATION: keep known limitations explicit and user-facing enough for feature consumers.
 - RELEASE VERDICT: issue ready-for-release only when all required gate evidence is present and passing.
@@ -62,13 +63,13 @@ Required Release Report sections:
 2. Release Scope: included functionality, excluded functionality, supported analysis type, elements, materials, I/O subset, and artifact scope.
 3. Gate Evidence Inventory: requirements, formulation, numerical review, I/O definition, reference model, implementation, build/test, reference verification, and physics evaluation status.
 4. Acceptance Traceability: requirement id, acceptance criterion, test id, reference model id, verification report, and release disposition.
-5. Validation Evidence: python scripts/validate_workspace.py, CMake/MSVC/CTest evidence, reference verification status, and physics evaluation status.
+5. Validation Evidence: Build/Test report's config-resolved CMake/MSVC/CTest commands, Harness Python pytest when applicable, reference verification status, and physics evaluation status.
 6. Known Limitations: unsupported Abaqus keywords, element/material/analysis constraints, deferred issues, accepted risks, and open items.
 7. Release Notes Draft: user-facing feature summary, verification scope, main limitations, artifact paths, and usage notes.
 8. Release Verdict: ready-for-release | needs-correction | needs-reference-verification | needs-physics-evaluation | needs-documentation | needs-upstream-decision | blocked.
 9. Handoff Recommendation: Coordinator Agent, Correction Agent, Reference Verification Agent, Physics Evaluation Agent, Requirement Agent, I/O Definition Agent, Reference Model Agent, or Implementation Planning Agent.
 10. No-Change Assertion: source, test, CMake, reference artifacts, and tolerance policies were not modified.
-11. Open Issues: missing evidence, contradictory upstream reports, unresolved defects, incomplete reference artifacts, or release documentation gaps.
+11. Open Issues: missing evidence, contradictory upstream reports, unresolved defects, missing declared comparison files, or release documentation gaps.
 
 Status rules:
 - ready-for-release: all required gates pass, every must requirement is traced, known limitations are documented, and no blocking evidence gap remains.
@@ -76,14 +77,16 @@ Status rules:
 - needs-reference-verification: reference comparison report is missing, failed, stale, or not pass-for-physics-evaluation.
 - needs-physics-evaluation: physics evaluation report is missing, failed, stale, or not pass-for-release-agent.
 - needs-documentation: gate evidence passes but release scope, limitations, traceability, or notes are incomplete.
-- needs-upstream-decision: requirements, tolerance, reference artifact, I/O, or acceptance evidence is missing or contradictory.
+- needs-upstream-decision: requirements, tolerance, required comparison file/mapping, I/O, or acceptance evidence is missing or contradictory.
 - blocked: no safe progress is possible without user or Coordinator Agent decision.
 
 Quality gate:
 - Do not issue ready-for-release without pass-for-release-agent, pass-for-physics-evaluation, and pass-for-reference-verification evidence.
 - Every must requirement must trace to release scope, acceptance criteria, test or reference evidence, and final disposition.
 - Known limitations and deferred issues must be included in the Release Notes Draft.
-- Missing evidence, contradictory upstream reports, unresolved defects, incomplete reference artifacts, or unavailable validation commands block release readiness.
+- Missing required evidence, contradictory upstream reports, unresolved defects, missing declared
+  comparison files, or unavailable validation commands block release readiness. Canonical naming,
+  README, metadata, provenance, or unrequested portfolio expansion do not.
 - A release readiness verdict is internal to FESA feature delivery and is not permission to publish, deploy, package, tag, commit, or externally release.
 
 Output language:

.codex/agents/requirement-agent.toml

@@ -46,7 +46,10 @@ Required Feature Requirement Specification sections:
 7. Output requirements.
 8. Verification quantities: nodal displacement, reaction, element internal force, stress, and any required strain, energy, or residual quantity.
 9. Tolerance policy: absolute, relative, and norm-based tolerance applicability.
-10. Reference artifact requirements: model.inp, metadata.json, <model-id>_displacements.csv, <model-id>_reactions.csv, <model-id>_internalforces.csv, <model-id>_stresses.csv, or an explicit N/A reason.
+10. Reference case requirements: exact existing `.inp` and only the CSV files required for
+    blocking or warning-only quantities, HDF5 projection, source-ID/component matching, and
+    tolerance. Do not require canonical names, README, metadata, provenance, or CSVs for
+    quantities outside the feature acceptance boundary.
 11. Requirement Verification Matrix.
 12. Open questions.
 13. Downstream handoff.
@@ -69,15 +72,16 @@ status: draft | needs-user-decision | approved
 Verification planning rules:
 - Every must requirement must have a verification method and acceptance criterion.
 - Numerical requirements must include units, coordinate system, and tolerance.
-- Reference-comparison requirements must identify the required reference artifact files.
+- Reference-comparison requirements must identify exact input/required CSV paths, blocking or
+  warning-only quantities, deterministic source-ID/component matching, and tolerance.
 - Use stored reference artifacts only; never request direct Abaqus or Nastran execution by the agent.
-- If reference artifacts are missing, hand off requirements to Reference Model Agent.
+- If a declared input or required comparison CSV is missing, hand off to Reference Model Agent.
 
 Downstream handoff rules:
 - Research Agent: theory sources, benchmark questions, and standards to investigate.
 - Formulation Agent: analysis type, target elements, material assumptions, DOFs, outputs, and numerical constraints.
 - I/O Definition Agent: input and output schema requirements.
-- Reference Model Agent: reference/<model-id>/ artifact requirements.
+- Reference Model Agent: lightweight reference-case inventory and comparison mapping.
 - Implementation Planning Agent: tests to write first and acceptance criteria.
 
 Output language:

.codex/config.toml

@@ -1,4 +1,4 @@
 #:schema https://developers.openai.com/codex/config-schema.json
 
 [features]
-codex_hooks = true
+hooks = true

.codex/hooks.json

@@ -1,25 +1,29 @@
 {
+  "description": "Harness TDD, command safety, and MSVC C/C++ validation hooks.",
   "hooks": {
     "PreToolUse": [
       {
-        "matcher": "^Bash$",
+        "matcher": "Bash|shell_command|PowerShell|apply_patch|Edit|MultiEdit|Write",
         "hooks": [
           {
             "type": "command",
-            "command": "python -c \"import pathlib, runpy, subprocess; root = pathlib.Path(subprocess.check_output(['git', 'rev-parse', '--show-toplevel'], text=True).strip()); runpy.run_path(str(root / '.codex' / 'hooks' / 'pre_commit_checks.py'), run_name='__main__')\"",
-            "timeout": 600,
-            "statusMessage": "Running pre-commit checks"
+            "command": "python3 -X utf8 \"$(git rev-parse --show-toplevel)/scripts/hooks/pre_tool_use.py\"",
+            "commandWindows": "python -X utf8 \"$(git rev-parse --show-toplevel)/scripts/hooks/pre_tool_use.py\"",
+            "timeout": 30,
+            "statusMessage": "Checking Harness policies"
           }
         ]
-      },
+      }
+    ],
+    "Stop": [
       {
-        "matcher": "^(apply_patch|Edit|Write)$",
         "hooks": [
           {
             "type": "command",
-            "command": "python -c \"import pathlib, runpy, subprocess; root = pathlib.Path(subprocess.check_output(['git', 'rev-parse', '--show-toplevel'], text=True).strip()); runpy.run_path(str(root / '.codex' / 'hooks' / 'tdd-guard.py'), run_name='__main__')\"",
-            "timeout": 30,
-            "statusMessage": "Checking TDD guard"
+            "command": "python3 -X utf8 \"$(git rev-parse --show-toplevel)/scripts/hooks/stop_validation.py\"",
+            "commandWindows": "python -X utf8 \"$(git rev-parse --show-toplevel)/scripts/hooks/stop_validation.py\"",
+            "timeout": 1800,
+            "statusMessage": "Running MSVC build and tests"
           }
         ]
       }

.codex/hooks/pre_commit_checks.py

@@ -1,89 +0,0 @@
-import json
-import re
-import subprocess
-import sys
-from pathlib import Path
-
-
-def _repo_root(cwd: Path) -> Path:
-    try:
-        root = subprocess.check_output(
-            ["git", "rev-parse", "--show-toplevel"],
-            cwd=cwd,
-            text=True,
-            stderr=subprocess.DEVNULL,
-        ).strip()
-    except (subprocess.CalledProcessError, FileNotFoundError):
-        return cwd
-    return Path(root)
-
-
-def _is_git_commit(command: str) -> bool:
-    return re.search(
-        r"^\s*git(?:\s+(?:-[A-Za-z]\s+\S+|--[A-Za-z0-9-]+(?:=\S+)?))*\s+commit\b",
-        command,
-    ) is not None
-
-
-def _deny(reason: str) -> None:
-    print(
-        json.dumps(
-            {
-                "hookSpecificOutput": {
-                    "hookEventName": "PreToolUse",
-                    "permissionDecision": "deny",
-                    "permissionDecisionReason": reason,
-                }
-            }
-        )
-    )
-
-
-def _tail(text: str, limit: int = 1200) -> str:
-    text = text.strip()
-    if len(text) <= limit:
-        return text
-    return text[-limit:]
-
-
-def _build_pre_commit_commands(root: Path) -> list[list[str]]:
-    return [
-        [sys.executable, "-m", "unittest", "discover", "-s", "scripts", "-p", "test_*.py"],
-        [sys.executable, "scripts/validate_workspace.py"],
-    ]
-
-
-def _run_checks(root: Path) -> str | None:
-    for command in _build_pre_commit_commands(root):
-        result = subprocess.run(command, cwd=root, capture_output=True, text=True)
-        if result.returncode != 0:
-            details = _tail(result.stdout + "\n" + result.stderr)
-            label = " ".join(command)
-            if details:
-                return f"{label} failed:\n{details}"
-            return f"{label} failed with exit code {result.returncode}."
-
-    return None
-
-
-def main() -> int:
-    try:
-        payload = json.load(sys.stdin)
-    except json.JSONDecodeError:
-        return 0
-
-    command = payload.get("tool_input", {}).get("command", "")
-    if not isinstance(command, str) or not _is_git_commit(command):
-        return 0
-
-    cwd = Path(payload.get("cwd") or Path.cwd())
-    root = _repo_root(cwd)
-    failure = _run_checks(root)
-    if failure:
-        _deny(f"PRE-COMMIT CHECKS: {failure}")
-
-    return 0
-
-
-if __name__ == "__main__":
-    raise SystemExit(main())

.codex/hooks/tdd-guard.py

@@ -1,205 +0,0 @@
-import json
-import subprocess
-import sys
-from pathlib import Path
-
-
-SOURCE_SUFFIXES = {".h", ".hpp", ".hh", ".hxx", ".c", ".cc", ".cpp", ".cxx", ".ixx"}
-TEST_SUFFIXES = {".h", ".hpp", ".hh", ".hxx", ".c", ".cc", ".cpp", ".cxx", ".ixx"}
-CONFIG_SUFFIXES = {".json", ".md", ".yml", ".yaml", ".txt", ".cmake"}
-
-
-def _repo_root(cwd: Path) -> Path:
-    try:
-        root = subprocess.check_output(
-            ["git", "rev-parse", "--show-toplevel"],
-            cwd=cwd,
-            text=True,
-            stderr=subprocess.DEVNULL,
-        ).strip()
-    except (subprocess.CalledProcessError, FileNotFoundError):
-        return cwd
-    return Path(root)
-
-
-def _extract_patch_paths(command: str) -> list[str]:
-    prefixes = (
-        "*** Add File: ",
-        "*** Update File: ",
-        "*** Delete File: ",
-        "*** Move to: ",
-    )
-    paths: list[str] = []
-    for raw_line in command.splitlines():
-        line = raw_line.strip()
-        for prefix in prefixes:
-            if line.startswith(prefix):
-                paths.append(line[len(prefix) :].strip())
-                break
-    return paths
-
-
-def _touched_paths(payload: dict) -> list[str]:
-    tool_input = payload.get("tool_input", {})
-    if not isinstance(tool_input, dict):
-        return []
-
-    file_path = tool_input.get("file_path")
-    if isinstance(file_path, str) and file_path:
-        return [file_path]
-
-    command = tool_input.get("command")
-    if isinstance(command, str):
-        return _extract_patch_paths(command)
-
-    return []
-
-
-def _normalize(path_text: str) -> str:
-    return path_text.replace("\\", "/").lower()
-
-
-def _is_test_path(path_text: str) -> bool:
-    normalized = _normalize(path_text)
-    name = normalized.rsplit("/", 1)[-1]
-    path = Path(path_text)
-    return (
-        "/tests/" in f"/{normalized}"
-        or "/test/" in f"/{normalized}"
-        or name.endswith("_test.cpp")
-        or name.startswith("test_")
-        or ".test." in name
-        or ".spec." in name
-    ) and path.suffix.lower() in TEST_SUFFIXES
-
-
-def _token(text: str) -> str:
-    return "".join(ch for ch in text.lower() if ch.isalnum())
-
-
-def _module_token(path: Path) -> str:
-    parts = [part.lower() for part in path.parts]
-    for marker in ("include", "src"):
-        if marker not in parts:
-            continue
-        idx = parts.index(marker)
-        if marker == "include" and idx + 2 < len(parts) and parts[idx + 1] == "fesa":
-            return _token(parts[idx + 2])
-        if marker == "src" and idx + 1 < len(parts):
-            return _token(parts[idx + 1])
-    return ""
-
-
-def _related_tokens(path: Path) -> set[str]:
-    tokens = {_token(_base_name(path))}
-    module = _module_token(path)
-    if module:
-        tokens.add(module)
-    return {token for token in tokens if token}
-
-
-def _candidate_test_paths(paths: list[str], cwd: Path, root: Path) -> list[Path]:
-    candidates: list[Path] = []
-    for path_text in paths:
-        resolved = _resolve_path(path_text, cwd)
-        if _is_test_path(str(resolved)):
-            candidates.append(resolved)
-
-    for test_root_name in ("tests", "test"):
-        test_root = root / test_root_name
-        if not test_root.is_dir():
-            continue
-        for suffix in TEST_SUFFIXES:
-            candidates.extend(test_root.rglob(f"*{suffix}"))
-
-    return candidates
-
-
-def _has_related_test(path: Path, candidate_tests: list[Path]) -> bool:
-    tokens = _related_tokens(path)
-    for test_path in candidate_tests:
-        test_token = _token(test_path.stem)
-        if any(token and token in test_token for token in tokens):
-            return True
-    return False
-
-
-def _is_exempt(path_text: str) -> bool:
-    normalized = _normalize(path_text)
-    path = Path(path_text)
-    name = path.name.lower()
-
-    if name == "cmakelists.txt":
-        return True
-    if _is_test_path(path_text):
-        return True
-    if path.suffix.lower() in CONFIG_SUFFIXES:
-        return True
-    if "/cmake/" in normalized:
-        return True
-
-    return False
-
-
-def _resolve_path(path_text: str, cwd: Path) -> Path:
-    path = Path(path_text)
-    if path.is_absolute():
-        return path
-    return (cwd / path).resolve()
-
-
-def _base_name(path: Path) -> str:
-    for suffix in sorted(SOURCE_SUFFIXES, key=len, reverse=True):
-        if path.name.lower().endswith(suffix):
-            return path.name[: -len(suffix)]
-    return path.stem
-
-
-def _guarded_paths(paths: list[str], cwd: Path, root: Path) -> list[str]:
-    missing_tests: list[str] = []
-    candidate_tests = _candidate_test_paths(paths, cwd, root)
-    for path_text in paths:
-        if _is_exempt(path_text):
-            continue
-
-        path = _resolve_path(path_text, cwd)
-        if path.suffix.lower() not in SOURCE_SUFFIXES:
-            continue
-        if not _has_related_test(path, candidate_tests):
-            missing_tests.append(_base_name(path))
-
-    return missing_tests
-
-
-def main() -> int:
-    try:
-        payload = json.load(sys.stdin)
-    except json.JSONDecodeError:
-        return 0
-
-    cwd = Path(payload.get("cwd") or Path.cwd())
-    root = _repo_root(cwd)
-    missing_tests = _guarded_paths(_touched_paths(payload), cwd, root)
-    if not missing_tests:
-        return 0
-
-    names = ", ".join(sorted(set(missing_tests)))
-    print(
-        json.dumps(
-            {
-                "hookSpecificOutput": {
-                    "hookEventName": "PreToolUse",
-                    "permissionDecision": "deny",
-                    "permissionDecisionReason": (
-                        "TDD GUARD: missing test file for "
-                        f"{names}. Write or add the test first."
-                    ),
-                }
-            }
-        )
-    )
-    return 0
-
-
-if __name__ == "__main__":
-    raise SystemExit(main())

.codex/skills/fem-theory-query/vault-path.txt

@@ -1,3 +1,3 @@
 # FEM wiki vault root path.
 # Edit this per PC. Use an absolute path to the vault that contains wiki/ and .raw/.
-D:\Obsidian\MultiPhysicsVault
+C:\git\MultiPhysicsVault

.codex/skills/fesa-cpp-msvc-tdd/SKILL.md

@@ -14,22 +14,39 @@ Read these first:
 - `AGENTS.md`
 - `docs/SOLVER_AGENT_DESIGN.md`
 - `docs/implementation-plans/README.md`
+- `docs/HARNESS.md`
+- `docs/HARNESS_WORKFLOW.md`
 - `docs/build-test-reports/README.md`
 - `docs/corrections/README.md`
 - `docs/implementation-plans/<feature-id>-implementation-plan.md`
 - Related requirements, formulation, numerical review, I/O definition, and reference model documents
 
+For Harness implementation, also read `.agents/skills/harness/SKILL.md`,
+`.codex/hooks.json`, the materialized phase indexes, and the Executor-selected current
+`stepN.md`.
+
 ## Workflow
 
-1. For planning, convert upstream documents into small ordered tasks and test ids.
-2. For implementation, follow `RED -> GREEN -> VERIFY`.
-3. RED: write the planned unit, integration, parser/I/O, or reference-comparison test first.
-4. RED: run the targeted test and verify the expected failure before production code.
-5. GREEN: implement the minimum C++17/MSVC-compatible code needed for the task.
-6. VERIFY: run the targeted command, then `python scripts/validate_workspace.py`.
-7. For C++ production changes, require a related C++ test file in the same patch or already present.
-8. For failure triage, classify as `configure | compile | link | test | reference-comparison | harness | environment | upstream-contract`.
-9. Fix implementation-owned failures only and keep changes traceable to the implementation plan.
+1. For planning, use the project-local `harness` skill to convert upstream documents into a
+   user-approved multi-Step draft. Materialize only planning files after approval; planning never
+   selects or runs a Step. Run `scripts/execute.py` only after a separate explicit user request.
+2. For implementation, require the approved plan, materialized phase files, and the
+   Executor-selected current `stepN.md`. Do not start another pending Step.
+3. Execute the current Step as `RED -> observed failure -> minimal GREEN -> focused/full VERIFY`.
+   Update only its Codex-owned `status` plus `summary`, `error_message`, or `blocked_reason`.
+   The Executor owns branch, pending-Step selection, retry, timestamps, commits, advancement,
+   and top-level phase status.
+4. Hooks are automatic through `.codex/hooks.json`: PreToolUse intercepts before edits and Stop
+   performs whole-project validation. Do not manually run their entry points as substitutes.
+5. RED: write the planned unit, integration, parser/I/O, or reference-comparison test first.
+6. RED: run the targeted test and verify the expected failure before production code.
+7. GREEN: implement the minimum C++17/MSVC-compatible code needed for the task.
+8. VERIFY: run the targeted command, then the full MSVC build/test commands resolved from `.harness/config.json` or the Harness defaults.
+9. For C++ production changes, require a related C++ test file in the same patch or already present.
+10. Treat PreToolUse as a test-file-existence guardrail, not proof that RED was observed. Record the RED and GREEN commands and results in the implementation report.
+11. Let Stop perform the final whole-project MSVC build/test before the Step ends.
+12. For failure triage, classify as `configure | compile | link | test | reference-comparison | harness | environment | upstream-contract`.
+13. Fix implementation-owned failures only and keep changes traceable to the implementation plan.
 
 ## Output Contract
 
@@ -43,17 +60,19 @@ Produce one of these, depending on role:
 Required validation commands:
 
 ```powershell
-python -m unittest discover -s scripts -p "test_*.py"
-python scripts/validate_workspace.py
-ctest -C Debug -R <feature-or-label>
+cmake -S . -B .harness/build -A x64
+cmake --build .harness/build --config Debug
+ctest --test-dir .harness/build -C Debug -R <feature-or-label> --output-on-failure
+ctest --test-dir .harness/build -C Debug --show-only=json-v1
+ctest --test-dir .harness/build -C Debug --output-on-failure
 ```
 
-Default MSVC path:
+Use configured CMake presets or direct MSBuild commands instead when
+`.harness/config.json` selects them. For Harness Python, Hook, or agent-config
+changes, also run:
 
 ```powershell
-cmake -S . -B build/msvc-debug -G "Visual Studio 17 2022" -A x64
-cmake --build build/msvc-debug --config Debug
-ctest --test-dir build/msvc-debug --output-on-failure -C Debug
+uv run --with pytest python -m pytest -v -rs
 ```
 
 ## Boundaries
@@ -67,12 +86,15 @@ ctest --test-dir build/msvc-debug --output-on-failure -C Debug
 - Do not run Abaqus, Nastran, or any reference solver.
 - Do not generate or modify Abaqus reference CSV files.
 - Do not approve release readiness.
+- During planning, do not block on canonical reference naming, README, metadata, provenance, or
+  an unrequested reference portfolio. Require only feature-declared input/CSV files, matching, and tolerance.
 
 ## Quality Gate
 
 - Every `must` requirement maps to at least one task and one test.
 - Each test has a clear RED condition, GREEN condition, linked task, and command.
 - CMake/CTest plans remain compatible with MSVC x64 Debug validation.
+- Stop validation is green for the whole discovered C/C++ project; a no-project pass is valid only when no C/C++ files and no build metadata exist.
 - Build/test reports record command, exit code, duration, stdout/stderr tail, and failure classification.
 - Correction attempts stop when repeated failure indicates upstream contract ambiguity.
 

.codex/skills/fesa-io-contract/SKILL.md

@@ -26,8 +26,10 @@ Read these first:
 4. Define supported keywords such as `*NODE`, `*ELEMENT`, `*MATERIAL`, `*ELASTIC`, `*BOUNDARY`, `*CLOAD`, `*STEP`, `*OUTPUT`, `*NODE OUTPUT`, and `*ELEMENT OUTPUT` only when required.
 5. Define Internal Model Contract at a semantic level without C++ APIs.
 6. Define Output HDF5 Schema for authoritative solver output `results.h5`.
-7. Define FESA HDF5 to Reference CSV Comparison Schema for normalized rows matched against Abaqus CSV files under `reference/<model-id>/`.
-8. Define units, coordinate system, component naming, output location, step/frame identity, and ID matching rules.
+7. Define only the FESA HDF5 projection and minimum source-ID/component mapping needed for
+   feature-declared blocking or warning-only CSV quantities.
+8. Define solver HDF5 units, coordinates, component names, locations, and step/frame identity.
+   Do not require duplicated CSV metadata or a CSV schema version for a single-step final-frame case.
 9. Define validation rules and open issues.
 
 ## Output Contract
@@ -40,7 +42,7 @@ Produce or revise `docs/io-definitions/<feature-id>-io.md` with:
 - History Data Mapping
 - Internal Model Contract
 - Output HDF5 Schema
-- FESA HDF5 to Reference CSV Comparison Schema
+- FESA HDF5 to Reference CSV Comparison Mapping
 - Validation Rules
 - Downstream Handoff
 
@@ -57,7 +59,8 @@ Produce or revise `docs/io-definitions/<feature-id>-io.md` with:
 
 - Every supported keyword has a documented purpose, required data, and unsupported-case behavior.
 - HDF5 schema is the authoritative solver output contract and must carry schema version, step/frame identity, units, coordinate system, output location, and component naming.
-- Reference CSV comparison row schema must define stable row ordering, ID fields, and component ordering for matching against Abaqus reference CSV.
+- Reference comparison must define exact existing CSV paths, source-ID and component columns,
+  deterministic matching, and missing/extra/duplicate/nonfinite prechecks. Never match by row order alone.
 - Unsupported Abaqus input is explicit: unsupported, ignored-with-warning, or requires user decision.
 - The I/O contract is compatible with requirements, formulation, and reference comparison needs.
 

.codex/skills/fesa-numerical-review/SKILL.md

@@ -26,8 +26,10 @@ Read these first:
 5. Review Jacobian rules, determinant checks, derivative transforms, and distortion handling.
 6. Review integration rule, Gauss points, weights, and full/reduced/selective integration policy.
 7. Check element residual, internal force, external force, stiffness, tangent, symmetry, and positive definiteness expectations.
-8. Assess rigid body modes, patch test readiness, hourglass, shear locking, volumetric locking, singular Jacobian, conditioning, and convergence risk.
-9. Decide status: `pass-for-implementation-planning`, `needs-formulation-revision`, `needs-research`, `needs-reference-model`, or `blocked`.
+8. Assess only rigid modes, patch tests, locking, singularity, conditioning, convergence, and
+   other risks required by the approved feature scope. Do not invent calibration or portfolio gates.
+9. Decide status: `pass-for-implementation-planning`, `needs-formulation-revision`,
+   `needs-research`, or `blocked`.
 
 ## Output Contract
 
@@ -58,7 +60,11 @@ Produce or revise `docs/numerical-reviews/<feature-id>-review.md` with:
 - Confirmed defects, risks, open questions, and test recommendations are separated.
 - Missing derivations are returned to Formulation Agent instead of being silently fixed.
 - Evidence gaps are routed to Research Agent or Reference Model Agent.
+- Missing downstream Reference Model documents, canonical naming, README, metadata, provenance,
+  extended portfolios, or comparison results do not block a formulation verdict.
 
 ## Handoff
 
-Send pass results to Implementation Planning Agent and Reference Model Agent. Send math defects to Formulation Agent, source gaps to Research Agent, and blocked decisions to Coordinator Agent.
+Send pass results to Implementation Planning Agent and optional test notes to Reference Model
+Agent. Send math defects to Formulation Agent, source gaps to Research Agent, and blocked decisions
+to Coordinator Agent.

.codex/skills/fesa-physics-sanity/SKILL.md

@@ -17,7 +17,7 @@ Read these first:
 - Reference Verification report with `pass-for-physics-evaluation`
 - `docs/reference-models/<feature-id>-reference-models.md`
 - Requirements, formulation, numerical review, and I/O definition documents
-- Solver results.h5, Abaqus reference CSV files under reference/<model-id>/, and optional FESA debug CSV views as read-only evidence
+- Solver results.h5, feature-declared Abaqus reference CSV files, and optional FESA debug CSV views as read-only evidence
 
 ## Workflow
 
@@ -29,7 +29,8 @@ Read these first:
 6. Check symmetry or expected zero conditions when the model defines them.
 7. Check element force balance and element internal force sign conventions when documented.
 8. Check stress/strain component naming, coordinate system, output location, and sign.
-9. Check rigid body mode symptoms, nonfinite values, energy/residual evidence, and model coverage.
+9. Check only rigid body, nonfinite, energy/residual, and model-coverage expectations explicitly
+   required by the feature. Do not invent expanded portfolios or calibration gates.
 10. Classify failures and route them to the owning agent.
 
 ## Output Contract
@@ -60,7 +61,7 @@ Produce or revise `docs/physics-evaluations/<feature-id>-physics-evaluation.md`
 
 - A physics pass requires documented expectations and reference verification pass evidence.
 - Use `needs-upstream-decision` when physical expectations, sign convention, or model purpose is missing.
-- Use `needs-reference-model` when the model does not cover the claimed feature.
+- Use `needs-reference-model` only when a feature-required case or declared physical expectation is missing.
 - `pass-for-release-agent` means Release Agent can audit release readiness; it is not release approval.
 
 ## Handoff

.codex/skills/fesa-reference-comparison/SKILL.md

@@ -1,11 +1,12 @@
 ---
 name: fesa-reference-comparison
-description: Use when comparing FESA solver HDF5 results against Abaqus reference CSV files for reference comparison, checking schema, units, ID matching, tolerance metrics, and reference verification status.
+description: Use when comparing FESA results.h5 quantities against feature-declared Abaqus CSV values or diagnosing reference tolerance, identity, row-set, or nonfinite-result failures.
 ---
 
 # FESA Reference Comparison
 
-Use this skill to compare generated solver outputs against stored reference artifacts without modifying either side.
+Compare generated FESA HDF5 values with only the Abaqus CSV quantities declared by the feature.
+The comparison tests observable values; it does not test Abaqus implementation equivalence.
 
 ## Inputs
 
@@ -17,19 +18,29 @@ Read these first:
 - Build/Test report with `pass-for-reference-verification`
 - `docs/reference-models/<feature-id>-reference-models.md`
 - `docs/io-definitions/<feature-id>-io.md`
-- Generated solver result HDF5, normally `results.h5`
-- Abaqus reference CSV files under `reference/<model-id>/`
-- Optional deterministic solver CSV views materialized from `results.h5` for debugging or review
+- Generated FESA `results.h5`
+- Declared reference `.inp` and required Abaqus CSV files
 
 ## Workflow
 
 1. Follow `ARTIFACT CHECK -> COMPARE -> CLASSIFY -> REPORT`.
-2. ARTIFACT CHECK: verify `metadata.json`, `model.inp`, generated solver `results.h5`, `reference/<model-id>/<model-id>_displacements.csv`, `reference/<model-id>/<model-id>_reactions.csv`, `reference/<model-id>/<model-id>_internalforces.csv`, `reference/<model-id>/<model-id>_stresses.csv`, reference CSV schema version, FESA HDF5 schema version, units, coordinate system, step/frame identity, ID matching, output location, component naming, and tolerance policy.
-3. Stop with `needs-reference-artifacts`, `needs-solver-results`, or `needs-upstream-decision` when required comparison inputs are missing.
-4. COMPARE FESA HDF5 datasets by normalizing their rows and matching them directly against Abaqus reference CSV rows.
-5. Apply upstream tolerance exactly. Do not loosen or reinterpret tolerance.
-6. Report max absolute error, max relative error, RMS error, norm error, worst id, worst component, missing rows, extra rows, and pass/fail.
-7. CLASSIFY failures as missing-reference-artifact, missing-solver-output, schema-mismatch, id-mismatch, unit-or-coordinate-mismatch, tolerance-failure, nonfinite-result, upstream-contract, or environment.
+2. ARTIFACT CHECK: verify the declared input, `results.h5`, every required CSV, HDF5
+   projection, source-ID/component mapping, row prechecks, blocking/warning behavior, and tolerance.
+3. Reject a missing input or required CSV as `needs-reference-artifacts`.
+4. Reject a missing HDF5 result or comparison command as `needs-solver-results`.
+5. Reject missing, extra, duplicate, or nonfinite required rows before tolerance evaluation.
+6. COMPARE: normalize HDF5 values and match CSV values by declared source identity and component.
+   Never match by row order alone.
+7. Apply the upstream tolerance exactly. Do not clamp values, drop rows, loosen tolerance, or
+   modify either artifact to obtain a pass.
+8. Report per-row decisions, max absolute error, max relative error, RMS error, norm error when
+   required, worst source ID/component, and pass/fail or warning per quantity.
+9. CLASSIFY failures as missing-reference-artifact, missing-solver-output, schema-mismatch,
+   id-mismatch, tolerance-failure, nonfinite-result, upstream-contract, or environment.
+
+Do not require canonical names, README, metadata, Abaqus version/provenance, duplicated CSV
+units/coordinates/step-frame fields, or a reference CSV schema version unless the feature
+requirements explicitly make one of them part of comparison acceptance.
 
 ## Output Contract
 
@@ -46,25 +57,21 @@ Produce or revise `docs/reference-verifications/<feature-id>-reference-verificat
 
 ## Boundaries
 
-- Do not edit source code.
-- Do not edit tests.
-- Do not edit CMake files.
-- Do not change requirements, formulations, I/O contracts, reference artifacts, or tolerance policies.
-- Do not change tolerance policies.
-- Do not run Abaqus, Nastran, or any reference solver.
-- Do not generate or modify Abaqus reference CSV files.
+- Do not edit source, tests, CMake, upstream contracts, reference artifacts, or tolerances.
+- Do not run Abaqus, Nastran, or another reference solver.
+- Do not generate or modify reference CSV files.
 - Do not approve physics validation or release readiness.
 
 ## Quality Gate
 
-- Every compared row has a deterministic matching rule.
-- Missing rows and extra rows are reported, not ignored.
-- Nonfinite values are reported explicitly.
-- `pass-for-physics-evaluation` means reference tolerance success only.
-- FESA solver `results.h5` is the authoritative solver output.
-- Abaqus reference CSV files are the authoritative reference result artifacts.
-- FESA debug CSV views are derived from `results.h5` for review only; do not treat FESA debug CSV views as authoritative solver output or reference artifacts.
+- Every declared required row has a deterministic source-ID/component match.
+- Missing/extra/duplicate/nonfinite required rows remain visible and fail before tolerance.
+- Warning-only quantities never change the blocking pass/fail verdict.
+- `pass-for-physics-evaluation` means required reference tolerance success only.
+- FESA `results.h5` remains authoritative solver output; Abaqus CSV remains external reference data.
 
 ## Handoff
 
-Send passing reports to Physics Evaluation Agent. Send implementation-owned mismatches to Correction Agent. Send missing artifacts to Reference Model Agent and HDF5/reference CSV schema conflicts to I/O Definition Agent.
+Send passing reports to Physics Evaluation Agent. Send implementation-owned mismatches to
+Correction Agent, missing declared files to Reference Model Agent, and HDF5 projection or
+identity-contract conflicts to I/O Definition Agent.

.codex/skills/fesa-reference-models/SKILL.md

@@ -1,11 +1,13 @@
 ---
 name: fesa-reference-models
-description: Use when designing FESA reference model portfolios, Abaqus input artifact bundles, metadata provenance, required Abaqus reference CSV files, coverage matrices, and implementation-planning handoffs.
+description: Use when a FESA feature needs existing Abaqus input/CSV reference cases, required comparison quantities, tolerance mapping, or implementation-planning handoff.
 ---
 
-# FESA Reference Models
+# FESA Reference Cases
 
-Use this skill to define test model portfolios and reference artifact contracts before implementation planning.
+Use this skill to inventory the minimum stored reference inputs and CSV quantities that a
+feature actually compares. Abaqus is an external numerical reference, not the FESA formulation
+or behavior specification.
 
 ## Inputs
 
@@ -15,55 +17,67 @@ Read these first:
 - `docs/SOLVER_AGENT_DESIGN.md`
 - `docs/reference-models/README.md`
 - `docs/requirements/<feature-id>.md`
-- `docs/research/<feature-id>-research.md`
 - `docs/formulations/<feature-id>-formulation.md`
 - `docs/numerical-reviews/<feature-id>-review.md`
 - `docs/io-definitions/<feature-id>-io.md`
+- Existing files under `reference/`
 
 ## Workflow
 
-1. Define reference strategy: code verification, solution verification, and benchmark/reference comparison.
-2. Build a model inventory: smoke, analytical, patch test, benchmark, regression, and negative/invalid-input models.
-3. For each model, record `model_id`, purpose, verified requirements, analysis type, element type, material, boundary conditions, loads, expected quantities, tolerance, source, and status.
-4. Define `reference/<model-id>/` artifact bundle requirements.
-5. Require `model.inp`, `metadata.json`, `<model-id>_displacements.csv`, `<model-id>_reactions.csv`, `<model-id>_internalforces.csv`, `<model-id>_stresses.csv`, and `README.md` unless explicitly not applicable.
-6. Define optional `<model-id>_strains.csv`, `<model-id>_energy_or_residual.csv`, and `<model-id>_<quantity>.csv` only when upstream acceptance criteria require them.
-7. Define metadata provenance, units, coordinate system, output requests, artifact status, reference_csv_schema_version, reference_csv_files, and limitations.
-8. Build a Coverage Matrix mapping requirement id, model id, compared quantity, FESA HDF5 dataset, reference CSV file, tolerance, verification method, and status.
+1. Read the feature requirements and list only blocking and warning-only reference quantities.
+2. Inventory each existing case using its exact directory, input filename, and required CSV filenames.
+3. Confirm the input and every required comparison CSV are present and readable.
+4. Record the FESA HDF5 dataset, source identity column, required component columns, and stable matching rule.
+5. Require unique source IDs, complete required row sets, and finite comparison values.
+6. Copy the approved tolerance and blocking/warning behavior without inventing or calibrating values.
+7. Map each reference-comparison requirement to at least one existing case when the feature requires that coverage.
+
+Do not require or create:
+
+- canonical directories or filenames;
+- legacy-alias approvals;
+- bundle `README.md` or `metadata.json`;
+- Abaqus version or generation provenance;
+- duplicated units, coordinates, step/frame, material, section, thickness, or element-type metadata;
+- a reference CSV schema version;
+- CSV files for quantities outside the approved comparison boundary;
+- an expanded benchmark portfolio unless the feature requirements explicitly require it.
+
+Read source element type, material, section, loads, constraints, and supported single-step
+identity from the `.inp`. Do not rename, repair, normalize, or generate reference artifacts.
 
 ## Output Contract
 
 Produce or revise `docs/reference-models/<feature-id>-reference-models.md` with:
 
 - Metadata
-- Reference Strategy
-- Model Inventory
-- Model Record
-- Abaqus Input Requirements
-- Artifact Bundle Contract
-- Metadata JSON Contract
-- Abaqus Reference CSV Requirements
-- Coverage Matrix
-- Artifact Acceptance Checklist
+- Reference Acceptance Scope
+- Reference Case Inventory
+- HDF5-to-CSV Comparison Mapping
+- Tolerance and Blocking/Warning Policy
+- Readiness Checklist
 - Open Issues and Downstream Handoff
 
 ## Boundaries
 
-- Do not implement code.
-- Do not implement parsers.
+- Do not implement code or parsers.
 - Do not design C++ APIs or file ownership.
-- Do not run Abaqus, Nastran, or any reference solver.
-- Do not generate or modify Abaqus reference CSV files.
+- Do not run Abaqus, Nastran, or another reference solver.
+- Do not generate or modify reference inputs or CSV files.
 - Do not compare solver results.
 - Do not approve release readiness.
 
 ## Quality Gate
 
-- Every `must` requirement maps to at least one model and compared quantity.
-- `model.inp` stays within the supported Abaqus keyword subset or records an open issue.
-- `metadata.json` includes provenance, Abaqus version/source, units, coordinate system, tolerance, reference_csv_schema_version, and reference_csv_files.
-- Missing required Abaqus reference CSV files keep the model at `needs-reference-artifacts`.
+- Every blocking or warning-only quantity names an exact input/CSV pair.
+- Every comparison defines an HDF5 projection, source-ID/component mapping, and tolerance.
+- Missing, extra, duplicate, and nonfinite required rows have an explicit fail-before-tolerance rule.
+- Use `needs-reference-artifacts` only when a declared input or required comparison CSV is missing.
+- Use `needs-user-decision` only when required quantities, matching, or tolerance are undefined.
+- Canonical naming, README, metadata, provenance, and unrequested portfolio coverage never block readiness.
 
 ## Handoff
 
-Send model order and tests that should fail first to Implementation Planning Agent. Send FESA HDF5 dataset paths, reference CSV schemas, matching, output location, and tolerance mapping to Reference Verification Agent. Send physical expectations to Physics Evaluation Agent.
+Send exact paths, HDF5 projection, source-ID/component matching, row prechecks, and tolerance to
+Implementation Planning Agent and Reference Verification Agent. Send only feature-required
+physical expectations to Physics Evaluation Agent.

.codex/skills/fesa-reference-models/agents/openai.yaml

@@ -1,4 +1,4 @@
 interface:
-  display_name: "FESA Reference Models"
-  short_description: "Design Abaqus CSV reference bundles"
-  default_prompt: "Use $fesa-reference-models to design Abaqus reference CSV artifact bundles."
+  display_name: "FESA Reference Cases"
+  short_description: "Inventory required input and CSV cases"
+  default_prompt: "Use $fesa-reference-models to inventory the existing Abaqus input and required CSV cases for a FESA feature."

.codex/skills/fesa-release-readiness/SKILL.md

@@ -24,8 +24,10 @@ Read these first:
 1. Follow `GATE AUDIT -> TRACEABILITY CHECK -> RELEASE DOCUMENTATION -> RELEASE VERDICT`.
 2. GATE AUDIT: confirm required reports exist, share the same `feature_id`, are not stale or contradictory, and carry required pass statuses.
 3. Require `pass-for-reference-verification`, `pass-for-physics-evaluation`, and `pass-for-release-agent`.
-4. TRACEABILITY CHECK: confirm each `must` requirement maps to acceptance criteria, test evidence, reference model evidence, and release scope.
-5. Record deferred requirements, unsupported Abaqus keywords, incomplete artifacts, unresolved defects, accepted risks, and known limitations.
+4. TRACEABILITY CHECK: confirm each `must` requirement maps to acceptance criteria, test evidence,
+   feature-required reference evidence when applicable, and release scope.
+5. Record deferred requirements, unsupported Abaqus keywords, missing required comparison files,
+   unresolved defects, accepted risks, and known limitations.
 6. RELEASE DOCUMENTATION: prepare a release checklist, Known Limitations, and Release Notes Draft.
 7. RELEASE VERDICT: issue `ready-for-release` only when all required evidence is present and passing.
 
@@ -59,7 +61,9 @@ Produce or revise `docs/releases/<feature-id>-release.md` with:
 - Do not issue `ready-for-release` without `pass-for-release-agent`, `pass-for-physics-evaluation`, and `pass-for-reference-verification`.
 - Every `must` requirement traces to release scope, acceptance criteria, test or reference evidence, and final disposition.
 - Known limitations and deferred issues are included in the Release Notes Draft.
-- Missing evidence, contradictory reports, unresolved defects, incomplete artifacts, or unavailable validation commands block release readiness.
+- Missing required evidence, contradictory reports, unresolved defects, missing declared comparison
+  files, or unavailable validation commands block release readiness. Canonical naming, README,
+  metadata, provenance, or unrequested portfolio expansion do not.
 
 ## Handoff
 

.codex/skills/fesa-requirements-baseline/SKILL.md

@@ -24,7 +24,8 @@ Read these first:
 3. Convert requested behavior into `shall` statements with ids like `FESA-REQ-<FEATURE>-###`.
 4. Define verification quantities: displacement, reaction, element force, stress, strain, energy, or residual.
 5. Record Tolerance Policy values or mark them `needs-user-decision`.
-6. Record Reference Artifact Requirements under `references/<feature-id>/`.
+6. Record a minimal Reference Case: exact existing input/required CSV paths, blocking and
+   warning-only quantities, HDF5 projection, source-ID/component matching, and tolerance.
 7. Build a Requirement Verification Matrix that maps requirement, source, verification method, acceptance criteria, tolerance, downstream agents, and status.
 8. Keep unresolved decisions visible as open issues; do not hide gaps behind vague wording.
 
@@ -37,7 +38,7 @@ Produce or revise `docs/requirements/<feature-id>.md` with:
 - Input and Output Requirements
 - Verification Quantities
 - Tolerance Policy
-- Reference Artifact Requirements
+- Reference Case Requirements
 - Requirement Verification Matrix
 - Open Questions and Downstream Handoff
 
@@ -53,8 +54,11 @@ Produce or revise `docs/requirements/<feature-id>.md` with:
 ## Quality Gate
 
 - Every `must` requirement has a verification method and acceptance criteria.
-- Every numerical requirement has units, coordinate system, and tolerance or an explicit owner for the decision.
-- Every reference-comparison requirement names required artifacts.
+- Every numerical solver-output requirement has units, coordinates, and tolerance when applicable.
+- Every reference-comparison requirement names exact required files, compared components,
+  source identity, blocking/warning behavior, and tolerance.
+- Do not require canonical names, README, metadata, provenance, or CSVs for quantities outside
+  the feature acceptance boundary.
 - Words like "accurate", "fast", and "Abaqus-like" are converted into measurable criteria or open questions.
 
 ## Handoff

.codex/skills/harness-review/SKILL.md

@@ -1,44 +0,0 @@
----
-name: harness-review
-description: Use when reviewing this C++/MSVC Harness repository: local changes, generated phase files, step outputs, implementation diffs, missing tests, MSVC build readiness, or compliance with AGENTS.md, docs/ARCHITECTURE.md, docs/ADR.md, and Harness acceptance criteria.
----
-
-# Harness Review
-
-## Overview
-
-Use this skill to review Harness work against the repository's persistent rules, architecture docs, C++/MSVC constraints, TDD guard policy, and executable verification requirements. Prioritize bugs, regressions, missing tests, and rule violations.
-
-## Review Process
-
-1. Read `/AGENTS.md`, `/docs/ARCHITECTURE.md`, and `/docs/ADR.md`.
-2. Inspect the changed files with `git status --short` and `git diff`.
-3. Check architecture, stack choices, C++ test coverage, critical rules, and MSVC/CMake readiness.
-4. Run relevant verification commands when feasible. If a command cannot be run, report that as residual risk.
-5. Lead with actionable findings. Keep summaries secondary.
-
-## Checklist
-
-| Item | Question |
-| --- | --- |
-| Architecture | Does the change follow `docs/ARCHITECTURE.md` ownership boundaries? |
-| Stack | Does the change stay within C++/MSVC/CMake decisions documented in `docs/ADR.md`? |
-| Tests | Are new or changed behaviors covered by Python Harness tests or C++ tests? |
-| TDD Guard | Would C++ production edits be blocked without related tests? |
-| Critical Rules | Does the change violate any `AGENTS.md` CRITICAL rule? |
-| Build | Do `python -m unittest discover -s scripts -p "test_*.py"` and `python scripts/validate_workspace.py` pass or provide an expected no-CMake message? |
-
-## Output Format
-
-If there are findings, list them first in severity order with file and line references when possible. Then include this table:
-
-| 항목 | 결과 | 비고 |
-| --- | --- | --- |
-| 아키텍처 준수 | PASS/FAIL | {상세} |
-| 기술 스택 준수 | PASS/FAIL | {상세} |
-| 테스트 존재 | PASS/FAIL | {상세} |
-| TDD Guard | PASS/FAIL | {상세} |
-| CRITICAL 규칙 | PASS/FAIL | {상세} |
-| 빌드/검증 가능 | PASS/FAIL | {상세} |
-
-When there are no findings, say that clearly, then mention any commands not run or remaining risk.

.codex/skills/harness-review/agents/openai.yaml

@@ -1,4 +0,0 @@
-interface:
-  display_name: "Harness Review"
-  short_description: "Review Harness changes safely"
-  default_prompt: "Use $harness-review to review Harness repository changes."

.codex/skills/harness-workflow/SKILL.md

@@ -1,130 +0,0 @@
----
-name: harness-workflow
-description: Use when planning or running this C++/MSVC Harness framework: reading AGENTS.md and docs/*.md, discussing implementation scope, creating or updating phases/index.json, phases/{task}/index.json, phases/{task}/stepN.md, or invoking scripts/execute.py for staged Codex execution.
----
-
-# Harness Workflow
-
-## Overview
-
-Use this skill to turn a user-approved task into small, self-contained Harness steps that another Codex session can execute reliably. Keep every step grounded in repository docs, C++/MSVC constraints, TDD, and executable acceptance criteria.
-
-## Workflow
-
-1. Read `AGENTS.md` and relevant files under `docs/`, especially `docs/PRD.md`, `docs/ARCHITECTURE.md`, and `docs/ADR.md`.
-2. Discuss unresolved product or technical decisions with the user before writing phase files.
-3. When the user asks for an implementation plan, draft steps and get approval before creating files.
-4. Create or update `phases/index.json`, `phases/{task-name}/index.json`, and one `phases/{task-name}/stepN.md` per step.
-5. Run the phase with `python scripts/execute.py {task-name}` when asked to execute it. Use `--push` only when the user asks to push.
-
-## Step Design Rules
-
-- Scope each step to one layer or module. Split steps when multiple modules would otherwise change together.
-- Make every step self-contained. Do not rely on prior conversation; include all required context and file paths.
-- Force context gathering. Each step must tell Codex which docs and previous outputs to read before editing.
-- Specify interfaces and signatures, not full implementations, unless exact code is required for a constraint.
-- Put core invariants directly in the step: idempotency, numerical conventions, data integrity, API contracts, or other non-negotiables.
-- Use executable acceptance criteria such as `python scripts/validate_workspace.py`, not abstract statements.
-- For C++ behavior changes, require tests first and name the expected test file or test executable.
-- Name steps with kebab-case slugs such as `project-setup`, `core-types`, or `solver-validation`.
-
-## Phase Files
-
-Create or update `phases/index.json`:
-
-```json
-{
-  "phases": [
-    {
-      "dir": "0-mvp",
-      "status": "pending"
-    }
-  ]
-}
-```
-
-Create `phases/{task-name}/index.json`:
-
-```json
-{
-  "project": "FESA Harness",
-  "phase": "<task-name>",
-  "steps": [
-    { "step": 0, "name": "project-setup", "status": "pending", "allowed_paths": ["CMakeLists.txt", "tests/"] },
-    { "step": 1, "name": "core-types", "status": "pending", "allowed_paths": ["src/fesa/core/", "tests/unit/"] },
-    { "step": 2, "name": "validation-path", "status": "pending", "allowed_paths": ["scripts/", "docs/"] }
-  ]
-}
-```
-
-Rules:
-
-- `project` comes from `AGENTS.md`.
-- `phase` matches the task directory name.
-- `steps[].step` starts at `0`.
-- Initial status is always `pending`.
-- Each step must declare non-empty `allowed_paths` using repository-relative paths, directory prefixes, or glob patterns.
-- Do not add timestamps when creating files. `scripts/execute.py` records `created_at`, `started_at`, `completed_at`, `failed_at`, and `blocked_at`.
-
-## Step Template
-
-```markdown
-# Step {N}: {name}
-
-## 읽어야 할 파일
-
-먼저 아래 파일들을 읽고 프로젝트의 아키텍처와 설계 의도를 파악하라:
-
-- `/AGENTS.md`
-- `/docs/ARCHITECTURE.md`
-- `/docs/ADR.md`
-- {previously created or modified files}
-
-이전 step에서 만들어진 코드를 꼼꼼히 읽고, 설계 의도를 이해한 뒤 작업하라.
-
-## 작업
-
-{Concrete instructions with file paths, interfaces, signatures, and rules.}
-
-## Tests To Write First
-
-- {Exact C++ or Python test file and behavior to add before implementation.}
-
-## Acceptance Criteria
-
-```bash
-python -m unittest discover -s scripts -p "test_*.py"
-python scripts/validate_workspace.py
-```
-
-## 검증 절차
-
-1. 위 AC 커맨드를 실행한다.
-2. 아키텍처 체크리스트를 확인한다:
-   - ARCHITECTURE.md 디렉토리 구조를 따르는가?
-   - ADR 기술 스택을 벗어나지 않았는가?
-   - AGENTS.md CRITICAL 규칙을 위반하지 않았는가?
-   - C++ 변경에는 관련 테스트가 존재하는가?
-3. 결과에 따라 `phases/{task-name}/index.json`의 해당 step을 업데이트한다:
-   - 성공: `"status": "completed"`, `"summary": "산출물 한 줄 요약"`
-   - 3회 수정 시도 후 실패: `"status": "error"`, `"error_message": "구체적 에러 내용"`
-   - 사용자 개입 필요: `"status": "blocked"`, `"blocked_reason": "구체적 사유"` 후 중단
-
-## 금지사항
-
-- JavaScript/TypeScript/npm fallback을 추가하지 마라. Reason: 이 Harness는 C++/MSVC 전용이다.
-- 기존 테스트를 깨뜨리지 마라.
-```
-
-## Execution And Recovery
-
-Run:
-
-```bash
-python scripts/execute.py {task-name}
-python scripts/execute.py {task-name} --push
-```
-
-`scripts/execute.py` creates or checks out `codex/{task-name}`, refuses dirty worktrees, requires per-step `allowed_paths`, stages only explicit allowed paths and runner housekeeping files, validates before every runner-created commit, injects `AGENTS.md` and `docs/*.md` into each prompt, carries completed step summaries forward, retries failed steps up to three times, and records timestamps.
-
-If a step is `error`, set it back to `pending` and remove `error_message` after fixing the cause. If a step is `blocked`, resolve `blocked_reason`, set it back to `pending`, remove `blocked_reason`, and rerun.

.codex/skills/harness-workflow/agents/openai.yaml

@@ -1,4 +0,0 @@
-interface:
-  display_name: "Harness Workflow"
-  short_description: "Plan staged Harness workflow steps"
-  default_prompt: "Use $harness-workflow to plan Harness phases and step files."

.gitignore

@@ -17,6 +17,11 @@ Testing/
 *.log
 __pycache__/
 *.pyc
+*.h5
+
+# local Harness configuration and build outputs
+.harness/config.json
+.harness/build/
 
 # phase execution outputs
 phases/**/phase*-output.json

.harness/config.example.json

@@ -0,0 +1,16 @@
+{
+  "version": 1,
+  "projectType": "auto",
+  "tdd": {
+    "testRoots": [
+      "tests",
+      "test"
+    ],
+    "testPatterns": [
+      "{stem}_test.cpp",
+      "{stem}_tests.cpp",
+      "test_{stem}.cpp",
+      "{stem}.test.cpp"
+    ]
+  }
+}

AGENTS.md

@@ -10,38 +10,115 @@
 - Abaqus `.inp` keyword subset input
 
 ## 프로젝트 정체성
-- FESA는 유한요소법 기반 구조해석 솔버 개발 프로젝트이다.
-- Harness는 솔버 자체가 아니라 요구조건, TDD, phase 실행, 검증을 통제하는 개발 운영 인프라이다.
-- 문서와 구현은 full Abaqus compatibility를 주장하지 않는다. 기능별로 승인된 Abaqus keyword subset만 지원한다.
+- FESA는 유한요소법 기반 구조해석 솔버를 단계적으로 구축하고 검증하는 프로젝트이다. 목표는 Abaqus를 흉내 내는 parser를 만드는 것이 아니라, 승인된 입력 범위에서 물리적으로 설명 가능하고 재현 가능한 해석 결과를 만드는 것이다.
+- 새 기능은 입력 keyword만 인식하거나 element kernel만 존재한다고 완성된 것이 아니다. Semantic model, equation system, 해법, 결과 복구, HDF5 외부 계약과 독립 검증 evidence가 하나의 추적 가능한 기능을 이뤄야 한다.
+- 프로젝트의 배경, 목적, 사용자, 범위는 `docs/PRD.md`에서 확인한다.
+- 전체 아키텍처와 모듈별 책임은 `docs/ARCHITECTURE.md`에서 확인한다.
+- 주요 아키텍처 결정과 그 이유 및 트레이드오프는 `docs/ADR.md`에서 확인한다.
+- AI 에이전트는 설계나 구현 결정을 내리기 전에 PRD에서 제품 범위를, ARCHITECTURE에서 소유권과 데이터 흐름을, ADR에서 이미 결정된 트레이드오프를 먼저 확인한다. 기능별 의미는 `docs/requirements/`, `docs/formulations/`, `docs/io-definitions/`, `docs/reference-models/`의 승인 문서를 source of truth로 삼는다.
+- Harness는 솔버 자체가 아니라 요구조건, TDD, phase 실행, 검증을 통제하는 개발 운영 인프라이다. 전체 실행 흐름은 `docs/HARNESS_WORKFLOW.md`, 설치와 설정은 `docs/HARNESS.md`를 따른다.
+- FESA는 Abaqus와 독립적인 솔버다. 문서와 구현은 full Abaqus compatibility뿐 아니라
+  Abaqus 요소 정식화, 적분, stabilization, 내부 상태 또는 결과 생성 절차의 동등성을
+  주장하거나 목표로 삼지 않는다. 수치 결과의 exact equality는 허용되지만 내부 동작
+  동등성의 evidence가 아니다.
+- 기능별로 승인된 Abaqus keyword subset만 입력 형식으로 지원한다. Abaqus 결과는 승인된
+  비교량의 외부 수치 reference일 뿐 FESA 내부 알고리즘 계약이 아니다.
 - 공식 solver output은 HDF5 `results.h5`이다.
 - reference 결과는 FESA와 같은 Abaqus `.inp` 모델을 Abaqus로 해석해 생성한 CSV 파일이다.
-- reference comparison은 FESA `results.h5`의 변위, 반력, 내력, 응력 dataset을 `reference/<model-id>/<model-id>_*.csv` 파일과 비교한다.
+- reference case는 기능 문서가 지정한 기존 `.inp`와 실제 비교에 필요한 Abaqus CSV 경로를
+  그대로 사용한다. canonical 이름, legacy-alias 승인, bundle `README.md`, `metadata.json`,
+  Abaqus version/provenance 또는 중복 unit/coordinate/step-frame/schema 기록은 readiness
+  조건이 아니다.
+- 비교기는 필요한 source row identity와 component를 결정적으로 대응시키고 누락, 추가,
+  중복, nonfinite 값을 tolerance 전에 거부한다. Reference artifact는 rename, rewrite 또는
+  보정하지 않는다.
 - CSV는 FESA 공식 output이 아니며, FESA HDF5에서 추출한 deterministic CSV view는 비교 디버깅/검토용 보조 artifact로만 둔다.
 
-## 아키텍처 규칙
-- CRITICAL: 기본 검증 경로는 `python scripts/validate_workspace.py`이다.
+## FESA 개발의 핵심 원칙
+
+### 물리와 수치 계약
+
+- CRITICAL: 구현보다 요구조건, 정식화, 부호, 단위, 좌표계, row identity와 tolerance 계약을 먼저 고정한다. 구현 편의를 위해 승인된 의미를 조용히 바꾸지 않는다.
+- CRITICAL: 해석 결과가 유한하고 선형계가 풀렸다는 사실만으로 correctness를 주장하지 않는다. Equilibrium, reaction, rigid-body mode, energy, symmetry와 reference identity를 기능에 맞게 검증한다.
+- Source label/instance identity와 internal index/equation index를 구분한다. Stable source identity는 진단, 결과, reference mapping 전 구간에서 보존한다.
+- 병렬 실행 여부와 관계없이 같은 입력은 같은 sparse structure, reduction order, result row order와 diagnostic order를 만들어야 한다.
+- Scale-aware validation은 formulation과 I/O 계약의 기준을 사용한다. 임의의 `max(1, ...)`, zero clamp, 누락 row 무시 또는 불일치 평균으로 오류를 숨기지 않는다.
+
+### 소유권과 의존성
+
 - CRITICAL: C++ 빌드는 CMake/MSVC/x64/Debug 기준으로 검증한다.
 - CRITICAL: 새 기능 또는 동작 변경은 테스트를 먼저 작성하고 실패를 확인한 뒤 구현한다.
 - CRITICAL: C++ production file을 바꿀 때는 관련 C++ test file이 있어야 한다.
-- CRITICAL: Abaqus reference artifact 생성, 수정, 복원은 명시적으로 요청된 phase에서만 수행한다.
-- CRITICAL: `harness-workflow` 스킬은 사용자가 명시적으로 허용하기 전까지 사용하지 않는다.
+- CRITICAL: Abaqus reference artifact 생성, 수정, 복원은 명시적으로 요청된 phase에서만 수행한다. 문서 또는 agent가 artifact naming이나 보조 metadata를 맞추기 위해 파일 변경을 요구하지 않는다.
+- CRITICAL: public header와 implementation 의존성 방향을 역전하지 않는다.
+- CRITICAL: 사람이 계약과 수치식을 대조할 수 있는 단순한 코드를 작성한다. 주석은 코드가 이미 말하는 동작보다 부호, 수명, 순서, backend 제약처럼 비자명한 이유를 설명한다.
 - Domain은 입력 파일에서 생성된 전체 모델 정의를 소유하고, 파싱 이후 가능한 한 불변으로 취급한다.
-- AnalysisModel은 현재 step에서 활성화된 elements, loads, boundary conditions, properties/materials의 view를 제공하며 Domain을 복사하지 않는다.
+- AnalysisModel은 현재 step에서 활성화된 elements, loads, boundary conditions, properties/materials의 non-owning view를 제공하며 Domain을 복사하지 않는다. 따라서 Domain은 AnalysisModel보다 오래 살아야 한다.
 - DofManager는 node별 자유도 정의, constrained/free mapping, equation numbering, sparse pattern ownership을 전담한다. Node 또는 Element 내부에 equation id를 분산 저장하지 않는다.
-- AnalysisState는 displacement, velocity, acceleration, temperature, external/internal force, residual, time/increment/iteration, element state를 소유한다.
-- MKL, TBB, HDF5 API는 solver core에 직접 노출하지 않는다. `LinearSolver`, `ParallelFor`, `ResultsWriter`, `Vector`, `Matrix`, `SparseMatrix` adapter 경계 뒤에 둔다.
+- AnalysisState는 해당 procedure가 실제로 사용하는 mutable solution과 recovery row만 소유한다. V0는 full displacement/external/internal force/residual/reaction과 step/frame 및 beam recovery rows만 보관하며 미래 state를 미리 할당하지 않는다.
+- MKL, TBB, HDF5, Win32 API와 vendor type은 public solver core에 노출하지 않는다. `LinearSolver`, `ParallelFor`, `ResultsWriter`, `Vector`, `Matrix`, `SparseMatrix` 경계 뒤에 둔다.
+- 해석 단계는 실패할 수 있는 candidate를 완성하고 검증한 뒤 소유 state/output에 반영한다. 실패 시 기존 state와 기존 최종 HDF5를 가능한 계약 범위에서 보존한다.
+
+### 선형 정적 해석 불변식
+
+- `Analysis::run()`의 실제 단계와 객체별 책임은 `docs/ARCHITECTURE.md`의 해석 실행 흐름을 따른다.
+- Full stiffness를 stable free/constrained 순서로 `Kff/Kfc/Kcf/Kcc`에 분할하고, `Kff` factorization을 load assembly보다 먼저 수행한다.
+- Effective RHS는 `Ff - Kfc * dc`이며 substitution 뒤 full displacement를 복구한다. 모든 DOF가 constrained인 유효한 모델의 `0 x 0 Kff`를 singular error로 바꾸지 않는다.
+- Reaction과 free-equilibrium evidence는 조립된 full residual `K*d - F`에서 구한다. Constrained 성분은 physical reaction이고 free 성분은 residual evidence다.
+- Sparse assembly는 element-local contribution과 stable COO ordering, 고정된 reduction을 사용한다. 병렬 worker가 global CSR storage를 직접 갱신하지 않는다.
+- Element end action, positive-local-x section resultant, Gauss generalized result와 section-point stress는 서로 다른 identity와 부호 계약을 가진다. Station mismatch를 평균으로 합치지 않는다.
+
+### 개발 운영 인프라
+
 - Codex custom agent의 `model_reasoning_effort` 기본값은 `extra high`로 둔다.
 - Harness runner는 `scripts/execute.py`에 둔다.
-- `scripts/execute.py`는 `codex/<phase-name>` branch prefix만 사용한다.
-- `scripts/execute.py` 실행 전 worktree는 clean 상태여야 한다.
-- 각 phase step은 non-empty `allowed_paths`를 선언해야 한다.
-- runner는 explicit allowed path와 runner housekeeping file만 stage하며 broad staging을 사용하지 않는다.
-- runner가 만드는 모든 commit 전에는 Harness Python self-test와 `python scripts/validate_workspace.py`가 통과해야 한다.
-- Codex hook 정책은 `.codex/hooks/`에 둔다.
+- `scripts/execute.py`는 `feat-<phase-name>` branch prefix를 사용한다.
+- runner는 `git add -A`로 변경사항을 stage하므로 실행 전 clean worktree 또는 별도 Git worktree를 사용한다.
+- Hook 연결은 `.codex/hooks.json`, 구현은 `scripts/hooks/`와 `scripts/msvc_harness/`에 둔다.
+- PreToolUse는 위험 명령과 C++ production file의 대응 테스트 존재 여부를 검사하는 guardrail이며 RED 실행을 증명하지 않는다.
+- Stop은 `.harness/config.json` 또는 자동 감지 결과에 따라 MSVC build와 test를 모두 검증한다.
 - Generated phase execution outputs remain ignored under `phases/**/step*-output.json`.
 
+## 현재 승인된 V0 기능 계약
+- `linear-static-3d-euler-beam`의 source of truth는 `docs/superpowers/specs/2026-08-08-linear-static-3d-euler-beam-design.md`이다. 관련 문서를 변경하거나 구현할 때 이 계약의 의미를 임의로 넓히지 않는다.
+- 입력 파일당 하나의 `*STEP, *STATIC`과 `TYPE=B33`만 지원한다. B31을 Euler 요소로 매핑하지 않고 `unsupported-element-formulation`으로 거부한다.
+- `*PART/*ASSEMBLY/*INSTANCE`는 identity instance와 stable source identity만 지원한다. instance transform과 nested assembly는 거부한다.
+- 선형 정적 실행 순서는 stiffness assembly와 constrained partition 뒤 `Kff`를 factorize하고, 그 다음 load vector와 effective RHS를 조립해 substitution하는 순서를 유지한다.
+- FESA는 output request와 무관하게 displacement, reaction, equilibrium end action, section resultant, generalized strain/resultant, axial `S11`을 HDF5에 기록한다. Beam stress의 Abaqus reference comparison은 N/A다.
+- B33 reference row는 component별 Abaqus scale로 `absolute_floor + 1e-6 * reference_scale`을 적용한다. Reference 값을 zero-clamp하거나 누락 row를 무시하지 않는다.
+- `reference/cantilever beam/` artifact는 rename, rewrite 또는 보정하지 않는다.
+
+## 승인된 MITC4 정책
+
+- Abaqus source `S4`와 `S4R`은 같은 FESA MITC4 정식화로 매핑하며 source type은 추적
+  정보로만 보존한다. Abaqus의 S4/S4R 알고리즘을 재현하지 않는다.
+- Full-integration FESA-MITC4의 blocking Abaqus reference case는
+  `reference/shell/`의 S4 input/displacement CSV만 현재 이름 그대로 사용한다.
+  S4R source 지원은 parser/common-kernel/deterministic assembly/HDF5 metadata test로
+  검증하며 `reference/shellR/` artifact를 acceptance comparison에 사용하지 않는다.
+- Global `U1/U2/U3`만 blocking reference quantity다. 모든 matched U row에는 고정
+  절대오차 `1.0e-5`를 적용한다. `UR1/UR2/UR3`도 고정 절대오차 `1.0e-5`로 비교하되
+  초과 시 warning만 남긴다. MITC4 tolerance 판정에는 `reference_scale`을 사용하지 않으며
+  B33의 component-scale 혼합 tolerance는 변경하지 않는다.
+- MITC4 drilling calibration, coefficient sweep, energy-ratio threshold와 별도 geometry/director
+  calibration(`NR-O01`~`NR-O04`)은 구현 범위가 아니다. 6-DOF 선형계에는 물리 회전
+  stiffness block의 양의 최소 대각항에 `1e-3`을 곱한 고정 numerical drilling
+  stabilization만 사용하며 drilling 방향 nodal moment는 지원하지 않는다.
+- Drilling stabilization은 physical generalized strain/resultant/stress에 포함하지 않으며
+  별도 drilling stiffness/ratio/energy HDF5 output을 요구하지 않는다.
+
+## 기능을 추가할 때의 판단 기준
+
+- 새 element는 요구조건과 formulation을 승인한 뒤 semantic mapping, property/material 연결, DOF/scatter, local kernel, deterministic assembly, recovery, HDF5 row identity, reference/physics evidence를 함께 설계한다.
+- 새 load 또는 constraint는 parser 인식만 추가하지 않는다. Source target resolution, stable application order, full-space assembly, partition/effective RHS, diagnostic과 결과 의미까지 연결한다.
+- 새 analysis procedure는 기존 선형 정적 lifecycle에 조건문을 누적하지 않는다. 필요한 state, equation, solver lifecycle과 recovery contract를 별도 요구조건·ADR·formulation으로 정의한다.
+- 새 backend는 기존 public interface를 유지하고 vendor lifecycle, integer/index conversion, runtime dependency와 failure translation을 adapter 내부에 격리한다.
+- 새 output quantity는 계산식뿐 아니라 units, coordinate system, source/internal identity, HDF5 schema, mandatory 여부, reference projection과 tolerance를 동시에 정의한다.
+- Element API에 kernel이 존재하는 것과 Abaqus keyword/CLI에서 그 기능을 노출하는 것은 별도 계약이다. 예를 들어 V0의 line-load kernel은 `*DLOAD` 지원을 뜻하지 않는다.
+
 ## 개발 프로세스
 - TDD를 기본으로 한다. 구현은 `RED -> GREEN -> VERIFY` 순서를 따른다.
+- CRITICAL: 빌드 경고를 새로 추가하지 말 것.
 - 기능 개발은 다음 gate를 순서대로 통과해야 한다.
   1. 요구조건 분석
   2. 연구자료 조사
@@ -54,12 +131,11 @@
   9. reference comparison
   10. physics sanity
   11. release readiness
-- 커밋 전 hook은 Harness Python self-test와 workspace validation을 실행해야 한다.
-- 커밋 메시지는 conventional commits 형식을 따른다: `feat:`, `fix:`, `docs:`, `refactor:`, `test:`.
-- Codex는 작업 완료 후 검증을 마치면 즉시 변경사항을 commit하고 push한다.
-- 계획이 필요한 장기 작업은 Harness phase로 나누고, 각 step은 독립 실행 가능해야 한다.
+- 커밋 메시지는 conventional commits 형식을 따른다: `feat:`, `fix:`, `docs:`, `refactor:`, `test:`, `chore:`.
 
 ## Agent/Skill Workflow
+AI 에이전트는 유한요소 구조해석 지식이 필요할 때 FEM wiki를 참조하기 위해 `.codex/skills/fem-theory-query` 스킬을 사용할 수 있다.
+
 | 개발 과정 | Agent | Skill | 산출물 |
 | --- | --- | --- | --- |
 | 요구조건 분석 | `requirement-agent` | `fesa-requirements-baseline` | `docs/requirements/<feature-id>.md` |
@@ -75,23 +151,44 @@
 | 물리 검토 | `physics-evaluation-agent` | `fesa-physics-sanity` | `docs/physics-evaluations/<feature-id>-physics-evaluation.md` |
 | 배포 준비 | `release-agent` | `fesa-release-readiness` | `docs/releases/<feature-id>-release.md` |
 
-## 명령어
-```bash
-python -m unittest discover -s scripts -p "test_*.py"
-python scripts/validate_workspace.py
-python scripts/execute.py <phase-dir>
-python scripts/execute.py <phase-dir> --push
+Implementation Planning Agent는 구현 계획 요청에서 `.agents/skills/harness`를 반드시
+사용한다. 먼저 여러 자기완결적 Step의 초안을 제시하고 사용자 승인을 받은 뒤에만
+`phases/index.json`, `phases/<task-name>/index.json`, `phases/<task-name>/stepN.md`를
+생성한다. Harness 실행은 별도 사용자 요청이 있을 때만 수행한다.
+
+## 최소 검증 진입점
+
+세부 target graph, dependency normalization과 Windows runtime staging은 `docs/ARCHITECTURE.md`와 실제 CMake 파일을 따른다. `.harness/config.json`이 존재하면 그 설정을 우선한다.
+
+### Harness Python 검증
+
+```powershell
+uv run --with pytest python -m pytest -v -rs
 ```
 
-## MSVC 검증 기본값
-- Generator: `Visual Studio 17 2022`
-- Platform: `x64`
-- Config: `Debug`
-- Build directory: `build/msvc-debug`
+### Phase 실행
 
-Override variables:
-- `HARNESS_VALIDATION_COMMANDS`
-- `HARNESS_CMAKE_GENERATOR`
-- `HARNESS_CMAKE_PLATFORM`
-- `HARNESS_CMAKE_CONFIG`
-- `HARNESS_BUILD_DIR`
+```powershell
+python scripts/execute.py <phase-name>
+python scripts/execute.py <phase-name> --push
+```
+
+### CMake/CTest 프로젝트
+
+```powershell
+$gtestSource = "C:/path/to/googletest"
+$mklDir = "C:/path/to/oneAPI/mkl/lib/cmake/mkl"
+$tbbDir = "C:/path/to/oneAPI/tbb/lib/cmake/tbb"
+$hdf5Dir = "C:/path/to/HDF5/cmake"
+
+cmake --fresh -S . -B .harness/build -G "Visual Studio 18 2026" -A x64 `
+  "-DFESA_GTEST_SOURCE_DIR=$gtestSource" `
+  "-DMKL_DIR=$mklDir" `
+  "-DTBB_DIR=$tbbDir" `
+  "-DHDF5_DIR=$hdf5Dir"
+cmake --build .harness/build --config Debug
+ctest --test-dir .harness/build -C Debug --show-only=json-v1
+ctest --test-dir .harness/build -C Debug --output-on-failure
+```
+
+`FESA_GTEST_SOURCE_DIR`는 approved local GoogleTest source checkout을 반드시 가리켜야 한다. MKL/TBB/HDF5가 기본 package search에서 발견되지 않는 환경에서는 나머지 세 config directory도 명시한다. FESA 제품 검증은 solution-only MSBuild가 아니라 CMake target과 CTest를 기준으로 한다.

CMakeLists.txt

@@ -0,0 +1,14 @@
+cmake_minimum_required(VERSION 3.25)
+
+project(FESA VERSION 0.1.0 LANGUAGES CXX)
+
+set(CMAKE_CXX_STANDARD 17)
+set(CMAKE_CXX_STANDARD_REQUIRED ON)
+set(CMAKE_CXX_EXTENSIONS OFF)
+
+include(cmake/FesaDependencies.cmake)
+
+enable_testing()
+
+add_subdirectory(src/fesa)
+add_subdirectory(tests)

cmake/FesaDependencies.cmake

@@ -0,0 +1,74 @@
+set(
+    FESA_GTEST_SOURCE_DIR
+    ""
+    CACHE PATH
+    "Path to the approved local GoogleTest source checkout"
+)
+
+if(NOT FESA_GTEST_SOURCE_DIR)
+    message(FATAL_ERROR "FESA_GTEST_SOURCE_DIR must name a local GoogleTest source checkout")
+endif()
+
+get_filename_component(
+    _fesa_gtest_source_dir
+    "${FESA_GTEST_SOURCE_DIR}"
+    ABSOLUTE
+    BASE_DIR "${CMAKE_SOURCE_DIR}"
+)
+
+if(NOT EXISTS "${_fesa_gtest_source_dir}/CMakeLists.txt")
+    message(
+        FATAL_ERROR
+        "FESA_GTEST_SOURCE_DIR does not contain a GoogleTest CMakeLists.txt: "
+        "${_fesa_gtest_source_dir}"
+    )
+endif()
+
+# Keep GoogleTest on the same MSVC runtime as FESA without changing its source tree.
+set(gtest_force_shared_crt ON CACHE BOOL "Use the shared MSVC runtime for GoogleTest" FORCE)
+add_subdirectory(
+    "${_fesa_gtest_source_dir}"
+    "${CMAKE_BINARY_DIR}/_deps/googletest-build"
+    EXCLUDE_FROM_ALL
+)
+
+find_package(MKL CONFIG REQUIRED)
+find_package(TBB CONFIG REQUIRED COMPONENTS tbb)
+find_package(HDF5 CONFIG REQUIRED)
+
+if(NOT TARGET MKL::MKL)
+    message(FATAL_ERROR "The oneMKL CONFIG package did not define MKL::MKL")
+endif()
+
+if(NOT TARGET TBB::tbb)
+    message(FATAL_ERROR "The oneTBB CONFIG package did not define TBB::tbb")
+endif()
+
+# Prefer the packaged shared C runtime when both variants exist. The Windows
+# static archive may carry compiler-runtime requirements that are not part of
+# the HDF5 imported target's transitive link interface.
+if(TARGET hdf5::hdf5-shared)
+    set(_fesa_hdf5_target hdf5::hdf5-shared)
+elseif(TARGET hdf5::hdf5-static)
+    set(_fesa_hdf5_target hdf5::hdf5-static)
+elseif(TARGET HDF5::HDF5)
+    set(_fesa_hdf5_target HDF5::HDF5)
+else()
+    message(FATAL_ERROR "The HDF5 CONFIG package did not define a supported C target")
+endif()
+
+# Stable FESA-owned targets keep package-specific target names out of later modules.
+add_library(fesa_dependency_mkl INTERFACE)
+target_link_libraries(fesa_dependency_mkl INTERFACE MKL::MKL)
+add_library(Fesa::MKL ALIAS fesa_dependency_mkl)
+
+add_library(fesa_dependency_tbb INTERFACE)
+target_link_libraries(fesa_dependency_tbb INTERFACE TBB::tbb)
+add_library(Fesa::TBB ALIAS fesa_dependency_tbb)
+
+add_library(fesa_dependency_hdf5 INTERFACE)
+target_link_libraries(fesa_dependency_hdf5 INTERFACE "${_fesa_hdf5_target}")
+add_library(Fesa::HDF5 ALIAS fesa_dependency_hdf5)
+
+unset(_fesa_gtest_source_dir)
+unset(_fesa_hdf5_target)

docs/ADR.md

@@ -6,18 +6,26 @@ FESA의 architecture decision은 solver correctness, verification traceability,
 ---
 
 ### ADR-001: FESA는 구조해석 솔버 프로젝트이고 Harness는 운영 인프라로 둔다
-**결정**: 저장소의 주 목적은 유한요소법 기반 구조해석 솔버 개발이다. Harness scaffold는 phase execution, TDD guard, commit validation, workspace validation을 제공하는 보조 계층으로 유지한다.
+**결정**: 저장소의 주 목적은 유한요소법 기반 구조해석 솔버 개발이다. Harness는 승인된 Step 계획, 독립 세션 실행, PreToolUse guardrail, Stop MSVC build/test 검증을 제공하는 보조 계층으로 유지한다.
 
 **이유**: 기존 문서가 Harness 중심이면 agent가 solver architecture, FEM verification, Abaqus/HDF5 계약보다 운영 스크립트에 과도하게 맞춰 행동한다.
 
-**트레이드오프**: Harness 문서의 비중은 낮아지지만, 검증 명령과 hook 정책은 계속 필수 운영 규칙으로 유지한다.
+**트레이드오프**: Harness 문서의 비중은 낮아지지만, `docs/HARNESS_WORKFLOW.md`의 실행 계약과 `.codex/hooks.json`의 검증 정책은 계속 필수 운영 규칙으로 유지한다.
 
 ### ADR-002: C++17/MSVC/CMake/CTest를 기본 구현 환경으로 둔다
-**결정**: 기본 solver 구현과 validation은 C++17 이상, Visual Studio 17 2022 generator, x64 platform, Debug config, CMake, CTest로 수행한다.
+**결정**: 기본 solver 구현과 validation은 C++17 이상, Visual Studio 17 2022 또는
+Visual Studio 18 2026 generator, x64 platform, Debug config, CMake, CTest로 수행한다.
+`.harness/config.json`이 없으면 CMake가 설치된 두 승인 generator 중 하나를 자동
+선택할 수 있으며, build/test evidence에는 실제 generator와 compiler version을 기록한다.
 
-**이유**: FESA의 목표 환경은 Windows/MSVC 기반 C++이다. CMake/CTest는 solver source tree가 추가되거나 확장될 때 가장 일관된 build/test entry point다.
+**이유**: FESA의 목표 환경은 Windows/MSVC 기반 C++이다. CMake/CTest는 solver source tree가 추가되거나 확장될 때 가장 일관된 build/test entry point다. VS17과 VS18을
+승인하면 현재 지원되는 MSVC 개발 환경에서 같은 C++17/x64/Debug 계약을 검증할 수 있다.
 
-**트레이드오프**: Visual Studio solution-only workflow는 기본 지원하지 않는다. 필요하면 `HARNESS_VALIDATION_COMMANDS`로 override한다.
+**트레이드오프**: FESA solver source는 CMake/CTest를 기본으로 유지한다. Generator별
+compiler 차이는 각 build/test report에 명시하고, 두 generator 중 하나에서만 관찰되는
+실패를 다른 generator의 성공으로 숨기지 않는다. Harness 자체는 `.harness/config.json`에
+solution과 test command를 명시한 직접 MSBuild 프로젝트도 검증할 수 있지만, 이는 FESA
+제품이 solution-only workflow를 지원한다는 의미가 아니다.
 
 ### ADR-003: Abaqus `.inp` full compatibility가 아니라 기능별 keyword subset을 지원한다
 **결정**: FESA parser는 Abaqus keyword/data/comment line 규칙을 따르되, 기능별로 승인된 keyword subset만 지원한다. 미지원 keyword는 명확한 diagnostic을 남긴다.
@@ -31,26 +39,28 @@ FESA의 architecture decision은 solver correctness, verification traceability,
 
 **이유**: 모델 정의, step activation, equation system, transient/nonlinear state가 섞이면 parser, assembler, solver, result writer가 강하게 결합된다. 분리된 상태 모델은 선형 정적 해석에서 시작해 비선형, 동적, thermal coupling으로 확장하기 쉽다.
 
-**트레이드오프**: 초기 class 수가 늘어난다. Phase 1에서는 interface를 얇게 유지하고 displacement 중심 state부터 구현한다.
+**트레이드오프**: 초기 class 수가 늘어난다. V0에서는 interface를 얇게 유지하고 실제 선형 정적 frame에 필요한 state만 구현한다.
 
 ### ADR-005: 공식 결과 파일은 HDF5로 하고 reference 결과는 Abaqus CSV로 둔다
-**결정**: FESA solver의 authoritative result output은 `results.h5` HDF5이다. Abaqus reference results는 `reference/<model-id>/` 아래 CSV 파일로 저장하며, verification은 FESA HDF5 rows와 Abaqus reference CSV rows를 documented IDs, components, units, coordinate system, step/frame identity, tolerance 기준으로 비교한다.
+**상태**: HDF5 authoritative output 결정은 유지하며 reference bundle governance 부분은 ADR-019로 대체됨.
+
+**결정**: FESA solver의 authoritative result output은 `results.h5` HDF5이다. Abaqus reference results는 기능별 reference model contract가 지정한 `reference/<model-id>/` 아래 CSV 파일로 저장하며, verification은 FESA HDF5 rows와 Abaqus reference CSV rows를 documented IDs, components, units, coordinate system, step/frame identity, tolerance 기준으로 비교한다. 신규 reference는 canonical 파일명을 사용하고, 승인된 기존 bundle의 legacy alias는 해당 기능 계약에 정확한 경로를 기록한 경우에만 허용한다.
 
 **이유**: 구조해석 결과는 step/frame, field/history, node/element/integration point location, units, coordinate system, schema version을 함께 가져야 한다. HDF5는 이 계층 구조와 metadata를 안정적으로 표현한다.
 
 **트레이드오프**: reference comparison은 FESA HDF5 dataset identity와 Abaqus CSV row identity를 모두 관리해야 한다. FESA HDF5에서 추출한 deterministic CSV view는 디버깅/검토용 보조 artifact로 허용하지만, 공식 solver output이나 reference artifact로 취급하지 않는다.
 
 ### ADR-006: 해석 알고리즘과 수치 backend는 Strategy와 Adapter 경계 뒤에 둔다
-**결정**: `Analysis`, `LinearSolver`, `TimeIntegrator`, `ConvergenceCriteria`는 Strategy로 구성하고, MKL, TBB, HDF5 API는 adapter 계층 뒤에 둔다.
+**결정**: `Analysis`, `LinearSolver`, `TimeIntegrator`, `ConvergenceCriteria`는 Strategy로 구성하고, MKL, TBB, HDF5 API는 adapter 계층 뒤에 둔다. `Vector`는 contiguous `double`, `Matrix`는 row-major contiguous `double`을 소유하고 dense 연산은 MKL CBLAS를 사용한다. `SparseMatrix`는 이들과 상속 관계가 없는 0-based CSR 전용 타입이며, PARDISO factorization과 substitution은 `LinearSolver` 경계 뒤에서 분리한다.
 
 **이유**: 선형 정적, 비선형 정적, 동적, frequency, heat transfer 해석은 공통 흐름을 공유하지만 알고리즘과 backend가 다르다. 외부 API를 core에 노출하면 테스트 double, backend 교체, dependency review가 어려워진다.
 
-**트레이드오프**: 단일 기능만 구현할 때는 adapter가 다소 장황해 보일 수 있다. 하지만 solver backend와 result writer는 장기적으로 교체 가능해야 한다.
+**트레이드오프**: 단일 기능만 구현할 때는 adapter가 다소 장황해 보일 수 있다. Row-major dense storage와 CSR sparse storage를 따로 유지해야 하지만 backend 의존성과 dense/sparse 의미가 core 모델에 섞이지 않는다.
 
 ### ADR-007: Analysis 실행 흐름은 Template Method로 고정한다
-**결정**: `Analysis::run()`은 `initialize -> buildAnalysisModel -> buildDofMap -> buildSparsePattern -> assemble -> applyBoundaryConditions -> solve -> updateState -> writeResults` 흐름을 고정한다.
+**결정**: `Analysis::run()`은 공통 lifecycle을 고정한다. 선형 정적 V0의 순서는 `parse input -> initialize Domain -> build AnalysisModel -> build DOF map/sparse pattern -> assemble stiffness -> partition constraints -> factorize Kff -> assemble load -> form effective RHS -> substitute -> reconstruct displacement -> recover results -> write HDF5`다. 강성행렬 factorization은 하중벡터 조립보다 먼저 수행하고, factorization과 substitution을 하나의 불투명한 solve 호출로 합치지 않는다.
 
-**이유**: 해석 procedure가 늘어나도 공통 실행 순서가 유지되어야 검증, logging, result writing, failure classification이 일관된다.
+**이유**: 해석 procedure가 늘어나도 공통 실행 순서가 유지되어야 검증, logging, result writing, failure classification이 일관된다. Factorization과 substitution을 분리하면 동일 강성행렬에 여러 RHS를 적용할 수 있고 각 실패 단계를 구조화된 diagnostic으로 분류할 수 있다.
 
 **트레이드오프**: 특수 해석 절차가 공통 흐름에 맞지 않는 경우 hook point가 필요하다. 초기에는 선형 정적 해석을 기준으로 최소 hook만 둔다.
 
@@ -69,15 +79,154 @@ FESA의 architecture decision은 solver correctness, verification traceability,
 **트레이드오프**: 초기 병렬화 범위가 제한된다. MKL 내부 thread와 TBB task arena의 oversubscription 정책을 별도로 문서화해야 한다.
 
 ### ADR-010: Abaqus reference artifact는 사람이 생성하거나 명시 승인된 절차로만 갱신한다
-**결정**: Agent는 Abaqus, Nastran 또는 reference solver를 직접 실행하지 않는다. reference artifact 생성, 수정, 복원은 명시 승인된 phase에서만 수행하고 provenance를 `metadata.json`에 기록한다.
+**상태**: Artifact read-only 및 실행 제한은 유지하며 metadata/provenance/naming 계약은 ADR-019로 대체됨.
+
+**결정**: Agent는 Abaqus, Nastran 또는 reference solver를 직접 실행하지 않는다. reference artifact 생성, 수정, 복원은 명시 승인된 phase에서만 수행한다. 모든 bundle의 provenance, generator/version, units, coordinate system, step/frame identity, schema, tolerance와 limitations는 승인된 기능별 Reference Model Contract에 기록한다. `metadata.json`은 선택 reference artifact이며, 부재만으로 bundle을 불완전하다고 판정하지 않는다. 파일이 존재하면 read-only 보조 자료로 inventory하고 계약 및 실제 artifact와 일치하는지 확인하며, 충돌은 숨기지 않고 upstream 계약 문제로 보고한다. 승인된 `cantilever-beam-b33` legacy baseline의 space-containing filename과 `README.md` N/A 예외는 유지한다.
 
 **이유**: reference 결과는 solver correctness의 기준이다. 생성 절차가 불명확하면 구현 결함과 reference artifact 오류를 구분할 수 없다.
 
-**트레이드오프**: reference 준비가 느려질 수 있다. 대신 검증 기준의 신뢰도와 감사 가능성이 높아진다.
+**트레이드오프**: Reference Model Contract가 필수 provenance의 단일 source of truth가 되어 별도 JSON 파일 없이도 bundle을 사용할 수 있다. 선택 `metadata.json`이 계약과 중복될 수 있으므로 존재 시 일관성 검사가 필요하다. Legacy filename과 `README.md` 예외는 일반 artifact 규칙을 복잡하게 하지만 exact path와 source commit을 고정하고 read-only로 취급해 감사 가능성을 유지한다.
 
-### ADR-011: C++ production 변경은 TDD guard와 workspace validation을 통과해야 한다
-**결정**: C++ production file 변경은 관련 C++ test file이 없으면 차단한다. 기본 검증은 `python -m unittest discover -s scripts -p "test_*.py"`와 `python scripts/validate_workspace.py`를 사용한다.
+### ADR-011: 구형 단일 검증 진입점 계약을 폐기한다
 
-**이유**: FEM solver 결함은 작은 부호, DOF ordering, integration rule 오류에서도 발생한다. 테스트 없는 변경을 막아야 reference validation 이전 단계에서 회귀를 줄일 수 있다.
+**상태**: ADR-012로 대체됨.
 
-**트레이드오프**: 초기 scaffolding 작업에서 guard가 엄격하게 느껴질 수 있다. 문서, CMake 설정, Harness metadata는 guard 대상에서 제외한다.
+**결정**: 삭제된 legacy validation entry point, legacy Python test discovery, 환경 변수 기반 command override를 Harness의 기본 검증 계약으로 사용하지 않는다.
+
+### ADR-012: Harness는 계획, 실행, Hook 검증의 세 계층으로 운영한다
+
+**결정**: 계획은 `.agents/skills/harness`, Step 실행과 Git 상태 관리는 `scripts/execute.py`, 도구 호출 전 정책과 종료 전 검증은 `.codex/hooks.json`에 연결된 `scripts/hooks/`가 담당한다. C++ production 변경은 관련 테스트 파일이 있어야 하며, 실제 RED 실패와 GREEN 성공은 같은 Step 안에서 확인한다. Stop은 `.harness/config.json` 또는 자동 감지 결과로 전체 MSVC build/test를 검증한다. Harness Python 변경은 `uv run --with pytest python -m pytest -v -rs`로 검증한다.
+
+**이유**: 테스트 파일 존재 검사, TDD 실행 증거, 전체 build/test는 서로 다른 책임이다. 이를 분리하면 Hook이 보장하는 범위를 과장하지 않으면서 Step 종료 시 green 상태를 강제할 수 있다.
+
+**트레이드오프**: PreToolUse만으로 구현 전 RED 실행을 증명할 수 없으므로 Implementation report에 RED/GREEN 명령과 결과를 기록해야 한다. C/C++가 없는 저장소는 Stop이 통과하므로 Harness Python 검증은 별도 acceptance command로 유지한다.
+
+### ADR-013: V0 선형 정적 해석은 단일 step B33 Euler beam으로 제한한다
+
+**결정**: 첫 end-to-end 제품 기능은 입력 파일당 하나의 `*STEP, *STATIC`을 해석하는 2절점 3D Euler–Bernoulli beam이다. Abaqus `TYPE=B33`만 이 요소로 매핑하고 B31은 `unsupported-element-formulation`으로 거부한다. `*PART/*ASSEMBLY/*INSTANCE`는 여러 identity instance와 stable source identity를 지원하지만 instance transform, nested assembly, 다중 step은 지원하지 않는다. Output-request keyword는 승인 allowlist에서 warning 후 no-op 처리하고 FESA 기본 HDF5 결과는 항상 생성한다.
+
+**이유**: B31은 transverse shear deformation을 포함하므로 Euler–Bernoulli 정식화와 의미가 다르다. 단일 step과 identity instance로 범위를 제한하면 parser wrapper, source identity, assembly, 해법 및 결과 복구를 end-to-end로 검증하면서 의미를 왜곡하지 않는다.
+
+**트레이드오프**: 기존 Abaqus 모델 중 B31, instance transform, 다중 step 또는 `*DLOAD`를 사용하는 입력은 거부된다. 이후 기능은 별도 요구조건과 formulation/reference gate를 거쳐 추가한다.
+
+### ADR-014: B33 cantilever baseline은 component-scale 혼합 tolerance로 비교한다
+
+**결정**: `reference/cantilever beam/`의 B33 input, displacement CSV, reaction CSV, elemental-force CSV를 V0 reference baseline으로 사용한다. Displacement와 reaction은 node identity로, section resultant는 CSV node station과 정규화된 FESA element endpoint로 비교한다. 같은 model, step/frame, quantity, component에 대해 `reference_scale = max(abs(reference rows))`를 계산하고 모든 row에 `absolute_floor + 1e-6 * reference_scale`을 적용한다. SI displacement/rotation absolute floor는 `1e-9`, force/moment floor는 `1e-3`이다. Beam stress는 출력하되 Abaqus stress reference comparison은 N/A다.
+
+**이유**: 자유단 moment처럼 이론적으로 0인 값에는 행별 상대오차가 정의되지 않으며 Abaqus 결과에 작은 수치 잔차가 남을 수 있다. Component scale을 사용하면 전체 물리량 크기에 비해 작은 잔차를 허용하면서 각 row를 결정적으로 판정할 수 있다.
+
+**트레이드오프**: 큰 component scale은 zero row의 허용폭을 넓힌다. 이를 완화하기 위해 quantity와 component를 섞지 않고 Abaqus 값만 scale에 사용하며, 모든 row의 absolute/normalized error와 worst row를 보고하고 누락·추가·nonfinite row를 tolerance 전에 실패시킨다.
+
+### ADR-015: 외부 CMake target을 FESA 경계로 정규화하고 Windows runtime closure를 명시한다
+
+**결정**: MKL, TBB, HDF5 CONFIG package가 제공하는 target은 dependency module에서
+`Fesa::MKL`, `Fesa::TBB`, `Fesa::HDF5`로 정규화한다. Product target은 이 경계만
+`PRIVATE` link하고 public header에 vendor/Win32 type을 노출하지 않는다. Approved Windows
+환경에서는 packaged shared HDF5 C target을 우선하며, CLI와 test executable 옆에 TBB,
+MKL, OpenMP, Intel math runtime, HDF5를 포함한 실제 runtime DLL closure를 POST_BUILD로
+stage한다.
+
+**이유**: Package version이나 shared/static variant에 따라 imported target 이름과 숨은
+runtime dependency가 달라질 수 있다. Configure와 link 성공만 확인하면 GoogleTest
+discovery 또는 배포된 CLI가 `0xc0000135`로 실패할 수 있다. FESA-owned target과 명시적
+runtime closure는 module code와 실행 환경을 package 세부사항에서 분리한다.
+
+**트레이드오프**: Windows staging CMake가 길어지고 새 dynamic dependency마다 runtime
+audit가 필요하다. 대신 개인 설치 경로를 source에 하드코딩하거나 developer `PATH`에
+의존하지 않고 build tree executable을 재현 가능하게 실행할 수 있다.
+
+### ADR-016: 결정론과 failure atomicity를 correctness contract로 취급한다
+
+**결정**: Parallel element 계산은 index별 독립 buffer만 쓰고, COO tuple ordering과
+floating-point sum은 join 이후 고정된 serial 순서로 수행한다. Result recovery, solver
+output, HDF5 writer는 candidate를 완성·검증한 뒤 caller-owned state 또는 final file에
+commit한다. HDF5는 same-directory temporary file을 checked close/reopen한 후에만 atomic
+finalization한다.
+
+**이유**: Reference comparison과 물리 검토는 row identity와 작은 수치 차이에 민감하다.
+Thread scheduling 또는 중간 실패가 sparse bytes, result order, 이전 output을 바꾸면 같은
+입력에 대한 evidence를 신뢰할 수 없다.
+
+**트레이드오프**: Serial reduction과 candidate copy가 throughput과 memory를 더 사용할 수
+있다. 성능 최적화는 동일한 ordering, failure preservation, reference 결과를 증명할 때만
+대체할 수 있으며, nondeterministic global sparse write는 허용하지 않는다.
+
+### ADR-017: Essential constraint는 stable elimination으로 적용하고 reaction은 full residual로 정의한다
+
+**결정**: V0는 DofManager의 stable free/constrained order로 full stiffness를
+`Kff/Kfc/Kcf/Kcc`로 분할하고 `Kff * df = Ff - Kfc * dc`를 푼 뒤 full displacement를
+복구한다. 모든 DOF가 constrained인 모델의 `0 x 0 Kff`는 유효한 trivial factorization과
+empty substitution이다. Recovery의 full residual `r = K*d - F`를 reaction vector로
+보존하며 constrained entry는 physical reaction, free entry는 equilibrium evidence다.
+
+**이유**: Equation numbering과 prescribed displacement를 한 owner가 관리하면 nonzero
+constraint, no/all/mixed constraint가 같은 수식과 stable order를 사용한다. Full residual은
+element end action을 별도로 합산하는 경로보다 조립·하중·해법 전체의 equilibrium을 직접
+검증한다.
+
+**트레이드오프**: Full K와 네 partition을 유지하는 메모리 비용이 있고 reaction vector의
+free entry가 정확한 0이라고 가정할 수 없다. V0에는 penalty, MPC, Lagrange multiplier를
+혼합하지 않으며, 추가 constraint policy는 별도 formulation과 equation/output 계약을
+요구한다.
+
+### ADR-018: Kernel 존재와 제품 노출을 분리하고 계층형 검증을 요구한다
+
+**결정**: Local element/load/recovery kernel이 존재해도 syntax, semantic Domain mapping,
+analysis orchestration, mandatory HDF5와 diagnostic 계약이 연결되지 않으면 CLI 지원으로
+간주하지 않는다. 검증은 unit, integration, reference comparison, physics sanity를 서로
+대체할 수 없는 계층으로 유지한다. Reference가 가능하지 않은 quantity는 명시적 N/A와
+analytical/schema/physics 대체 evidence를 요구한다.
+
+**이유**: Unit test는 수식과 validation을, integration test는 lifetime과 호출 순서를,
+reference comparison은 외부 solver와의 수치 일치를, physics sanity는 공통-mode 오류와
+model adequacy를 검출한다. 한 계층의 성공만으로 parser exposure 또는 물리 correctness를
+추론하면 지원 범위와 검증 강도가 과장된다.
+
+**트레이드오프**: 작은 기능도 여러 계약과 evidence를 함께 준비해야 하므로 개발 속도가
+느려진다. 대신 `*DLOAD`처럼 kernel은 있지만 입력에 노출되지 않은 기능, stress처럼
+mandatory output이지만 Abaqus reference가 N/A인 기능을 정확하게 표현할 수 있다.
+
+### ADR-019: Abaqus는 입력 형식과 외부 수치 reference이며 FESA 내부 동작 계약이 아니다
+
+**결정**: FESA는 Abaqus와 독립적인 솔버다. 기능별 승인 `.inp` subset을 입력으로
+사용하고, 기능이 blocking으로 선언한 FESA HDF5 quantity만 기존 Abaqus CSV와 승인
+tolerance로 비교한다. Abaqus 요소 정식화, 적분, stabilization, 내부 상태와 결과 생성
+절차를 재현하거나 동등하게 구현하지 않는다. Exact numerical equality는 허용되지만
+내부 동작 동등성의 evidence가 아니다.
+
+Reference case readiness에는 선언된 `.inp`, 실제 비교에 필요한 CSV, deterministic
+source-ID/component matching과 tolerance만 필요하다. 기존 path와 filename을 그대로
+사용하며 canonical naming, legacy-alias 승인, bundle `README.md`, `metadata.json`, Abaqus
+version/provenance, 중복 units/coordinates/model/step/frame/material/section 정보와 CSV schema
+version은 요구하지 않는다. Reference artifact는 계속 read-only이며 누락, 추가, 중복,
+nonfinite required row는 tolerance 전에 실패한다.
+
+**이유**: Reference comparison의 목적은 FESA의 독립 정식화가 승인된 observable quantity를
+충분히 가깝게 계산하는지 판정하는 것이다. 수치 비교에 사용되지 않는 artifact
+거버넌스가 formulation review나 implementation planning을 차단하면 제품 검증보다 문서
+형식 준수가 우선된다. 같은 정보는 `.inp`, CSV header와 feature contract에서 직접 얻을
+수 있다.
+
+**트레이드오프**: Reference 생성 환경을 사후에 완전히 재구성하는 감사 기능은 줄어든다.
+대신 비교 대상과 source-row/component mapping, tolerance, artifact immutability는 유지해
+false match와 결과 보정을 방지한다. 더 강한 provenance가 필요한 기능은 해당 요구조건이
+명시적으로 추가할 수 있으나 프로젝트 기본 gate로 자동 승격하지 않는다.
+
+### ADR-020: MITC4 displacement reference는 고정 절대오차로 판정한다
+
+**결정**: Full-integration FESA-MITC4의 sole S4 reference comparison은 matched global
+`U1/U2/U3` row에 고정 절대오차 `1.0e-5`를 적용해 pass/fail을 판정한다.
+`UR1/UR2/UR3`도 고정 절대오차 `1.0e-5`로 비교하지만 초과는 deterministic warning만
+생성한다. Reference scale은 보고용 통계로 남을 수 있으나 MITC4 row tolerance 또는
+normalized error의 분모를 결정하지 않는다. ADR-014의 B33 component-scale 혼합
+tolerance는 변경하지 않는다.
+
+**이유**: Abaqus S4는 FESA-MITC4와 동일한 요소 정식화가 아니므로 B33에서 승인한 매우
+엄격한 component-scale tolerance를 그대로 재사용하는 것은 독립 솔버의 observable
+displacement 검증 목적에 맞지 않는다. 고정 절대오차는 현재 사용자 단위계에서 승인된
+차이를 명시적으로 제한하면서 zero clamp나 row omission 없이 모든 displacement row를
+동일하게 판정한다.
+
+**트레이드오프**: Model scale이 크게 달라지면 고정 절대오차의 상대적 엄격도가 달라질 수
+있다. 따라서 이 값은 현재 승인된 MITC4 S4 case의 기능 완료 기준이며 개발 완료 후
+별도 reference-verification evidence와 함께 재점검한다.

docs/ARCHITECTURE.md

@@ -3,212 +3,289 @@
 ## 목표
 FESA의 아키텍처 목표는 Abaqus `.inp` subset을 내부 semantic model로 변환하고, 유한요소 equation system을 구성해 구조해석 결과를 HDF5로 저장하며, reference comparison과 physics sanity가 가능한 C++17/MSVC 솔버 구조를 제공하는 것이다.
 
+FESA의 element formulation과 numerical path는 Abaqus와 독립적이다. Abaqus `.inp`는
+승인된 입력 형식이고 Abaqus CSV는 기능별 blocking quantity의 외부 수치 reference다.
+Abaqus 내부 적분, stabilization, state 또는 recovery 동작은 FESA architecture contract가
+아니다.
+
 핵심 품질 속성:
 - FEM formulation traceability
 - explicit I/O contracts
 - sparse linear algebra backend isolation
 - deterministic verification
 - incremental feature addition
-- Harness 기반 TDD와 workspace validation
+- Harness 기반 TDD
 
-## 디렉토리 구조
+현재 승인된 V0 end-to-end 기능은 `linear-static-3d-euler-beam`이다. 상세 계약의
+source of truth는
+`docs/superpowers/specs/2026-08-08-linear-static-3d-euler-beam-design.md`이며, 이 문서는
+그 계약을 전체 solver architecture의 모듈과 데이터 흐름에 배치한다. 아래에 나타난
+비선형, 동적, thermal 및 다른 element 계층은 장기 확장 경계이며 V0 지원 범위가 아니다.
+
+## 현재 구현된 디렉토리 구조
 ```text
+include/fesa/               # backend-neutral public C++ API
 src/
   fesa/
-    core/                 # ids, status, diagnostics, units, small value types
+    analysis/             # Analysis lifecycle, V0 LinearStaticAnalysis
+    app/                  # CLI application and main
+    assembly/             # deterministic stiffness/load assembly, ParallelFor adapter
+    constraints/          # essential-constraint elimination and reconstruction
+    core/                 # source identity, status, diagnostics
+    elements/             # V0 EulerBeam3D kernel and recovery
+    fem/                  # DOF/equation numbering and sparse pattern
     io/
-      abaqus/             # .inp lexer/parser, keyword subset, include policy
-      hdf5/               # HDF5 result writer/reader, schema versioning
-    model/                # semantic model: nodes, elements, sets, materials, sections, steps
-    fem/                  # DOF space, equation numbering, quadrature, shape functions
-    elements/             # truss/bar, beam, plane, solid, shell element routines
-    materials/            # elastic/plastic material contracts and state variables
-    assembly/             # local-to-global mapping, sparse pattern, COO/CSR assembly
-    constraints/          # essential BC, MPC, penalty or elimination policies
+      abaqus/             # .inp syntax reader and semantic Domain mapper
+      hdf5/               # private HDF5 writer and atomic finalization
+    math/                 # owning Vector, row-major Matrix, 0-based CSR SparseMatrix
+    model/                # concrete V0 semantic records and immutable Domain
+    results/              # recovery records, full residual, ResultsWriter boundary
     solvers/
-      linear/             # MKL PARDISO backend, iterative backend boundary
-      nonlinear/          # Newton control, residual/tangent norms, increments
-    analysis/             # static, modal, dynamic, nonlinear procedure drivers
-    results/              # recovery, field/history output, diagnostics
-    validation/           # comparison metrics and tolerance helpers
+      linear/             # LinearSolver interface and MKL PARDISO adapter
 tests/
-  unit/
-  integration/
-  reference/
+  unit/                    # local contracts and failure paths
+  integration/             # analysis orchestration and CLI contracts
+  reference/               # HDF5-to-Abaqus projection and comparison
 reference/
-  <model-id>/
-    model.inp
-    metadata.json
-    <model-id>_displacements.csv
-    <model-id>_reactions.csv
-    <model-id>_internalforces.csv
-    <model-id>_stresses.csv
+  <case-dir>/              # declared read-only Abaqus input/required CSV pair
+.agents/
+  skills/                 # Harness and review skills
 .codex/
-  hooks/                  # Codex hook scripts
-  skills/                 # FESA solver and Harness instructions
+  hooks.json              # PreToolUse/Stop hook registration
+  agents/                 # FESA workflow custom agents
+  skills/                 # FESA solver workflow skills
 docs/                     # Product, architecture, ADR, workflow artifacts
 scripts/
   execute.py              # Phase step executor
-  validate_workspace.py   # Default validation entry point
-  test_*.py               # Harness self-tests
+  hooks/                   # PreToolUse/Stop hook implementations
+  msvc_harness/            # MSVC project discovery and validation adapters
 phases/                   # Optional generated phase plans
 ```
 
+`materials/`, nonlinear/dynamic analysis, MPC/penalty policies, general element factories,
+history output과 production validation module은 장기 확장 경계이지 현재 구현된 module이
+아니다. 새 디렉토리와 추상 계층은 승인된 기능이 실제로 필요로 할 때 추가한다.
+
 ## Harness Execution Layer
-`scripts/execute.py`:
-- creates or checks out `codex/<phase-name>`
-- refuses to run on a dirty worktree
-- requires per-step `allowed_paths`
-- stages only explicit allowed paths and runner housekeeping files
-- runs Python Harness self-tests and workspace validation before every runner-created commit
+
+Harness는 solver core와 분리된 세 계층의 개발 운영 인프라다.
+
+- 계획 계층: `.agents/skills/harness`가 사용자 승인 전 Step 초안을 만들고, 승인 후 `phases/` 파일을 생성한다.
+- 실행 계층: `scripts/execute.py`가 `feat-<phase-name>` 브랜치에서 Step마다 독립 Codex 세션을 실행하고 상태와 커밋을 관리한다.
+- 검증 계층: `.codex/hooks.json`이 `scripts/hooks/pre_tool_use.py`와 `scripts/hooks/stop_validation.py`를 연결한다. Stop 검증은 `scripts/msvc_harness/`를 통해 MSVC build와 test를 실행한다.
+
+Runner는 `git add -A`를 사용하므로 clean worktree 또는 별도 Git worktree가 실행 전제다. 전체 동작 계약은 `docs/HARNESS_WORKFLOW.md`, 설치와 `.harness/config.json` 설정은 `docs/HARNESS.md`를 source of truth로 삼는다.
+
+## CMake target과 dependency graph
+
+Root CMake project는 C++17, extension off, CMake 3.25 이상을 요구하고
+`cmake/FesaDependencies.cmake`, `src/fesa`, `tests`를 차례로 구성한다.
+
+```text
+MKL CONFIG package  ─> Fesa::MKL  ─┐
+TBB CONFIG package  ─> Fesa::TBB  ─┼─> fesa_solver (STATIC) ─> fesa_cli
+HDF5 CONFIG package ─> Fesa::HDF5 ─┘             │
+                                                  ├─> fesa_unit_tests
+approved local GoogleTest source ─> GTest targets ├─> fesa_integration_tests
+                                                  └─> fesa_reference_tests
+```
+
+- `FESA_GTEST_SOURCE_DIR`는 네트워크 fetch 대신 승인된 local GoogleTest source checkout을 가리키는 필수 cache path다.
+- MKL, TBB, HDF5는 CONFIG package로 탐지한다. Package search가 설치를 찾지 못하면 `MKL_DIR`, `TBB_DIR`, `HDF5_DIR`를 configure 때 지정한다.
+- Package별 imported target 이름은 `Fesa::MKL`, `Fesa::TBB`, `Fesa::HDF5`로 정규화한다. Product module은 vendor target 이름을 직접 선택하지 않는다.
+- HDF5 package가 shared와 static C target을 모두 제공하면 approved Windows environment에서는 shared target을 우선한다. Static archive의 숨은 compiler-runtime 요구가 link interface 밖으로 새는 것을 피하기 위한 결정이다.
+- `fesa_solver`는 외부 dependency를 `PRIVATE`으로 link하고 `/W4 /WX`를 사용한다. 따라서 public header는 MKL/TBB/HDF5/Win32 type을 포함하지 않아야 한다.
+- Test executable은 unit, integration, reference 경계를 분리하며 `fesa_tests` target은 세 executable을 build하는 aggregate target이다. Reference target에만 source/build root compile definition을 제공한다.
+
+### Windows runtime closure
+
+Configure 성공은 executable이 GoogleTest discovery 또는 CLI 실행 시 필요한 DLL을 찾는다는
+뜻이 아니다. `fesa_cli`와 세 test executable의 POST_BUILD 단계는 TBB, MKL thread/core/default
+dispatch, OpenMP, `libmmd.dll`, HDF5를 포함한 imported-target runtime DLL을 executable 옆에
+복사한다. 새 dynamic backend를 도입할 때는 link 성공뿐 아니라 clean environment에서의
+post-build discovery/실행까지 runtime closure로 다뤄야 한다. 개인 설치 absolute path를
+CMake source에 기록하지 말고 config package와 imported target metadata를 확장한다.
 
 ## 모듈 경계
 - `core`는 외부 라이브러리에 의존하지 않는다.
 - `io/abaqus`는 syntax와 semantic mapping만 담당하고 해석 알고리즘을 알지 않는다.
 - `model`은 Abaqus keyword 문자열이 아니라 solver semantic model을 가진다.
-- `fem`은 DOF, interpolation, quadrature, local/global mapping을 제공하되 특정 analysis procedure에 종속되지 않는다.
-- `elements`와 `materials`는 local residual/tangent/stress recovery 계약을 제공한다.
-- `assembly`는 sparse pattern 생성과 local contribution 조립을 담당한다.
-- `constraints`는 essential BC, MPC, penalty/elimination 정책을 분리한다.
-- `solvers`는 MKL/TBB 세부 구현을 감추는 backend boundary를 가진다.
+- `fem`의 `DofManager`는 DOF, equation ordering, scatter와 sparse pattern을 소유한다.
+- `elements`는 local/global stiffness, transformation, optional load kernel과 recovery를 제공한다. V0 material/section은 concrete Domain record다.
+- `assembly`는 element-local contribution과 full nodal load를 stable full-DOF space에 조립한다.
+- `constraints`는 V0 essential BC elimination과 full/reduced vector 변환을 담당한다. MPC와 penalty는 현재 범위가 아니다.
+- `solvers`는 `LinearSolver` 뒤에 MKL PARDISO 세부 구현을 감춘다. TBB는 `assembly/ParallelFor`, HDF5는 `results/ResultsWriter` 경계 뒤에 각각 격리된다.
 - `analysis`는 step/history data를 받아 procedure를 실행하고 solver backend와 result writer를 조율한다.
-- `results`는 HDF5 schema를 통해 nodal, element, integration-point, diagnostic output을 분리한다.
+- `results`는 full residual과 beam rows를 복구하고 backend-neutral writer contract를 제공한다. HDF5 schema 구현은 `io/hdf5`가 담당한다.
 - test helper는 production parser/solver 내부 상태를 우회하지 않는다.
 
+## V0 입력 경계
+
+V0 parser는 keyword와 parameter를 case-insensitive하게 해석하되 source label의 원문을
+보존한다. 지원하는 model/procedure keyword는 다음과 같다.
+
+- `*HEADING`
+- `*PART`, `*END PART`
+- `*NODE`
+- `*ELEMENT, TYPE=B33`
+- `*NSET`, `*ELSET`, including `GENERATE`
+- `*MATERIAL`, `*ELASTIC`
+- `*BEAM GENERAL SECTION, SECTION=GENERAL`
+- `*SECTION POINTS`
+- `*ASSEMBLY`, `*END ASSEMBLY`
+- `*INSTANCE`, `*END INSTANCE`
+- `*BOUNDARY`, `*CLOAD`
+- `*STEP`, `*STATIC`, `*END STEP`
+
+Part 내부 label은 `SourceEntityId { instance_name, source_label }`로 보존하고 Domain은
+별도 stable internal index를 부여한다. 같은 part의 여러 identity instance는 허용하지만
+translation/rotation data와 nested assembly는 구조화된 unsupported diagnostic으로
+거부한다. 입력 파일당 하나의 static step만 허용하고 두 번째 step은 오류다.
+
+`*PREPRINT`, `*RESTART`, `*TRANSVERSE SHEAR STIFFNESS`, `*OUTPUT, FIELD`,
+`*OUTPUT, HISTORY`, `*NODE OUTPUT`, `*ELEMENT OUTPUT`, `*CONTACT OUTPUT` 및 그에 속한
+미지원 output variable data는 warning 후 no-op 처리한다. 이 allowlist 밖의 미지원
+model-affecting keyword는 오류다. FESA output은 Abaqus output request에 좌우되지 않는다.
+
+## V0 beam과 section 계약
+
+`EulerBeam3D`는 2절점과 절점당 `[UX, UY, UZ, URX, URY, URZ]` 6 DOF를 사용하며 축,
+두 방향 Euler–Bernoulli 굽힘과 Saint-Venant 비틀림을 제공한다. Beam tangent를 local
+`x`, Abaqus first section axis `n1`을 local `y`, `t x n1`을 local `z`로 둔다.
+`*BEAM GENERAL SECTION`의 `A, I11, I12, I22, J`는 `Iy=I11`, `Iz=I22`로 매핑하고
+V0는 `I12=0`만 허용한다. `E`, `G`, `A`, `Iy`, `Iz`, `J`는 양수여야 하며 zero-length
+element와 tangent에 평행한 guide vector를 scale-aware tolerance로 거부한다.
+
+요소 API는 stiffness, transformation, load와 recovery 책임을 분리한다.
+
+```cpp
+Matrix localStiffness() const;
+Matrix globalStiffness() const;
+Vector localEquivalentLoad(const ConstantLocalLineLoad& load) const;
+BeamRecovery recover(const Vector& globalElementDisplacement) const;
+```
+
+`localEquivalentLoad`는 formulation의 constant local line-load kernel을 unit test하기
+위한 계약이다. V0 parser는 `*DLOAD`나 distributed-load Domain object를 생성하지 않으므로
+CLI pipeline에서는 이 kernel을 호출하지 않는다. Stiffness와 recovery는 formulation의
+2점 Gauss rule과 부호 규약을 따른다.
+
 ## 핵심 객체 모델
+
 ```text
 Domain
-├── Node
-├── Element
-├── Material
-├── Property
-├── NodeSet
-├── ElementSet
-├── BoundaryCondition
-├── Load
-└── StepDefinition
+├── owns nodes, B33 elements, materials, beam sections, sets
+├── owns boundary conditions, nodal loads, one static step
+└── owns source path/identity and mapping warnings
 
 AnalysisModel
-├── active elements
-├── active loads
-├── active boundary conditions
-├── active properties/materials
-└── equation system view
+├── non-owning view into Domain
+├── stable active element/BC/load indices
+└── reachable material/section indices
+
+DofManager
+├── owns node x [UX,UY,UZ,URX,URY,URZ] full-DOF numbering
+├── owns stable free/constrained order and prescribed values
+├── owns element scatter maps
+└── owns full-space CSR structural pattern
 
 AnalysisState
 ├── displacement U
-├── velocity V
-├── acceleration A
-├── temperature T
 ├── external force Fext
 ├── internal force Fint
-├── residual R
-├── current time / increment / iteration
-└── element state / integration point state
-
-DofManager
-├── node dof definitions
-├── constrained/free dof mapping
-├── equation numbering
-├── sparse matrix pattern ownership
-└── full/reduced vector reconstruction
+├── residual R and full-index reaction
+├── StepFrameIdentity
+└── endpoint, Gauss and S11 recovery rows
 
 Analysis
-├── LinearStaticAnalysis
-├── NonlinearStaticAnalysis
-├── DynamicAnalysis
-├── FrequencyAnalysis
-└── HeatTransferAnalysis
+└── LinearStaticAnalysis
 
-Element
-├── Element1D
-│   ├── Truss
-│   └── Beam
-├── Element2D
-│   ├── MITC3
-│   └── MITC4
-└── Element3D
-    ├── Hexahedral
-    ├── Tetrahedral
-    ├── Wedge
-    └── Pyramid
-
-BoundaryCondition
-├── Fix
-├── RBE2
-└── RBE3
-
-Load
-├── NodalLoad
-├── PressureLoad
-└── BodyForce
-
-Results
-├── ResultStep
-├── ResultFrame
-├── FieldOutput
-└── HistoryOutput
+Vector
+Matrix
+SparseMatrix
 ```
 
+Nonlinear/static, dynamic, frequency, heat-transfer procedure와 general element/material/load
+base hierarchy는 이 구조 위의 가능한 확장 방향일 뿐 현재 public API가 아니다. 사용 사례가
+승인되기 전에 V0 concrete record를 speculative hierarchy로 감싸지 않는다.
+
 ## 상태 관리
 - `Domain`은 입력 파일에서 만들어진 전체 모델 정의를 소유한다. 파싱 이후에는 가능한 한 불변으로 취급한다.
-- `AnalysisModel`은 현재 step에서 활성화되는 해석 객체들의 실행 view이다. `Domain`을 복사하지 않고 참조 또는 id 기반 view로 구성한다.
+- `LinearStaticAnalysis`가 `Domain`을 소유하고, 그 뒤에 `AnalysisModel`, `DofManager`, `AnalysisState`, stiffness/RHS를 순서대로 만든다. 재사용 시에는 역순으로 해제하여 이전 Domain을 가리키는 view를 남기지 않는다.
+- `AnalysisModel`은 현재 step에서 활성화되는 해석 객체들의 실행 view이다. `Domain`을 복사하지 않으므로 Domain이 반드시 더 오래 살아야 한다.
 - `DofManager`는 자유도와 방정식 번호를 전담한다. `Node` 또는 `Element` 내부에 equation id를 분산 저장하지 않는다.
-- `AnalysisState`는 해석 중 변하는 물리량과 반복 상태를 소유한다. Phase 1에서는 displacement 중심으로 최소 구현하되, 기하비선형과 thermal-stress coupling을 위해 element/internal state 확장 지점을 유지한다.
-- 결과는 `ResultStep` -> `ResultFrame` -> `FieldOutput`/`HistoryOutput` 구조로 관리한다.
+- `AnalysisState`는 V0 frame에 필요한 다섯 full-DOF vector와 recovery rows만 소유한다. Velocity, acceleration, temperature, iteration history, nonlinear element state는 해당 procedure가 승인될 때 별도 계약으로 추가한다.
+- Result recovery는 모든 candidate vector/row를 검증한 뒤 state에 반영한다. 실패한 recovery가 앞선 유효 state를 부분적으로 덮어쓰지 않아야 한다.
 
 ## 데이터 흐름
 ```text
 Abaqus input file
--> InputParser
--> Domain 생성
--> StepDefinition 루프
--> AnalysisModel 생성
--> DofManager로 자유도/방정식 번호 생성
--> sparse pattern 생성
--> Analysis 실행
--> Assembler로 전역 행렬/벡터 조립
--> BoundaryCondition 적용
--> LinearSolver 또는 nonlinear/time integration loop
--> AnalysisState 갱신
--> ResultsWriter로 step/frame/history 저장
--> 다음 step 진행
+-> syntax parse and semantic mapping
+-> immutable Domain 생성
+-> 단일 step AnalysisModel view 생성
+-> DofManager DOF/scatter map/sparse pattern 생성
+-> element stiffness 계산과 deterministic COO-to-CSR 조립
+-> free/constrained partition 생성
+-> LinearSolver::factorize(Kff)
+-> full nodal load vector 조립
+-> effective RHS = Ff - Kfc * dc
+-> LinearSolver::solve(rhs, df) substitution
+-> full displacement 복구
+-> full residual/reaction = K*d - F 및 element result 복구
+-> ResultsWriter로 results.h5 atomic finalization
 ```
 
+강성행렬 factorization은 하중벡터 조립보다 먼저 수행한다. 반력은 element end action의
+별도 합이 아니라 조립된 전체 residual에서 구한다. Constrained component는 physical
+reaction이고 free component는 equilibrium residual evidence로 full-index vector에 남긴다.
+
 ## 해석 실행 흐름
-`Analysis::run()`은 Template Method로 다음 큰 흐름을 고정한다. 해석 종류별 class는 필요한 단계만 재정의한다.
+`Analysis::run()`은 Template Method로 다음 여덟 hook의 순서와 fail-fast 경계를 고정한다.
 
-```text
-initialize
-buildAnalysisModel
-buildDofMap
-buildSparsePattern
-assemble
-applyBoundaryConditions
-solve
-updateState
-writeResults
-```
+| 순서 | Hook | 주요 작업과 생성되는 소유 객체 | 순서/실패 불변식 |
+| --- | --- | --- | --- |
+| 1 | `initialize(request)` | `.inp` syntax read, semantic map, owned immutable `Domain`, sorted warnings | 이전 run의 dependent object를 역순으로 제거하고 parse/map 실패를 input category로 반환한다. |
+| 2 | `buildAnalysisModel()` | non-owning `AnalysisModel` view | Domain을 복사하지 않으며 Domain lifetime 안에서만 사용한다. |
+| 3 | `buildDofMapAndSparsePattern()` | `DofManager`, zero-initialized `AnalysisState` | Stable full/free/constrained numbering과 structural pattern을 한 소유자에게 둔다. |
+| 4 | `assembleAndPartitionStiffness()` | full CSR K와 `Kff/Kfc/Kcf/Kcc` | Element-local buffer를 deterministic하게 reduce하고 structural zero와 stable order를 보존한다. |
+| 5 | `factorize()` | retained `Kff` factorization | 모든 load assembly보다 먼저 호출한다. Valid fully constrained model의 `0 x 0 Kff`는 trivial success다. |
+| 6 | `assembleLoadsAndEffectiveRhs()` | full F와 `Ff-Kfc*dc` | Semantic load source order와 finite sum을 보존하며 solver를 호출하지 않는다. |
+| 7 | `substituteAndReconstruct()` | free solution과 full displacement | Factorization을 재수행하지 않고 substitution한 뒤 prescribed value를 stable order로 복구한다. |
+| 8 | `recoverAndWriteResults()` | full residual/reaction, beam rows, final HDF5 | Recovery candidate를 원자적으로 commit하고 writer 성공 뒤에만 최종 output을 교체한다. |
 
-비선형 정적해석은 이 흐름을 Newton-Raphson 반복 루프 안에서 사용하고, 동적해석은 time step/frame 루프 안에서 사용한다.
+비선형 정적 및 동적 해석은 V0 범위가 아니며 별도 ADR과 formulation을 승인한 뒤 이
+lifecycle과 state/equation 계약을 확장한다. 기존 hook 사이에 조용히 반복·증분·시간 적분
+동작을 삽입하지 않는다.
 
 ## 설계 패턴
-- Strategy Pattern: `Analysis`, `LinearSolver`, `TimeIntegrator`, `ConvergenceCriteria`를 교체 가능한 전략으로 둔다.
+- Strategy/Adapter Pattern: 현재 교체 가능한 public 경계는 `LinearSolver`, `ParallelFor`, `ResultsWriter`다. Vendor API는 concrete adapter implementation 안에만 둔다.
 - Template Method Pattern: `Analysis::run()`은 공통 실행 흐름을 고정하고 세부 단계는 procedure별로 재정의한다.
-- Factory + Registry Pattern: Abaqus keyword와 내부 객체 생성을 분리한다. 예: `*Element, type=S4` -> `MITC4ElementFactory`.
-- Adapter Pattern: MKL, TBB, HDF5 API는 solver core에 직접 노출하지 않는다.
-- Runtime Polymorphism: 요소, 재료, 하중, 경계조건은 base interface를 통해 다룬다. 대규모 모델 성능 최적화가 필요하면 assembly 내부에서 타입별 batch 처리 또는 kernel 분리를 추가한다.
+- Syntax/Semantic separation: `AbaqusInputReader`는 syntax record를 만들고 `AbaqusDomainMapper`가 승인된 keyword 의미를 concrete Domain record로 변환한다.
+- Runtime Polymorphism: V0에서는 backend 경계에만 사용한다. 요소/재료/하중 base hierarchy와 factory/registry는 두 번째 실제 구현이 필요해질 때 trade-off를 다시 결정한다.
 - RAII: MKL handle, HDF5 file/dataset, temporary solver workspace의 수명과 오류 처리를 wrapper에 묶는다.
 
 ## Sparse Matrix Policy
-- assembly는 초기에는 COO triplet 수집 후 CSR finalize를 기준으로 한다.
-- `SparseMatrix`는 solver core가 사용하는 추상 contract이고 MKL PARDISO backend는 CSR input contract만 받는다.
-- matrix symmetry, definiteness, singularity diagnostic을 구조화된 diagnostic으로 남긴다.
-- deterministic assembly를 위해 TBB element loop는 thread-local contribution buffer 또는 two-pass sparse assembly를 사용한다.
+- Assembly는 element마다 index-addressed contribution buffer를 만들고, join 뒤 COO tuple을 stable order로 정렬해 한 thread에서 순서대로 합산한 후 CSR로 finalize한다.
+- `SparseMatrix`는 0-based CSR 데이터를 소유하는 별도 타입이며 dense `Matrix`를
+  상속하지 않는다. MKL PARDISO backend는 adapter 경계에서 필요한 descriptor와 indexing을
+  변환한다.
+- CSR row offset, sorted-unique column, dimensions, finite values를 construction boundary에서 검증하며 structural zero를 삭제하지 않는다.
+- Parallel worker는 global sparse matrix나 shared reduction accumulator를 직접 갱신하지 않는다. Worker별 failure slot과 contribution만 쓰고, deterministic reduction은 join 뒤에 수행한다.
+- Matrix symmetry와 factorization/substitution failure는 solver adapter가 구조화된 solver diagnostic으로 번역한다. 승인되지 않은 regularization이나 fallback으로 singularity를 숨기지 않는다.
+
+## Dense Math Policy
+
+- `Vector`는 contiguous `double` 데이터와 크기를 소유하고 copy, dot, Euclidean norm,
+  scale, axpy를 MKL CBLAS adapter로 수행한다.
+- `Matrix`는 row-major contiguous `double` 데이터와 dimensions를 소유하고
+  matrix-vector 및 matrix-matrix 연산에 `CBLAS_ROW_MAJOR`를 사용한다.
+- 두 타입은 copy/move semantics와 bounds-checked access를 제공한다.
+- MKL header와 MKL-specific type은 adapter implementation 밖으로 노출하지 않는다.
 
 ## Parallel Policy
-- 첫 번째 oneTBB 적용 지점은 element-local matrix/residual 계산이다.
-- 전역 sparse write는 thread-local buffer 또는 deterministic reduction으로 제한한다.
+- `ParallelFor`는 `[0,count)` index-addressed 독립 작업만 노출하며 `SerialParallelFor`와 `TbbParallelFor`가 같은 observable contract를 가진다.
+- 첫 oneTBB 적용 지점은 element-local stiffness 계산이다. 각 callback은 자기 index의 output slot만 쓴다.
+- 전역 sparse write와 부동소수 reduction은 parallel callback 밖의 deterministic 단계로 제한한다.
 - MKL 내부 thread와 TBB element loop가 oversubscription을 만들지 않도록 thread count와 task arena 정책을 명시한다.
 
 ## HDF5 Result Schema
@@ -216,10 +293,12 @@ writeResults
 /metadata
 /model/nodes
 /model/elements
-/steps/<step-name>/frames/<frame-id>/nodal/displacement
-/steps/<step-name>/frames/<frame-id>/nodal/reaction
-/steps/<step-name>/frames/<frame-id>/element/stress
-/steps/<step-name>/frames/<frame-id>/element/strain
+/steps/<step-name>/frames/0/nodal/displacement
+/steps/<step-name>/frames/0/nodal/reaction
+/steps/<step-name>/frames/0/element/end_force_local
+/steps/<step-name>/frames/0/element/section_resultant
+/steps/<step-name>/frames/0/element/generalized_strain
+/steps/<step-name>/frames/0/element/stress_s11
 /diagnostics
 ```
 
@@ -228,44 +307,77 @@ Schema requirements:
 - field output과 history output을 구분한다.
 - reference comparison을 위한 row identity는 node id, element id, integration point id, step/frame id를 포함한다.
 - FESA solver는 `results.h5`를 authoritative output으로 쓴다.
-- Abaqus reference results는 `reference/<model-id>/` 아래 CSV 파일이다.
-- Verification은 documented IDs, components, units, coordinate system, step/frame identity, tolerance 기준으로 FESA HDF5 rows와 Abaqus reference CSV rows를 비교한다.
+- Abaqus reference results는 기능 문서가 선언한 기존 CSV 파일이다. Directory/file
+  naming, README, metadata 또는 provenance는 architecture readiness 조건이 아니다.
+- Verification은 기능이 요구하는 source identity와 component를 결정적으로 대응시키고
+  승인 tolerance를 적용한다. Missing/extra/duplicate/nonfinite required row는 숫자 비교
+  전에 실패한다. 단일 step/final-frame 기능은 별도 CSV step/frame 열을 요구하지 않는다.
 - FESA HDF5에서 추출한 deterministic CSV view는 optional debugging/review artifact이며 공식 solver output 또는 reference artifact가 아니다.
+- Writer는 final과 같은 directory의 임시 HDF5에 전체 schema를 쓴 뒤 flush, checked close,
+  read-only reopen/self-check를 수행한다. Existing final은 `ReplaceFileW`, 새 final은
+  `MoveFileExW(..., MOVEFILE_WRITE_THROUGH)`로 완료하며 실패 시 temporary artifact를
+  정리하고 불완전한 파일을 정상 `results.h5`로 노출하지 않는다.
 
-## Test Architecture
-- unit: parser, DOF map, shape functions, material law, sparse assembly, HDF5 schema
-- integration: small `.inp` to HDF5 end-to-end
-- reference: FESA `results.h5` rows and Abaqus reference CSV rows comparison
-- physics: equilibrium, sign, symmetry, rigid body mode, stress sanity
-- harness: hooks, phase executor, workspace validation
+## V0 결과 복구와 reference normalization
 
-## Hook 흐름
-```text
-apply_patch/Edit/Write
--> .codex/hooks/tdd-guard.py
--> C++ production changes require related tests
+- Nodal displacement와 reaction은 global `[UX, UY, UZ, URX, URY, URZ]` 순서다.
+- Equilibrium end action은 local `[FX,FY,FZ,MX,MY,MZ]`, endpoint section resultant는
+  `[N,T,My,Mz]`, generalized strain/resultant는 두 Gauss point에 기록한다.
+- General beam section stress는 section point의 axial `S11`만 복구한다. Section point가
+  없으면 centroid `(0,0)`을 `source=fesa-default`로 기록한다.
+- 승인된 `reference/cantilever beam/cantilever beam elemental forces.csv`는 node station
+  기준 `SF1/SM1/SM2/SM3`을 제공한다. FESA endpoint를 동일한 section-cut 부호로
+  정규화하고 interior node의 두 endpoint가 tolerance 안에서 일치하는지 먼저 확인한 뒤
+  `SF1 -> N`, `SM1 -> My`, `SM2 -> Mz`, `SM3 -> T`로 비교한다.
+- Reference tolerance는 같은 model, step/frame, quantity, component의 Abaqus rows에서
+  `reference_scale = max(abs(reference_value))`를 구하고 각 row에
+  `absolute_floor + 1e-6 * reference_scale`을 적용한다. SI displacement/rotation floor는
+  `1e-9`, force/moment floor는 `1e-3`이다.
+- Beam stress는 HDF5 schema와 unit/analytical test로 검증하지만 Abaqus reference
+  comparison은 N/A다.
 
-git commit command
--> .codex/hooks/pre_commit_checks.py
--> Python Harness self-tests
--> scripts/validate_workspace.py
+## CLI와 diagnostics
+
+```powershell
+fesa.exe <model.inp> --output <results.h5>
 ```
 
-## Validation 흐름
-```text
-HARNESS_VALIDATION_COMMANDS set
--> run exact commands
+`--output`을 생략하면 현재 작업 디렉터리의 `results.h5`를 사용한다. Exit code는
+`0=success`, `2=usage`, `3=input syntax/semantic mapping`, `4=model validation`,
+`5=factorization/substitution`, `6=HDF5 output`으로 고정한다. Diagnostic은 `severity`,
+`code`, `file`, `line`, `keyword`, `entity_identity`, `message`를 가지며 stderr에
+deterministic한 순서로 출력한다.
 
-CMakePresets.json has msvc-debug configure preset
--> cmake --preset msvc-debug
--> cmake --build preset binary dir --config Debug
--> ctest --test-dir preset binary dir -C Debug
+## 기능 확장 플레이북
 
-CMakeLists.txt exists
--> cmake -S . -B build/msvc-debug -G "Visual Studio 17 2022" -A x64
--> cmake --build build/msvc-debug --config Debug
--> ctest --test-dir build/msvc-debug --output-on-failure -C Debug
+다음 표는 코드 위치만이 아니라 함께 바뀌어야 하는 계약 경계를 나타낸다. 한 열만
+구현하고 다른 열을 생략하면 internal utility 또는 실험 kernel일 수는 있어도 제품 기능은
+아니다.
 
-No CMake project
--> print guidance and exit successfully
-```
+| 기능 유형 | 시작 전에 고정할 것 | 주요 구현 경계 | 함께 검증할 것 | 피해야 할 shortcut |
+| --- | --- | --- | --- | --- |
+| 새 element/material | DOF, interpolation, constitutive law, integration, local axes/sign, feature-approved validity boundary | Domain record와 mapper, element kernel, DofManager scatter/pattern, SparseAssembler, ResultRecovery | feature-required invariants/tests and blocking reference quantities | 서로 다른 물리를 같다고 주장, source ID와 internal index 혼용, 검증 전 범용 hierarchy 추가 |
+| 새 load/constraint | Abaqus target grammar, application order, units, follower 여부, prescribed-value 의미 | Syntax/mapper, Domain target, full-space LoadAssembler 또는 constraint partition, diagnostics | set/direct target ambiguity, multi-instance identity, nonfinite sum, `Ff-Kfc*dc`, reaction | Element load kernel 존재를 parser 지원으로 간주, penalty를 elimination에 몰래 혼합 |
+| 새 analysis procedure | governing equation, state variables, increment/time lifecycle, tangent/residual, convergence와 output frame | 별도 Analysis implementation, procedure-specific state/equation owner, solver interface extension | orchestration order, failure atomicity, restart/frame identity, numerical benchmark | V0 hook 사이에 조건문으로 반복/시간 적분 삽입, 사용하지 않는 future state 선할당 |
+| 새 numerical backend | matrix/index contract, lifecycle, reusable state, failure taxonomy, thread/runtime policy | 기존 `LinearSolver` 또는 `ParallelFor` interface의 concrete adapter, CMake normalized target | empty/dimension/extreme-scale input, repeated call, failed-output preservation, clean runtime discovery | Vendor type을 public header에 노출, silent fallback/regularization, absolute install path 고정 |
+| 새 output/reference quantity | 물리 정의, location, sign, units, coordinates, stable row identity, mandatory 여부, tolerance | Result record/recovery, AnalysisState, ResultsWriter/HDF5 schema, comparator projection | schema dtype/shape, ordering, nonfinite rejection, identity inventory, reference N/A 대체 evidence | 서로 다른 result identity 혼합, station mismatch 평균, output request로 mandatory result 제거 |
+
+모든 확장은 PRD의 제품 완료 정의와 요구조건→정식화→I/O→구현→reference→physics gate를
+따른다. 기존 feature contract에 없는 범위를 편의상 “Abaqus compatible”이라고 넓히지 않는다.
+
+## MITC4 확장 경계
+
+MITC4가 구현될 때 Abaqus `S4`와 `S4R` source type은 같은 FESA formulation을 선택한다.
+Source type은 metadata/diagnostic identity로 보존하지만 FESA integration 또는 hourglass
+경로를 선택하지 않는다. 6-DOF embedding의 비물리 drilling coordinate에는 physical
+rotational stiffness block의 positive minimum diagonal에 `1e-3`을 곱한 고정 numerical
+stabilization만 둔다. Drilling calibration, artificial-energy policy와 별도 drilling result
+dataset은 이 기능 범위가 아니다.
+
+Full-integration FESA-MITC4의 reference comparison은 `reference/shell/` S4의 기존 input 및
+displacement CSV만 사용한다. Global `U1/U2/U3`만 blocking이고 모든 matched row에 고정
+절대오차 `1.0e-5`를 적용한다. `UR1/UR2/UR3`도 고정 절대오차 `1.0e-5`로 비교하되
+warning-only evidence다. MITC4 판정에는 component scale을 사용하지 않으며 B33의 기존
+혼합 tolerance는 변경하지 않는다. S4R은
+같은 kernel을 선택하는 source mapping과 metadata를 unit/integration tests로 검증하며
+`reference/shellR/` artifact는 acceptance comparison에 포함하지 않는다.

docs/HARNESS.md

@@ -0,0 +1,139 @@
+# Harness 운영 가이드
+
+## Requirements
+
+Windows, Python 3.10 이상, Codex CLI가 필요하다. CMake 프로젝트에는 Visual Studio의
+Desktop development with C++ 워크로드와 MSBuild, CMake/CTest를 설치한다.
+
+## 프로젝트 자동 감지
+
+프로젝트 형식은 다음 순서로 결정한다: `.harness/config.json`의 명시적 type, 루트의
+CMake metadata, 하나의 `.sln`, 하나의 `.vcxproj` 순서다. C/C++가 아닌 저장소는
+건너뛰며, C/C++ 파일은 있지만 CMake/solution metadata가 없는 orphan-C++ 저장소는
+오류로 처리한다.
+
+설정 파일은 선택 사항이다. 기본 자동 감지와 `.harness/build` 경로를 그대로 사용할
+때는 만들지 않아도 된다. 프로젝트별 override가 필요하면 다음처럼 예시를 복사한다.
+
+```powershell
+Copy-Item .harness/config.example.json .harness/config.json
+```
+
+계획을 승인해 phase 파일을 만든 뒤 Executor를 실행한다.
+
+```powershell
+python scripts/execute.py <phase-name>
+python scripts/execute.py <phase-name> --push
+```
+
+Executor가 시작하는 Codex 세션은 기본적으로 `workspace-write` sandbox를 사용한다.
+Windows native sandbox에서 MSVC compiler-id의 `cl.exe`가 정지하는 것이 재현되고 같은
+명령이 sandbox 밖에서 정상 완료되는 경우에만, 사용자 승인을 받은 격리된 clean
+worktree에서 다음처럼 해당 실행에 한정해 fallback을 지정할 수 있다.
+
+```powershell
+$env:FESA_HARNESS_CODEX_SANDBOX = "danger-full-access"
+python scripts/execute.py <phase-name>
+Remove-Item Env:FESA_HARNESS_CODEX_SANDBOX
+```
+
+허용값은 `workspace-write`와 `danger-full-access`뿐이다. 후자는 Codex Step에 workspace
+밖의 파일 접근 권한도 부여하므로 일반 기본값으로 설정하지 않는다. 어느 모드에서도
+`.codex/hooks.json`의 PreToolUse와 Stop hook은 자동으로 실행된다.
+
+## Harness Python 검증
+
+이 저장소의 테스트와 최종 acceptance 검증은 pytest를 시스템 Python에 설치하지 않고
+다음 명령으로 실행한다.
+
+```powershell
+uv run --with pytest python -m pytest -v -rs
+```
+
+## CMake preset 설정
+
+`projectType`을 `cmake`로 지정하거나 자동 감지를 사용한다. `cmake.sourceDir`,
+`binaryDir`, `configurePreset`, `buildPreset`, `testPreset`은 preset을 사용할 때 함께
+지정해야 한다. 빌드 산출물은 저장소의 `.harness/build/`처럼 격리된 경로에 둔다.
+
+```json
+{
+  "version": 1,
+  "projectType": "cmake",
+  "cmake": {
+    "sourceDir": ".",
+    "binaryDir": "out/build/windows-debug",
+    "configurePreset": "windows-debug",
+    "buildPreset": "windows-debug",
+    "testPreset": "windows-debug"
+  }
+}
+```
+
+```powershell
+cmake --preset windows-debug
+cmake --build --preset windows-debug
+ctest --preset windows-debug --output-on-failure
+```
+
+Preset을 쓰지 않는 경우에는 같은 격리된 build directory를 명시한다.
+
+```powershell
+cmake -S . -B .harness/build -A x64
+cmake --build .harness/build --config Debug
+ctest --test-dir .harness/build -C Debug --show-only=json-v1
+ctest --test-dir .harness/build -C Debug --output-on-failure
+```
+
+## 직접 MSBuild 설정
+
+`projectType`을 `msbuild`로 설정하면 `msbuild.solution`, `configuration`, `platform`을
+지정한다. 직접 MSBuild 프로젝트에서는 `msbuild.testCommand`가 필수이며, 테스트 실행
+파일과 인수를 JSON 배열로 적는다.
+
+```json
+{
+  "version": 1,
+  "projectType": "msbuild",
+  "msbuild": {
+    "solution": "MyProject.sln",
+    "configuration": "Debug",
+    "platform": "x64",
+    "testCommand": ["build/tests/Debug/MyProjectTests.exe"]
+  }
+}
+```
+
+```powershell
+MSBuild.exe MyProject.sln /m /p:Configuration=Debug /p:Platform=x64
+.\build\tests\Debug\MyProjectTests.exe
+```
+
+## TDD 확장
+
+`tdd.testRoots`와 `tdd.testPatterns`로 테스트 위치와 이름을 확장한다. 패턴마다
+`{stem}`이 필요하다. `main`, 테스트, 외부 의존성, 생성 파일, build directory 같은
+기본 제외 항목은 Harness가 관리하며, `tdd.exclude`의 사용자 제외 항목은 이를
+대체하지 않고 추가한다.
+
+```json
+{
+  "version": 1,
+  "tdd": {
+    "testRoots": ["tests", "integration-tests"],
+    "testPatterns": ["{stem}_test.cpp", "test_{stem}.cpp"],
+    "exclude": ["legacy/generated/**"]
+  }
+}
+```
+
+## 실패 복구
+
+- Visual Studio C++ workload가 없으면 Installer에서 Desktop development with C++를 설치한 뒤 다시 실행한다.
+- solution 또는 project가 여러 개라서 모호하면 `projectType`과 `msbuild.solution`을 명시한다.
+- MSVC가 아닌 컴파일러가 감지되면 MSVC Developer Command Prompt에서 실행하거나 toolchain을 MSVC로 전환한다.
+- CTest가 0개 테스트를 보고하면 `enable_testing()`과 테스트 등록을 확인한다.
+- 직접 MSBuild 구성에 test command가 없으면 `msbuild.testCommand` 배열을 추가한다.
+- timeout 또는 명령 실패 시 Stop 응답의 stage, 안전한 argv 배열, 작업 디렉터리,
+  종료 코드와 출력 tail을 확인하고 해당 명령을 단독으로 다시 실행한다. Harness는
+  별도의 로그 파일을 만들지 않는다.

docs/HARNESS_WORKFLOW.md

@@ -0,0 +1,614 @@
+# Harness Framework 동작 과정
+
+이 문서는 자연어 요구사항을 받은 뒤 Harness Framework가 계획을 만들고, 독립된
+Codex 세션에서 Step을 실행하고, MSVC로 C++ 프로젝트를 검증하는 전체 과정을
+설명한다. 설치 및 설정 예시는 [Harness 운영 가이드](HARNESS.md)를 참고한다.
+
+## 1. 핵심 구조
+
+Harness Framework는 다음 세 계층으로 구성된다.
+
+1. **계획 계층**: 요구사항을 분석하고 사용자가 승인할 실행 가능한 Step으로 변환한다.
+2. **실행 계층**: Step Executor가 Step마다 독립 Codex 세션을 실행하고 상태와 Git
+   커밋을 관리한다.
+3. **검증 계층**: PreToolUse 훅이 편집 전 정책을 검사하고, Stop 훅이 종료 전 MSVC
+   빌드와 테스트를 실행한다.
+
+전체 흐름은 다음과 같다.
+
+```text
+사용자 요구사항
+    ↓
+프로젝트 탐색 및 요구사항 논의
+    ↓
+Step 초안 작성
+    ↓
+사용자 승인
+    ↓
+phases/index.json, task index, stepN.md 생성
+    ↓
+Step Executor 시작
+    ↓
+각 Step을 독립 Codex 세션에서 실행
+    ├─ 도구 호출 전: PreToolUse 정책 검사
+    └─ 응답 종료 전: Stop MSVC 빌드·테스트
+    ↓
+성공: 커밋 후 다음 Step
+실패: 수정 또는 최대 3회 재시도
+차단: 사용자 개입을 기다리며 중단
+```
+
+자연어 요구사항만으로 Executor가 자동 시작되지는 않는다. 계획을 사용자가 승인하고
+phase 파일을 생성한 다음 `scripts/execute.py`를 실행해야 구현 루프가 시작된다.
+
+## 2. 요구사항 탐색과 구체화
+
+예를 들어 사용자가 다음 요구사항을 전달했다고 가정한다.
+
+> CMake 기반 C++20 라이브러리에 `divide()` 함수를 추가하고, 0으로 나누면 예외를
+> 발생시키며 GoogleTest 테스트를 작성한다.
+
+계획을 작성하기 전에 다음 자료를 확인한다.
+
+- `AGENTS.md`
+- `docs/PRD.md`
+- `docs/ARCHITECTURE.md`
+- `docs/ADR.md`
+- 관련 제품 코드와 테스트
+- `.harness/config.json`
+
+이 탐색을 통해 다음 조건을 구체화한다.
+
+- 사용하는 MSVC toolset과 C++ 표준
+- CMake 프로젝트인지 Visual Studio solution/project인지
+- 테스트 프레임워크와 테스트 실행 방법
+- public header와 implementation의 의존성 방향
+- 수정할 모듈과 범위 밖 항목
+- 실행 가능한 Acceptance Criteria 명령
+
+요구사항에 결정되지 않은 부분이 있으면 구현 전에 사용자와 논의한다. 위 예에서는
+예외 타입, 정수 또는 부동소수점 연산 여부, public API와 ABI 변경 허용 여부가 이에
+해당한다.
+
+## 3. 요구사항을 Step으로 분해
+
+사용자가 구현 계획 작성을 요청하면 요구사항을 작은 Step으로 나눈다. Step 설계
+규칙은 [Harness Workflow](../.agents/skills/harness/SKILL.md)에 정의되어 있다.
+
+각 Step은 다음 조건을 만족해야 한다.
+
+- 하나의 모듈 또는 명확한 한 가지 책임만 다룬다.
+- 다른 대화 내용을 참조하지 않아도 실행할 수 있도록 자기완결적으로 작성한다.
+- 먼저 읽을 문서와 이전 Step의 관련 파일을 명시한다.
+- 클래스와 함수 시그니처 수준으로 작업 범위를 설명한다.
+- 실제 실행 가능한 빌드·테스트 명령을 Acceptance Criteria로 사용한다.
+- 성공, 오류, 사용자 개입 필요 상태의 판정 기준을 적는다.
+- 범위 밖 기능과 기존 테스트 회귀를 명시적으로 금지한다.
+
+예시 Step은 다음과 같은 내용을 포함할 수 있다.
+
+```text
+Step 0: division-api
+
+읽어야 할 파일
+- AGENTS.md
+- include/calculator.hpp
+- src/calculator.cpp
+- tests/calculator_test.cpp
+
+작업
+- divide(double lhs, double rhs)의 실패 테스트를 먼저 추가한다.
+- rhs가 0이면 std::invalid_argument가 발생하도록 최소 구현한다.
+
+Acceptance Criteria
+- CMake/MSBuild 빌드가 성공한다.
+- 전체 테스트가 성공한다.
+- 새로운 컴파일러 경고가 없다.
+```
+
+### TDD와 Step 경계
+
+프로젝트 규칙은 실패하는 테스트를 먼저 요구하지만 Stop 훅은 Codex가 Step을 종료할
+때 전체 테스트 성공을 요구한다. 따라서 다음처럼 실패 상태를 Step 사이에 남겨둘 수
+없다.
+
+```text
+Step 0: 실패하는 테스트만 추가하고 종료
+Step 1: 제품 코드를 구현해 테스트 통과
+```
+
+실제 red-green 순서는 하나의 Codex 실행 안에서 완료되어야 한다.
+
+```text
+테스트 작성
+→ 테스트 실패 확인
+→ 최소 제품 코드 구현
+→ 테스트 성공 확인
+→ Step 종료
+```
+
+즉, 테스트가 구현보다 먼저 작성되는 순서는 지키되 각 Step은 최종적으로 green
+상태여야 한다.
+
+## 4. 사용자 승인 후 생성되는 파일
+
+Step 초안을 사용자가 승인한 뒤에만 다음 파일을 생성한다.
+
+```text
+phases/
+├── index.json
+└── add-division/
+    ├── index.json
+    ├── step0.md
+    ├── step1.md
+    └── ...
+```
+
+### 4.1 Top-level index
+
+`phases/index.json`은 여러 task의 상태를 관리한다.
+
+```json
+{
+  "phases": [
+    {
+      "dir": "add-division",
+      "status": "pending"
+    }
+  ]
+}
+```
+
+### 4.2 Task index
+
+`phases/add-division/index.json`은 task 내부 Step의 상태를 관리한다.
+
+```json
+{
+  "project": "Calculator",
+  "phase": "add-division",
+  "steps": [
+    {
+      "step": 0,
+      "name": "division-api",
+      "status": "pending"
+    }
+  ]
+}
+```
+
+상태별 기록은 다음과 같이 나뉜다.
+
+| 상태 | Codex가 기록 | Executor가 기록 |
+|---|---|---|
+| `completed` | `summary` | `completed_at` |
+| `error` | `error_message` | `failed_at` |
+| `blocked` | `blocked_reason` | `blocked_at` |
+
+Executor는 task의 `created_at`과 Step의 `started_at`도 기록한다. `summary`는 다음
+독립 Codex 세션이 이전 Step의 핵심 산출물과 결정을 이해할 수 있도록 한 줄로
+작성한다.
+
+### 4.3 Step 파일
+
+각 `stepN.md`에는 다음 내용이 들어간다.
+
+- 읽어야 할 파일
+- 작업 범위와 인터페이스
+- 핵심 동작 및 불변 조건
+- Acceptance Criteria 명령
+- 아키텍처·ADR·CRITICAL 규칙 확인 절차
+- 성공, 오류, 차단 상태 기록 방법
+- 범위 밖 변경 금지사항
+
+Step은 독립 Codex 실행의 전체 작업 지시서이므로 이전 대화만 참조하는 표현을 넣지
+않는다.
+
+## 5. Step Executor 시작
+
+계획 파일을 생성한 뒤 다음 명령으로 실행한다.
+
+```powershell
+python scripts/execute.py add-division
+```
+
+완료된 브랜치를 원격 저장소에 자동 push하려면 `--push`를 추가한다.
+
+```powershell
+python scripts/execute.py add-division --push
+```
+
+[Step Executor](../scripts/execute.py)는 시작할 때 다음 작업을 수행한다.
+
+1. phase 디렉터리와 task index가 존재하는지 검사한다.
+2. 이전 실행에서 `error` 또는 `blocked`로 끝난 Step이 있는지 검사한다.
+3. `feat-{phase-name}` 브랜치를 생성하거나 checkout한다.
+4. `AGENTS.md`와 `docs/*.md`를 guardrail로 읽는다.
+5. task의 `created_at`이 없으면 기록한다.
+6. 첫 번째 `pending` Step부터 순차 실행한다.
+
+`AGENTS.md`와 모든 `docs/*.md` 내용은 각 Codex 프롬프트에 직접 삽입된다. 따라서
+이 문서들은 참고 자료가 아니라 실제 실행 입력이다. 서로 충돌하거나 placeholder가
+남아 있으면 Codex도 그 모순을 입력으로 받는다.
+
+## 6. Step마다 독립 Codex 세션 실행
+
+Executor는 각 Step을 다음 형태의 독립 프로세스로 실행한다.
+
+```text
+codex exec
+  --json
+  --sandbox <workspace-write|danger-full-access>
+  --dangerously-bypass-hook-trust
+  --cd <repository-root>
+  -
+```
+
+기본값은 `workspace-write`다. `FESA_HARNESS_CODEX_SANDBOX` 환경 변수는
+`workspace-write` 또는 `danger-full-access`만 허용한다. Windows native sandbox에서
+MSVC compiler-id의 `cl.exe` 정지가 재현되고 동일 명령이 sandbox 밖에서 통과하는
+환경에서는, 사용자 승인을 받은 격리된 clean worktree 실행에 한해서
+`danger-full-access` fallback을 사용할 수 있다. 이 override는 hook trust 또는 hook
+등록을 끄지 않으며 PreToolUse와 Stop 검증은 동일하게 실행된다.
+
+Codex에 전달하는 프롬프트는 다음 내용의 조합이다.
+
+```text
+AGENTS.md와 docs 문서
++ 이전에 완료된 Step의 summary
++ 이전 시도의 오류(재시도인 경우)
++ Executor 공통 작업 규칙
++ 현재 stepN.md
+```
+
+이전 Step의 전체 대화나 Codex 세션은 전달하지 않는다. task index에 기록한
+`summary`만 다음 Step에 누적한다.
+
+Codex 실행 결과의 exit code, stdout, stderr는 다음 파일에 저장한다.
+
+```text
+phases/{task-name}/step{N}-output.json
+```
+
+## 7. 도구 호출 전 PreToolUse 검사
+
+[`.codex/hooks.json`](../.codex/hooks.json)은 shell 및 파일 편집 도구에
+[PreToolUse 훅](../scripts/hooks/pre_tool_use.py)을 등록한다. Codex가 실제 명령이나
+편집을 수행하기 전에 이 훅이 요청을 검사한다.
+
+### 7.1 위험 명령 차단
+
+다음 유형의 명령은 요구사항과 관계없이 차단한다.
+
+- `git reset --hard`
+- `git push --force` 또는 `--force-with-lease`
+- `rm -rf`
+- `Remove-Item -Recurse -Force`
+- `rmdir /s /q`
+- `DROP TABLE`
+
+위험 패턴이 발견되면 훅은 차단 이유를 stderr로 출력하고 종료 코드 2를 반환한다.
+그러면 해당 도구 호출은 실행되지 않는다.
+
+### 7.2 C++ TDD 검사
+
+`apply_patch`, `Edit`, `MultiEdit`, `Write`로 다음 C/C++ 확장자의 파일을 편집하려
+하면 [TDD 정책](../scripts/msvc_harness/tdd_policy.py)을 검사한다.
+
+```text
+.c .cc .cpp .cxx .h .hpp .hxx
+```
+
+일반 제품 코드를 수정하려면 대응되는 테스트 파일이 먼저 존재해야 한다. 예를 들어
+`src/calculator.cpp`의 기본 대응 테스트 이름은 다음과 같다.
+
+```text
+calculator_test.cpp
+calculator_tests.cpp
+test_calculator.cpp
+calculator.test.cpp
+```
+
+테스트는 다음 위치에서 검색한다.
+
+- `.harness/config.json`의 `tdd.testRoots`
+- 제품 파일과 같은 디렉터리 아래 `tests/`
+- 제품 파일과 같은 디렉터리 아래 `test/`
+
+다음 파일과 디렉터리는 대응 테스트 존재 검사가 면제된다.
+
+- 테스트 파일 자체
+- `main.cpp`
+- `.harness/build/**`, `build/**`, `out/**`
+- `cmake-build-*/**`
+- `third_party/**`, `external/**`, `vendor/**`
+- `generated/**`
+- `tdd.exclude`에 추가한 경로
+
+`tdd.exclude`는 기본 제외 항목을 대체하지 않고 추가한다.
+
+### 7.3 TDD 검사가 보장하는 범위
+
+현재 TDD 훅이 직접 보장하는 것은 대응되는 이름의 테스트 파일이 존재한다는
+사실이다. 다음 항목까지 증명하지는 않는다.
+
+- 테스트가 이번 요구사항을 실제로 검증하는가
+- 구현 전에 테스트가 실제로 실패했는가
+- 테스트의 assertion과 경계 조건이 충분한가
+- 기존 테스트 파일을 이번 변경과 함께 수정했는가
+
+또한 shell 명령의 리다이렉션 등으로 C++ 파일을 쓰는 경우 shell 위험 패턴 검사는
+적용되지만 경로 기반 TDD 검사는 적용되지 않는다. 따라서 이 훅은 완전한 TDD
+증명기가 아니라 테스트 우선 편집을 유도하는 guardrail이다.
+
+## 8. Codex 종료 전 Stop 검증
+
+Codex가 Step 작업을 끝내고 응답을 종료하려 하면
+[Stop 훅](../scripts/hooks/stop_validation.py)이 실행된다. Stop 훅은 변경 파일만이
+아니라 발견된 C/C++ 프로젝트 전체를 빌드하고 테스트한다.
+
+### 8.1 저장소 루트와 재진입 방지
+
+Stop 훅은 `git rev-parse --show-toplevel`로 프로젝트 루트를 결정한다. Git 저장소를
+찾을 수 없으면 현재 디렉터리를 사용한다.
+
+빌드나 테스트의 자식 프로세스에는 `CODEX_STOP_VALIDATION_ACTIVE=1`을 전달한다.
+같은 훅이 자식 프로세스에서 다시 진입하면 즉시 성공 처리하여 검증 재귀를 막는다.
+
+### 8.2 설정 로드
+
+[설정 로더](../scripts/msvc_harness/config.py)는 `.harness/config.json`을 읽는다.
+파일이 없으면 다음 기본값을 사용한다.
+
+- `version`: 1
+- `projectType`: `auto`
+- CMake source: 저장소 루트
+- preset 미사용 시 binary directory: `.harness/build`
+- configuration: `Debug`
+- platform: `x64`
+- 테스트 루트: `tests`, `test`
+- 기본 테스트 이름 패턴 네 개
+
+설정은 다음 조건을 엄격하게 검사한다.
+
+- 알 수 없는 필드를 거부한다.
+- `version`은 숫자 1만 허용한다.
+- `projectType`은 `auto`, `cmake`, `msbuild`만 허용한다.
+- 저장소 상대 경로만 허용한다.
+- 저장소 밖으로 해석되는 경로를 거부한다.
+- CMake preset을 사용하면 `configurePreset`, `buildPreset`, `testPreset`,
+  `binaryDir`를 모두 요구한다.
+- 모든 `tdd.testPatterns`에 `{stem}`을 요구한다.
+
+### 8.3 프로젝트 자동 감지
+
+[프로젝트 탐색기](../scripts/msvc_harness/discovery.py)는 다음 순서로 프로젝트를
+선택한다.
+
+1. `projectType: cmake` 또는 `projectType: msbuild` 명시 설정
+2. 루트의 `CMakePresets.json`
+3. 루트의 `CMakeUserPresets.json`
+4. 루트의 `CMakeLists.txt`
+5. 루트의 단일 `.sln`
+6. 루트의 단일 `.vcxproj`
+
+자동 감지 결과는 다음처럼 처리한다.
+
+| 저장소 상태 | 결과 |
+|---|---|
+| CMake metadata가 있음 | CMake 프로젝트 선택 |
+| 하나의 `.sln` 또는 `.vcxproj`가 있음 | MSBuild 프로젝트 선택 |
+| 여러 solution/project가 있음 | 설정으로 하나를 지정하라는 오류 |
+| C/C++ 파일과 build metadata가 모두 없음 | 검증할 프로젝트가 없으므로 통과 |
+| C/C++ 파일은 있지만 build metadata가 없음 | orphan C++ 프로젝트 오류 |
+
+### 8.4 MSVC 도구 탐색
+
+[도구 탐색기](../scripts/msvc_harness/toolchain.py)는 `vswhere.exe`로 다음을
+확인한다.
+
+- Visual Studio 설치 경로
+- Desktop development with C++ workload
+- `MSBuild.exe`
+
+CMake 프로젝트에서는 다음 우선순위로 CMake와 CTest를 선택한다.
+
+1. PATH에서 발견한 독립 `cmake.exe`와 `ctest.exe`
+2. Visual Studio에 번들된 CMake와 CTest
+
+따라서 새로 설치한 CMake의 `bin` 디렉터리가 PATH에 반영되어 있으면 독립 CMake를
+우선 사용한다.
+
+## 9. 빌드 시스템별 검증 계획
+
+### 9.1 CMake preset 미사용
+
+[CMake adapter](../scripts/msvc_harness/adapters/cmake.py)는 다음 검증 계획을 만든다.
+
+```powershell
+cmake -S <source> -B .harness/build -A x64
+cmake --build .harness/build --config Debug
+ctest --test-dir .harness/build -C Debug --show-only=json-v1
+ctest --test-dir .harness/build -C Debug --output-on-failure
+```
+
+명령 성공 외에 다음 결과도 검사한다.
+
+- 생성된 CMake compiler metadata의 `CMAKE_CXX_COMPILER_ID`가 `MSVC`인가
+- CTest JSON에 한 개 이상의 테스트가 있는가
+
+따라서 빌드가 성공해도 MinGW 등 다른 컴파일러를 사용했거나 CTest가 테스트를 한
+개도 발견하지 못하면 실패한다.
+
+### 9.2 CMake preset 사용
+
+`.harness/config.json`에 preset을 완전히 지정하면 다음 형태로 실행한다.
+
+```powershell
+cmake --preset <configurePreset>
+cmake --build --preset <buildPreset>
+ctest --preset <testPreset> --show-only=json-v1
+ctest --preset <testPreset> --output-on-failure
+```
+
+이 경우 모든 명령은 `cmake.sourceDir`에서 실행하고 compiler metadata 검사는 설정한
+`binaryDir`에서 수행한다.
+
+### 9.3 직접 MSBuild
+
+[MSBuild adapter](../scripts/msvc_harness/adapters/msbuild.py)는 다음 순서로 실행한다.
+
+```powershell
+MSBuild.exe <solution-or-vcxproj> /m /nologo `
+  /p:Configuration=<configuration> `
+  /p:Platform=<platform>
+
+<msbuild.testCommand>
+```
+
+직접 MSBuild 프로젝트는 표준 테스트 탐색 명령이 없으므로
+`.harness/config.json`의 `msbuild.testCommand`가 반드시 필요하다. 이 값이 없으면
+Stop 검증이 실패한다.
+
+## 10. 명령 실행 안전성과 제한시간
+
+[검증 실행기](../scripts/msvc_harness/process.py)는 다음 안전 규칙을 적용한다.
+
+- 명령을 shell 문자열이 아닌 argv 배열로 실행한다.
+- `shell=False`를 사용한다.
+- 각 명령의 working directory가 저장소 내부인지 검사한다.
+- 명령별 제한시간과 Stop 전체 제한시간 중 더 짧은 값을 적용한다.
+- 종료 코드가 0이 아니면 즉시 해당 stage를 실패 처리한다.
+
+Stop 훅의 전체 제한시간은 저장소 탐색, toolchain 탐색, configure, build, test discovery,
+test를 모두 포함해 1,800초다. `.codex/hooks.json`의 Stop command timeout도 1,800초다.
+
+실패 메시지에는 다음 진단 정보를 포함한다.
+
+- 실패 stage
+- 안전하게 표현한 argv 배열
+- working directory
+- 종료 코드
+- stdout과 stderr의 마지막 8,000자
+
+Harness는 별도 빌드 로그 파일을 생성하지 않는다.
+
+## 11. 성공, 실패, 차단 처리
+
+### 11.1 Stop 검증 성공
+
+빌드와 테스트가 모두 성공하면 Stop 훅은 출력 없이 종료한다. Codex가 정상 종료하면
+Executor가 task index를 다시 읽는다.
+
+Codex가 Step을 다음처럼 기록한 경우:
+
+```json
+{
+  "step": 0,
+  "name": "division-api",
+  "status": "completed",
+  "summary": "divide API와 0 나누기 테스트를 추가함"
+}
+```
+
+Executor는 `completed_at`을 기록하고 변경사항을 커밋한 뒤 다음 `pending` Step을
+실행한다.
+
+### 11.2 Stop 검증 실패
+
+Stop 훅은 Codex hook protocol에 따라 다음 형태의 응답을 출력한다.
+
+```json
+{
+  "continue": false,
+  "stopReason": "build failed ...",
+  "systemMessage": "build failed ..."
+}
+```
+
+Codex 프로세스에 대한 훅 자체의 종료 코드는 0이지만 `continue: false`가 Codex의
+응답 종료를 막는다. Codex는 같은 세션에서 오류를 확인하고 수정을 계속한다.
+
+### 11.3 Executor 재시도
+
+Codex 프로세스가 끝났는데 Step 상태가 `completed` 또는 `blocked`가 아니면 Executor가
+새 Codex 세션으로 재시도한다.
+
+```text
+첫 번째 시도 실패
+→ 오류를 다음 프롬프트에 삽입
+→ 두 번째 독립 Codex 실행
+→ 다시 실패하면 세 번째 독립 Codex 실행
+→ 세 번째도 실패하면 error 기록 후 종료
+```
+
+즉, 실패 복구에는 두 층이 있다.
+
+1. Stop 훅이 같은 Codex 세션에서 수정하도록 요구한다.
+2. 세션 자체가 성공하지 못하면 Executor가 새 세션으로 최대 3회 재시도한다.
+
+### 11.4 사용자 개입 필요
+
+인증, API 키, 수동 설치처럼 Codex가 자동으로 해결할 수 없는 문제가 있으면 Step을
+`blocked`로 기록한다. Executor는 `blocked_at`과 top-level 상태를 갱신하고 종료 코드
+2로 중단한다.
+
+재개하려면 원인을 해결하고 해당 Step을 `pending`으로 되돌린 뒤
+`blocked_reason`을 제거하고 다시 실행한다. `error`도 같은 방식으로 `pending`으로
+되돌리고 `error_message`를 제거한 뒤 재실행한다.
+
+## 12. Git 커밋과 phase 완료
+
+Step이 성공하면 제품 변경과 Harness metadata를 분리해 다음 형식으로 커밋한다.
+
+```text
+feat(add-division): step 0 — division-api
+chore(add-division): step 0 output
+```
+
+두 번째 커밋의 `output`은 task index의 Step 상태와 summary 같은 Harness metadata를
+뜻한다. 원시 Codex 실행 기록인 `stepN-output.json`은 `.gitignore` 대상이며 커밋에
+포함되지 않는다.
+
+모든 Step이 완료되면 Executor는 다음 작업을 수행한다.
+
+- task의 `completed_at` 기록
+- `phases/index.json`의 task 상태를 `completed`로 변경
+- 최종 metadata 커밋
+- `--push` 사용 시 `origin/feat-{phase-name}`으로 push
+
+커밋 과정은 `git add -A`를 사용한다. 실행 전에 작업 트리에 관련 없는 사용자
+변경사항이 남아 있으면 그 변경도 Step 커밋에 포함될 수 있다. 따라서 깨끗한
+worktree 또는 별도 Git worktree에서 실행하는 것이 안전하다.
+
+## 13. 요구사항 종류별 동작
+
+| 받은 요구사항 또는 변경 | PreToolUse 동작 | Stop 동작 |
+|---|---|---|
+| 새 C++ 제품 파일 추가 | 대응 테스트가 먼저 없으면 차단 | 전체 빌드·테스트 |
+| 기존 C++ 구현 또는 header 수정 | 대응 테스트 파일 존재 여부 검사 | 전체 빌드·테스트 |
+| 테스트 파일 추가 | TDD 차단 없이 허용 | 모든 테스트가 성공해야 종료 |
+| `main.cpp` 수정 | TDD 대응 테스트 검사 면제 | 전체 빌드·테스트 |
+| 문서, JSON, Python 수정 | C++ TDD 검사 없음 | C++ 프로젝트가 있으면 전체 검증 |
+| 위험한 Git 또는 삭제 명령 | 즉시 차단 | 도달하지 않음 |
+| C++ 파일은 있지만 build metadata 없음 | 편집은 허용될 수 있음 | orphan 프로젝트 오류 |
+| 직접 MSBuild인데 `testCommand` 없음 | 편집은 허용될 수 있음 | 설정 오류로 종료 차단 |
+| C/C++가 전혀 없는 저장소 | 관련 편집 검사 없음 | 검증할 프로젝트가 없어 통과 |
+
+## 14. 적용 전 준비사항
+
+이 저장소는 대상 C++ 프로젝트에 맞게 채워 사용하는 템플릿이다. 실행 전 다음을
+확인한다.
+
+1. `AGENTS.md`의 프로젝트명, toolset, C++ 표준, 테스트 프레임워크, CRITICAL 규칙을
+   실제 값으로 교체한다.
+2. `docs/PRD.md`, `docs/ARCHITECTURE.md`, `docs/ADR.md`의 placeholder와 예시를 실제
+   프로젝트 정보로 교체한다.
+3. 기본 자동 감지로 충분하지 않을 때만 `.harness/config.example.json`을 참고해
+   `.harness/config.json`을 만든다.
+4. CMake 또는 MSBuild metadata와 테스트 실행 방법을 확인한다.
+5. `phases/`가 없다면 요구사항 논의와 계획 승인을 거쳐 task 파일을 먼저 만든다.
+6. Executor 실행 전에 Git working tree가 깨끗한지 확인한다.
+
+특히 `AGENTS.md`와 `docs/*.md`는 각 Codex 실행에 그대로 주입된다. C++ 프로젝트에서
+TypeScript 예시나 미완성 placeholder가 남아 있으면 실제 작업 지시와 충돌할 수 있다.

docs/MITC4_SUPP.md

@@ -0,0 +1,604 @@
+# MITC4 구현 회고 및 보충 기록
+
+## 1. 문서 목적과 범위
+
+이 문서는 `linear-static-mitc4-shell` 기능을 요구조건부터 `dev` 병합 검증까지
+진행하면서 실제로 겪은 시행착오, 실수, 어려움과 그 해결 방법을 기록한다. 새 계약을
+정의하는 문서가 아니라, 이미 승인된 요구조건·정식화·I/O·reference·release 문서를
+보충하는 회고 자료다. 계약이 충돌하면 이 문서가 아니라 다음 문서를 우선한다.
+
+- `docs/requirements/linear-static-mitc4-shell.md`
+- `docs/formulations/mitc4-shell-formulation.md`
+- `docs/io-definitions/linear-static-mitc4-shell-io.md`
+- `docs/reference-models/linear-static-mitc4-shell-reference-models.md`
+- `docs/numerical-reviews/linear-static-mitc4-shell-review.md`
+- `docs/releases/linear-static-mitc4-shell-release.md`
+
+라인 참조는 회고 작성 시점의 기준 커밋 `6c41cde41af4d6cd474b008e5ae81769fff0aa79`
+을 사용한다. `path:line`은 이 기준 커밋의 파일과 라인을 뜻한다. 중간 실패가 최종
+phase ledger에서 정상 완료 상태로 교체된 경우에는 `commit:path:line`으로 historical
+snapshot을 표시한다. 이후 파일이 수정되면 라인이 이동할 수 있으므로 커밋과 검색어를
+함께 확인해야 한다.
+
+이 문서는 다음 세 범주를 구분한다.
+
+1. **실수 또는 결함**: 승인된 의미와 다른 동작, 잘못된 가정, 환경 실패의 오분류.
+2. **계약 변경에 따른 재작업**: 구현 결함이 아니라 승인 범위나 tolerance가 바뀌어
+   이미 작성한 문서·테스트·비교기를 수정한 경우.
+3. **예상된 TDD RED와 수치적 어려움**: 계획된 실패로 아직 없는 동작을 확인하거나,
+   shell 요소 특성상 조심해서 해결해야 했던 문제. 이것을 구현 실수로 과장하지 않는다.
+
+## 2. 주요 시행착오 요약
+
+| ID | 분류 | 문제 또는 어려움 | 핵심 해결 | 대표 근거 |
+| --- | --- | --- | --- | --- |
+| `RET-01` | 프로세스 실수 | numerical review가 수치 정식화 외의 bundle 행정 정보를 readiness blocker로 취급함 | FESA 독립 솔버 원칙과 실제 비교에 필요한 최소 계약으로 gate를 재정의함 | `docs/ADR.md:189`, `docs/numerical-reviews/linear-static-mitc4-shell-review.md:80` |
+| `RET-02` | 프로세스 어려움 | Planning Agent, Implementation Agent, Executor, hook의 소유권이 모호했음 | 승인·materialize·Step 실행·상태/커밋 책임을 분리함 | `.codex/agents/implementation-agent.toml:46`, `.agents/skills/harness/SKILL.md:16` |
+| `RET-03` | 환경 결함 | Windows sandbox helper 실패가 프로세스 종료 코드 `0` 안에 숨고 Step 0이 갱신되지 않음 | 진단 marker를 종료 코드보다 먼저 검사하고 승인된 sandbox override를 추가함 | `scripts/execute.py:247`, `scripts/execute.py:306` |
+| `RET-04` | 수치적 어려움 | 20 physical DOF MITC4를 외부 24 DOF shell 계약에 넣으면서 drilling을 분리해야 했음 | physical과 drilling congruence를 분리하고 회전 대각항만으로 고정 안정화를 계산함 | `docs/formulations/mitc4-shell-formulation.md:759`, `src/fesa/elements/mitc4_shell.cpp:597` |
+| `RET-05` | 기하 처리 어려움 | warped mesh와 공유 절점에서 initial director의 방향·순서·유효성을 결정해야 했음 | source-order 정렬, 면적 가중 평균, 양의 incident-normal 방향, 전 적분점 `J>0` 검사를 사용함 | `src/fesa/model/shell_geometry.cpp:275`, `src/fesa/model/shell_geometry.cpp:317` |
+| `RET-06` | 범위 경계 | 선형 구현에 future geometric-nonlinear tangent 정식화가 섞일 위험이 있었음 | 선형 24 DOF 구현과 조건부 nonlinear 20-to-24 pullback을 명시적으로 분리함 | `docs/formulations/mitc4-shell-formulation.md:1112`, `docs/numerical-reviews/linear-static-mitc4-shell-review.md:71` |
+| `RET-07` | parser 결함 | 같은 이름의 Abaqus `NSET`과 `ELSET`을 중복 entity로 잘못 거부함 | node-set과 element-set namespace를 분리함 | `src/fesa/io/abaqus/domain_mapper.cpp:401`, `tests/unit/io/abaqus/domain_mapper_test.cpp:439` |
+| `RET-08` | comparator 결함 | Abaqus CSV와 HDF5 instance name의 대소문자 차이가 row identity mismatch를 만듦 | 비교 key만 ASCII 대문자로 정규화하고 source identity 출력은 보존함 | `tests/reference/mitc4_reference_comparison.cpp:122`, `tests/reference/mitc4_reference_comparison_test.cpp:539` |
+| `RET-09` | 계약 재작업 | 동일한 FESA kernel 결과를 Abaqus S4와 S4R 두 reference에 동시에 맞출 수 없었음 | full-integration FESA의 blocking reference를 S4 하나로 제한하고 S4R은 비-reference test로 검증함 | `docs/requirements/linear-static-mitc4-shell.md:201`, `docs/requirements/linear-static-mitc4-shell.md:205` |
+| `RET-10` | 계약 재작업 | B33 혼합 tolerance가 독립 shell 정식화 비교에 지나치게 엄격해 kernel 결함과 계약 차이를 혼동함 | invariant/patch 검증 후 MITC4 고정 절대 tolerance `1.0e-5`로 계약과 비교기를 함께 변경함 | `docs/ADR.md:215`, `tests/reference/mitc4_reference_comparison.cpp:35` |
+| `RET-11` | 통합 어려움 | prescribed-only shell에서 이미 상쇄된 `K*d`만으로 residual을 정규화하면 정상 roundoff가 단위 residual이 됨 | `Kff*df`, `Kfc*dc`, `Ff`의 물리적 항 크기로 정규화함 | `src/fesa/results/result_recovery.cpp:674`, `phases/linear-static-mitc4-shell/index.json:102` |
+| `RET-12` | 상태/출력 안전성 | recovery 또는 HDF5 inventory가 뒤에서 실패할 때 기존 정상 state/output을 손상할 위험이 있었음 | candidate state와 temporary HDF5를 완전히 검증한 뒤 atomic commit/replace함 | `src/fesa/results/result_recovery.cpp:925`, `src/fesa/io/hdf5/hdf5_results_writer.cpp:2579` |
+| `RET-13` | 병합 환경 오염 | `dev` worktree의 ignored B33 `.h5`가 exact reference inventory test를 실패시킴 | reference를 수정하지 않고 ignored 파일을 quarantine으로 이동한 뒤 전체 검증함 | `.gitignore:20`, `tests/reference/b33_reference_comparison_test.cpp:178` |
+
+## 3. 계약과 개발 프로세스에서의 시행착오
+
+### 3.1 Numerical Review가 행정 메타데이터에 과도하게 의존함 (`RET-01`)
+
+#### 문제
+
+초기 numerical review는 정식화의 수학적 준비 상태뿐 아니라 canonical bundle 이름,
+`README.md`, provenance, units, step/frame 설명까지 갖춰야 implementation planning으로
+넘어갈 수 있다고 판단했다. `metadata.json` 자체는 optional로 정리했지만, 그 주변의
+행정 정보가 여전히 primary verdict를 `needs-reference-model`로 유지했다.
+
+Historical evidence는 다음과 같다.
+
+- `ebb2657:docs/numerical-reviews/linear-static-mitc4-shell-review.md:12` — status가
+  `needs-reference-model`이었다.
+- `0428759:docs/numerical-reviews/linear-static-mitc4-shell-review.md:94` — alias,
+  README, provenance, unit, step/frame, schema, tolerance를 open blocker로 묶었다.
+- `0428759:docs/numerical-reviews/linear-static-mitc4-shell-review.md:702` — `NR-O01`부터
+  `NR-O04`까지 calibration을 implementation-planning blocker로 남겼다.
+
+#### 원인
+
+Reference artifact의 재현성 감사와 현재 기능의 수치 readiness를 같은 gate로 취급했다.
+또한 Abaqus가 제공하는 bundle 관리 방식과 FESA가 실제로 비교에 필요한 observable
+quantity 계약을 충분히 분리하지 못했다. 결과적으로 정식화 결함이 아닌 문서 형식이
+수치 검토를 막았다.
+
+#### 해결
+
+프로젝트 정책을 다음처럼 다시 고정했다.
+
+- FESA는 Abaqus의 내부 알고리즘을 재현하는 솔버가 아니다
+  (`docs/ADR.md:189-195`).
+- readiness에 필요한 것은 선언된 input/CSV, deterministic source row mapping,
+  component와 tolerance다 (`docs/ADR.md:197-202`).
+- `NR-O01`은 고정 drilling 계수 결정으로 닫고, `NR-O02`부터 `NR-O04`까지는 승인
+  범위에서 제거했다 (`docs/numerical-reviews/linear-static-mitc4-shell-review.md:74-77`).
+- 과거 blocker였던 canonical naming, README, `metadata.json`, provenance와 expanded
+  portfolio가 formulation verdict를 막지 않는다고 명시했다
+  (`docs/numerical-reviews/linear-static-mitc4-shell-review.md:80-83`).
+
+관련 정책 변경 커밋은 `5c08f1c`(independent reference validation policy),
+`73df844`(MITC4 verification/drilling scope 단순화), `60b42f4`(numerical review pass)다.
+
+#### 교훈
+
+Reference gate에는 “이 정보가 실제 row matching 또는 수치 판정에 사용되는가?”를 먼저
+물어야 한다. 사용되지 않는 행정 메타데이터를 모든 기능의 blocking requirement로
+자동 승격하면 독립 솔버의 물리 검증보다 형식 준수가 우선된다.
+
+### 3.2 Harness 역할과 Step 소유권이 처음부터 충분히 명확하지 않았음 (`RET-02`)
+
+#### 문제
+
+구현 계획 승인, phase 파일 materialize, Harness 실행, Step 선택, 구현, timestamp와
+commit 기록의 주체가 여러 agent 문서에 분산되어 있었다. 이 상태에서는 Planning Agent가
+실행까지 시작하거나, Implementation Agent가 다음 Step으로 넘어가거나, hook을 수동
+검증 명령처럼 실행하는 실수가 생길 수 있었다.
+
+#### 해결
+
+다음 소유권을 agent와 Harness 문서에 중복 없이 고정했다.
+
+- Planning Agent는 multi-Step draft 승인 후에만 phase 파일을 만들고 Step을 실행하지
+  않는다 (`.codex/agents/implementation-planning-agent.toml:52-60`).
+- Implementation Agent는 Executor가 선택한 현재 `stepN.md` 하나만
+  `RED -> GREEN -> VERIFY`로 수행한다 (`.codex/agents/implementation-agent.toml:46-60`).
+- branch, retry, timestamp, commit과 next-Step selection은 Executor 소유다
+  (`.codex/agents/implementation-agent.toml:64-67`).
+- hook은 등록된 PreToolUse/Stop lifecycle로 자동 실행하며 수동 호출로 대체하지 않는다
+  (`.agents/skills/harness/SKILL.md:16-25`).
+- 계획 승인은 실행 승인이 아니며 별도의 사용자 요청이 있어야 한다
+  (`docs/HARNESS_WORKFLOW.md:41-42`).
+
+이 개선은 `85cd17d`, `ab69a3d`, `713b41b`, `65d5e07`, `18296a1`, `a058ef7`
+커밋에 걸쳐 정리됐다.
+
+#### 교훈
+
+Agentic phase에서 “무엇을 할 것인가”뿐 아니라 “누가 상태를 바꾸는가”를 계약해야 한다.
+특히 implementation summary와 executor timestamp/commit을 한 주체가 모두 소유하게 하면
+재시도와 감사 이력이 쉽게 꼬인다.
+
+### 3.3 Windows sandbox 실패가 정상 종료처럼 보임 (`RET-03`)
+
+#### 문제
+
+Step 0의 첫 Harness 실행은 세 번 재시도한 뒤에도 Step status를 갱신하지 못했다.
+historical ledger는 `8dd4d72:phases/linear-static-mitc4-shell/index.json:10`에
+`[3회 시도 후 실패] Step did not update status`를 기록한다. 실제 원인은 구현 코드가
+아니라 Windows sandbox helper의 `orchestrator_helper_launch_failed`였다. 더 까다로운 점은
+이 진단이 Codex JSON output 안에 있으면서 process exit code는 `0`일 수 있었다는 것이다.
+
+#### 해결
+
+- `_codex_environment_failure()`가 exit code를 보기 전에 diagnostic text에서 sandbox
+  helper marker를 검사하도록 바꿨다 (`scripts/execute.py:306-314`).
+- 기본 `workspace-write`는 유지하되, 승인된 격리 worktree에 한해서
+  `FESA_HARNESS_CODEX_SANDBOX=danger-full-access`를 허용했다
+  (`scripts/execute.py:247-254`, `docs/HARNESS_WORKFLOW.md:247-252`).
+- unknown mode는 fail-closed로 거부하고, exit code `0` 안의 helper failure도 잡는
+  회귀 테스트를 추가했다 (`tests/test_execute.py:77-111`).
+
+수정 커밋은 `0d50625`이며, 이후 Harness Python suite `7/7`이 통과했다
+(`docs/releases/linear-static-mitc4-shell-release.md:176-178`).
+
+#### 교훈
+
+Agent runner에서는 OS process exit code만 신뢰하면 안 된다. 하위 orchestrator가 구조화된
+출력 안에 fatal environment error를 기록하는 경우가 있으므로, 알려진 환경 실패 marker와
+상태 전이를 함께 검사해야 한다.
+
+## 4. 정식화와 수치 구현의 어려움
+
+### 4.1 20 physical DOF와 24 global DOF 사이의 경계 (`RET-04`)
+
+#### 어려움
+
+MITC4의 physical field는 절점당 translation 3개와 director-tangent rotation 2개, 즉
+총 20 DOF다. 반면 FESA shell 외부 계약은 절점당 6 DOF, 총 24 DOF다. 남는 네 개의
+director-parallel 회전은 drilling 좌표이며 physical MITC4 strain에 들어가면 안 된다.
+
+초기의 “작은 diagonal stiffness를 더한다”는 수준의 설명만으로는 다음 실수가 가능했다.
+
+- translation과 rotation diagonal을 섞어 단위가 다른 값으로 `k_d`를 정하는 문제;
+- drilling energy를 physical shell energy나 stress recovery에 섞는 문제;
+- 20 DOF weak form에 24 DOF external work를 직접 결합하는 문제;
+- 작은 값이므로 rigid mode나 rank 검증을 생략하는 문제.
+
+Numerical Review에서 이 위험은 `NR-C02`부터 `NR-C04`로 추적됐다
+(`docs/numerical-reviews/linear-static-mitc4-shell-review.md:68-70`).
+
+#### 해결
+
+정식화와 코드를 두 경로로 나눴다.
+
+1. `K20`은 MITC tying shear와 physical constitutive matrix만으로 적분한다
+   (`src/fesa/elements/mitc4_shell.cpp:597-636`).
+2. `k_d` reference는 절점당 두 개, 총 여덟 개 physical tangent-rotation diagonal의
+   finite positive 값만 사용한다 (`src/fesa/elements/mitc4_shell.cpp:638-655`).
+3. `k_d = 1.0e-3 * min(R+)`를 적용한다
+   (`src/fesa/elements/mitc4_shell.cpp:662-676`).
+4. physical과 drilling을 별도 congruence로 24 DOF에 올린 후 마지막에만 합한다
+   (`src/fesa/elements/mitc4_shell.cpp:669-681`).
+5. recovery는 global 24 DOF를 physical 20 DOF로 projection한 뒤 계산하므로 pure drill이
+   strain/resultant/stress/physical energy에 기여하지 않는다
+   (`src/fesa/elements/mitc4_shell.cpp:699-714`).
+
+이를 energy congruence, rank와 six rigid modes, patch field, fixed drilling factor,
+pure-drill exclusion 테스트로 각각 검증했다
+(`tests/unit/elements/mitc4_shell_test.cpp:618`, `:647`, `:697`, `:752`, `:828`).
+
+#### 교훈
+
+수치 안정화는 크기만 작은 physical stiffness가 아니다. coordinate map, 단위, virtual
+work와 output 의미를 별도 경계로 정의해야 한다. 안정화 항을 physical result에서 제외하는
+테스트가 coefficient 자체의 테스트만큼 중요하다.
+
+### 4.2 Initial director와 warped/shared-node geometry의 결정성 (`RET-05`)
+
+#### 어려움
+
+“초기 법선벡터를 두께 방향으로 사용한다”는 결정은 단일 평면 요소에는 단순하지만,
+공유 절점과 warped mesh에서는 다음 선택을 추가로 요구했다.
+
+- element normal의 부호를 어느 source connectivity 순서로 정할지;
+- 여러 incident element normal을 어떤 순서와 weight로 평균할지;
+- 반대 방향 normal, fold, zero-area, local reversal을 허용할지;
+- stiffness, tying, recovery가 서로 다른 geometry inventory를 사용하지 않게 할지.
+
+#### 해결
+
+- source connectivity로 center normal과 element orientation을 결정했다.
+- required surface points에서 finite/nonzero measure와 positive orientation을 먼저
+  검사했다 (`src/fesa/model/shell_geometry.cpp:275-300`).
+- 공유 절점의 incident element를 stable source identity 순서로 정렬했다
+  (`src/fesa/model/shell_geometry.cpp:317-327`).
+- 모든 incident normal 쌍이 같은 positive hemisphere에 있는지 확인한 다음 면적 가중
+  평균을 계산했다 (`src/fesa/model/shell_geometry.cpp:328-364`).
+- geometry validity를 center, stiffness, tying, recovery point inventory 전체에서
+  fail-closed로 검사했다. Calibration angle이나 distortion cutoff를 새로 만들지는 않았다
+  (`docs/formulations/mitc4-shell-formulation.md:593`,
+  `docs/numerical-reviews/linear-static-mitc4-shell-review.md:76-77`).
+
+평면·회전·warped geometry, stable area weighting, invalid Jacobian/opposed normal,
+validation-point inventory 테스트가 각각 존재한다
+(`tests/unit/model/shell_geometry_test.cpp:101`, `:153`, `:184`, `:244`).
+
+#### 교훈
+
+자동 normal 생성은 단순한 vector 계산이 아니라 mesh topology와 deterministic reduction
+계약이다. 순서를 명시하지 않으면 병렬화나 input order 변화가 director와 결과에 영향을
+줄 수 있다.
+
+### 4.3 Geometric-nonlinear tangent를 선형 구현으로 오인할 위험 (`RET-06`)
+
+#### 어려움
+
+정식화 문서에는 future geometric-nonlinear tangent도 포함했지만, 현재 제품 범위는 선형
+정적이다. 20-coordinate director chart의 material/geometric tangent만 적는 것으로
+global 24 DOF nonlinear element가 완성되는 것은 아니다. finite rotation update,
+`Phi: R24 -> R20`, 그 1·2차 미분, chart recentering과 objective drilling potential이
+필요하다.
+
+#### 해결
+
+- nonlinear 식이 Section 15.3까지 20-coordinate physical chart에만 존재하며 완전한
+  global 24 DOF element가 아니라고 명시했다
+  (`docs/formulations/mitc4-shell-formulation.md:1112-1113`).
+- conditional pullback에는 map-curvature Hessian 항을 유지하고, 미정인 coordinate map과
+  drilling을 future-only blocker로 남겼다
+  (`docs/numerical-reviews/linear-static-mitc4-shell-review.md:71`).
+- current review의 open question은 nonlinear rotation/map/output/state 계약뿐이며 현재
+  선형 planning을 차단하지 않는다
+  (`docs/numerical-reviews/linear-static-mitc4-shell-review.md:85-90`).
+- 구현 phase에는 linear `K20 -> K24`와 고정 drilling만 넣고 nonlinear state나 tangent
+  API를 만들지 않았다.
+
+#### 교훈
+
+문서에 수식이 있다는 사실과 제품 계약이 닫혔다는 사실은 다르다. 특히 nonlinear
+coordinate map의 Hessian을 생략한 채 “consistent tangent”라고 부르면 이후 Newton
+iteration의 일관성을 잘못 주장하게 된다.
+
+## 5. Parser와 결과 파이프라인의 실제 결함
+
+### 5.1 Abaqus NSET/ELSET namespace를 하나로 처리함 (`RET-07`)
+
+#### 증상
+
+Step 13 reference E2E는 comparator contract test가 통과한 뒤에도 모든 S4/S4R case에서
+HDF5 생성 전에 `duplicate-entity`로 실패했다. historical ledger
+`32f0e59:phases/linear-static-mitc4-shell/index.json:113`은 part `NSET Set-1`과
+`ELSET Set-1`을 같은 namespace로 검사한 것이 원인임을 기록한다. Step 13의 test-only
+소유 범위에서 production parser를 고칠 수 없었기 때문에 세 번 재시도 후 upstream
+correction이 필요했다.
+
+#### 원인과 해결
+
+기존 `containsSetName()`은 part의 node set과 element set 양쪽을 함께 검색했다.
+Abaqus input에서는 두 종류가 별도 namespace이므로 같은 이름이 유효하다.
+
+- part helper가 전달받은 set 종류 하나만 검색하도록 변경했다
+  (`src/fesa/io/abaqus/domain_mapper.cpp:401-408`).
+- assembly helper도 `isNodeSet`이 같은 항목만 비교하도록 변경했다
+  (`src/fesa/io/abaqus/domain_mapper.cpp:410-418`).
+- part와 assembly에서 같은 이름의 NSET/ELSET을 허용하되 같은 종류의 실제 중복은
+  계속 거부하는 회귀 테스트를 추가했다
+  (`tests/unit/io/abaqus/domain_mapper_test.cpp:439`).
+
+수정 커밋은 `b805683`이다.
+
+#### 교훈
+
+Source label text가 같다는 이유만으로 semantic identity가 같은 것은 아니다. parser의
+duplicate 검사는 `(entity kind, scope, source name)` 전체 identity를 사용해야 한다.
+
+### 5.2 Reference instance identity의 대소문자 차이를 그대로 비교함 (`RET-08`)
+
+#### 증상과 원인
+
+Parser namespace를 고친 뒤 reference precheck에서 Abaqus CSV의 `part-1-1`과 FESA HDF5의
+`Part-1-1`이 다른 key로 취급됐다. CSV field whitespace는 이미 trim했지만 Abaqus name의
+case-insensitive 의미를 row identity comparator에 적용하지 않았다.
+
+#### 해결
+
+- comparator ordering/equality key에서 instance name을 ASCII uppercase로 정규화했다
+  (`tests/reference/mitc4_reference_comparison.cpp:122-142`).
+- report에는 HDF5가 보존한 stable source identity를 그대로 남겼다. 즉 비교를 위해 source
+  artifact를 rename하거나 rewrite하지 않았다.
+- lowercase CSV identity가 정상 match되는 회귀 테스트를 추가했다
+  (`tests/reference/mitc4_reference_comparison_test.cpp:539`).
+
+수정 커밋은 `56833ab`이다.
+
+#### 교훈
+
+Identity normalization은 어느 계층에서 어떤 목적으로 하는지 제한해야 한다. comparator
+key의 case normalization과 source identity 보존을 분리하면 matching은 견고해지면서도
+진단·HDF5 identity가 조용히 바뀌는 문제를 피할 수 있다.
+
+### 5.3 Prescribed-only free residual normalization (`RET-11`)
+
+#### 증상
+
+Step 12의 nonzero prescribed-displacement shell case는 실제 equilibrium을 만족했지만
+free-residual 검증에서 실패했다. 이미 상쇄된 `K*d` 또는 외력만 normalization scale로
+쓰면 `Ff=0`이고 `Kff*df`와 `Kfc*dc`가 서로 상쇄되는 case에서 작은 roundoff가 상대적으로
+`1`에 가까운 residual처럼 보일 수 있었다. Phase ledger가 이 실패와 해결을 기록한다
+(`phases/linear-static-mitc4-shell/index.json:102-107`).
+
+#### 해결
+
+free residual `Kff*df + Kfc*dc - Ff`의 세 물리 항을 따로 평가하고 그 최대 norm을
+denominator로 사용했다 (`src/fesa/results/result_recovery.cpp:674-697`). 임의의
+`max(1, ...)` floor는 넣지 않았고, scale과 residual이 둘 다 정확히 0일 때만 normalized
+residual을 0으로 처리했다.
+
+Integration test는 `Ff=0`인데 `-Kfc*dc`만으로 effective RHS가 생기는 것을 직접 확인한다
+(`tests/integration/analysis/linear_static_analysis_test.cpp:440-464`).
+
+#### 교훈
+
+Residual normalization은 최종 합의 크기만 보면 안 된다. 서로 상쇄되는 원래 방정식 항의
+물리적 scale을 보존해야 prescribed load, zero load와 mixed constraint를 같은 기준으로
+검증할 수 있다.
+
+### 5.4 Recovery state와 HDF5 output의 실패 원자성 (`RET-12`)
+
+#### 어려움
+
+Shell 결과는 displacement 하나가 아니라 residual/reaction, GP strain/resultant,
+BOTTOM/MIDDLE/TOP stress, frame, physical energy와 equilibrium evidence를 함께 commit한다.
+뒤쪽 row가 invalid일 때 일부 vector만 기존 `AnalysisState`에 반영하거나, 기존 정상
+`results.h5`를 불완전한 새 파일로 바꾸면 실패가 이전 성공 상태를 손상한다.
+
+TDD 과정에서 다음 문제가 드러났다.
+
+- invalid shell candidate가 이전 state를 덮을 수 있음
+  (`phases/linear-static-mitc4-shell/index.json:78-83`);
+- beam-only recovery 뒤 stale shell evidence가 남을 수 있음
+  (`phases/linear-static-mitc4-shell/index.json:85-91`);
+- invalid HDF5 inventory가 기존 final output을 안전하지 않게 교체할 수 있음
+  (`phases/linear-static-mitc4-shell/index.json:93-99`).
+
+#### 해결
+
+- recovery는 완전한 `candidateState`를 복사해 모든 shell row를 검증하고 마지막에 한 번만
+  move-commit한다 (`src/fesa/results/result_recovery.cpp:925-940`).
+- HDF5 writer는 unique temporary file에 쓰고 닫은 뒤 read-only로 reopen/self-check한
+  파일만 final path로 교체한다 (`src/fesa/io/hdf5/hdf5_results_writer.cpp:2579-2592`).
+- drilling energy와 unsupported point stress가 accidental output으로 생기지 않았는지도
+  self-check한다 (`src/fesa/io/hdf5/hdf5_results_writer.cpp:2449-2455`).
+- invalid shell inventory가 기존 final bytes를 보존하는 회귀 테스트를 추가했다
+  (`tests/unit/io/hdf5/hdf5_results_writer_test.cpp:1359`).
+
+#### 교훈
+
+Solver output의 원자성은 HDF5 backend만의 책임이 아니다. recovery candidate의 의미적
+완전성, temporary file의 구조적 완전성, final replacement 순서를 모두 지켜야 한다.
+
+## 6. Reference comparison에서의 재작업
+
+### 6.1 S4와 S4R을 동시에 blocking reference로 사용한 모순 (`RET-09`)
+
+#### 증상
+
+초기 reference plan은 S4와 S4R 두 Abaqus bundle을 모두 blocking comparison으로
+사용했다. 그러나 FESA 계약은 두 source type을 같은 full-integration FESA-MITC4 kernel에
+매핑한다. 실제 Abaqus S4와 S4R은 동일한 내부 정식화가 아니므로 두 Abaqus reference
+결과도 달랐다.
+
+Historical ledger `cf769aa:phases/linear-static-mitc4-shell/index.json:113`은 다음 불가능한
+상태를 수치로 기록한다.
+
+- 두 FESA deck은 heading과 `TYPE=S4/S4R` 외에는 같고 동일 stiffness를 생성함;
+- Abaqus center `U3`는 두 reference 사이에 `8.190036e-7` 차이가 남;
+- 당시 더 큰 tolerance도 약 `1.02456e-9`여서 하나의 공통 FESA 결과가 두 reference를
+  동시에 통과할 수 없음.
+
+이는 kernel을 S4와 S4R에 따라 다르게 만들라는 신호가 아니었다. 그렇게 하면 “둘 다
+동일한 FESA formulation”이라는 승인 계약과 Abaqus 비동등성 원칙을 위반한다.
+
+#### 해결
+
+- blocking Abaqus comparison은 `reference/shell/`의 S4 input/displacement CSV 하나로
+  고정했다 (`docs/requirements/linear-static-mitc4-shell.md:201-205`).
+- `reference/shellR/`은 acceptance에서 소비하지 않는다
+  (`docs/requirements/linear-static-mitc4-shell.md:202`).
+- S4R 지원은 parser identity, 동일 sparse stiffness, HDF5 source metadata test로
+  검증한다 (`tests/unit/io/abaqus/domain_mapper_test.cpp:538`,
+  `tests/unit/assembly/sparse_assembler_test.cpp:324`,
+  `tests/unit/io/hdf5/hdf5_results_writer_test.cpp:1167`).
+- S4 E2E test만 유지했다 (`tests/reference/mitc4_reference_cases_test.cpp:159-169`).
+
+문서 변경은 `91b2df9`, test 변경은 `f92c17d`에 기록됐다.
+
+#### 교훈
+
+입력 label을 지원하는 것과 그 label 이름을 가진 외부 solver element를 reference로
+사용하는 것은 별도 결정이다. 공통 internal formulation이면 acceptance reference도 그
+formulation의 observable 목적에 맞는 하나를 선택해야 한다.
+
+### 6.2 Reference 실패를 kernel 결함과 tolerance 결함으로 분리하기 (`RET-10`)
+
+#### 증상
+
+S4-only gate로 줄인 뒤에도 25개의 nonzero `U3` row가 당시 B33식 tolerance를 넘었다.
+historical ledger `8994ce9:phases/linear-static-mitc4-shell/index.json:113`은 worst row
+`Part-1-1/node 2/U3`에서 다음을 기록한다.
+
+- absolute error: `1.90378534915144e-7`;
+- 당시 tolerance: `1.0237408203e-9`;
+- normalized error: `185.9636`.
+
+이 시점에 tolerance만 즉시 키우면 실제 MITC4 kernel 부호·tying·Jacobian 결함을 숨길 수
+있고, 반대로 Abaqus S4와 동일하지 않은 FESA-MITC4에 B33 수준의 엄격한 tolerance를 계속
+강제하면 올바른 독립 정식화를 실패로 오판할 수 있었다.
+
+#### 독립 조사와 해결
+
+먼저 reference 결과와 독립적인 다음 검사를 통과시켰다.
+
+- 20-to-24 energy congruence와 six rigid modes/rank
+  (`tests/unit/elements/mitc4_shell_test.cpp:618-647`);
+- membrane, bending, transverse shear와 twist patch
+  (`tests/unit/elements/mitc4_shell_test.cpp:697`);
+- pure drilling의 physical recovery/energy exclusion
+  (`tests/unit/elements/mitc4_shell_test.cpp:828`);
+- S4/S4R common stiffness와 deterministic assembly
+  (`tests/unit/assembly/sparse_assembler_test.cpp:324`);
+- authoritative FESA HDF5에서 같은 stable error가 발생하며 comparator 자체의 row mismatch가
+  아님을 확인함.
+
+그 뒤 user-approved contract를 MITC4 고정 절대 tolerance `1.0e-5`로 변경했다.
+
+- ADR은 U blocking, UR warning-only와 reference scale의 diagnostic-only 성격을 고정한다
+  (`docs/ADR.md:215-222`).
+- comparator는 모든 row에 하나의 fixed tolerance를 적용한다
+  (`tests/reference/mitc4_reference_comparison.cpp:35`, `:755-767`).
+- 경계 바로 아래와 위, UR warning-only를 회귀 테스트한다
+  (`tests/reference/mitc4_reference_comparison_test.cpp:662`, `:712`).
+- final reference verification에서 같은 worst absolute error는 tolerance의 약 `0.0190`이고
+  U `147/147`, UR `147/147`, warning `0`으로 통과했다
+  (`docs/reference-verifications/linear-static-mitc4-shell-reference-verification.md:138-157`).
+
+문서 변경 커밋은 `f1be807`, comparator 완료 커밋은 `426cce1`이다.
+
+#### 교훈
+
+Reference mismatch가 보이면 먼저 element invariant와 patch test로 kernel을 독립 검증하고,
+row identity/schema와 authoritative HDF5를 확인한 다음 tolerance 계약을 판단해야 한다.
+Tolerance 완화가 kernel 조사보다 먼저 오면 결함 은폐가 되고, 외부 solver 내부 동등성을
+가정한 과도한 tolerance는 false failure가 된다.
+
+## 7. 정상적인 TDD RED와 실제 재작업의 구분
+
+Phase ledger의 대부분 RED는 계획된 TDD 증거다. 다음 실패들은 “처음부터 구현이 잘못됐다”는
+뜻이 아니라, 해당 Step이 소유한 behavior가 아직 없음을 테스트가 정확히 검출한 것이다.
+
+| Step | 예상된 RED | GREEN에서 추가한 핵심 동작 | 근거 |
+| --- | --- | --- | --- |
+| 0-1 | shell semantic type과 mapping 부재 | S4/S4R source identity와 공통 FESA-MITC4 model | `phases/linear-static-mitc4-shell/index.json:5-19` |
+| 2 | `shell_geometry.hpp` 부재 | deterministic normal/director와 geometry validation | `phases/linear-static-mitc4-shell/index.json:21-27` |
+| 3 | `mitc4_shell.hpp` 부재 | 20 DOF kinematics, tying, constitutive, fixed quadrature | `phases/linear-static-mitc4-shell/index.json:29-35` |
+| 4-5 | stiffness와 recovery API 부재 | physical/drilling stiffness 분리와 pure-drill-free recovery | `phases/linear-static-mitc4-shell/index.json:37-51` |
+| 6-7 | shell scatter/assembly 부재 | 24-entry scatter와 source-ordered 576-entry COO reduction | `phases/linear-static-mitc4-shell/index.json:53-67` |
+| 8 | drilling direction moment를 허용함 | aggregate moment projection 검사와 RHS 이전 거부 | `phases/linear-static-mitc4-shell/index.json:69-75` |
+| 9-11 | state/recovery/HDF5 shell inventory 부재 | atomic state commit과 self-checked HDF5 replace | `phases/linear-static-mitc4-shell/index.json:77-99` |
+| 12 | prescribed-only normalization 실패 | `Kff/Kfc/Ff` term-scale normalization | `phases/linear-static-mitc4-shell/index.json:101-107` |
+
+반면 `RET-03`, `RET-07`, `RET-08`은 실제 환경 또는 코드 결함이었다. `RET-01`,
+`RET-09`, `RET-10`은 upstream 정책·범위·tolerance 결정이 바뀌어 발생한 재작업이다.
+이 구분을 유지해야 TDD의 의도된 실패를 품질 문제로 잘못 집계하지 않는다.
+
+## 8. `dev` 병합 검증에서 발견한 ignored artifact 오염 (`RET-13`)
+
+### 8.1 증상
+
+Feature branch 자체와 병합 직후 MITC4 test는 통과했지만, `C:\git\FESADev`의 `dev`
+worktree에서 full CTest를 실행하자 기존 B33 reference test 하나가 실패했다.
+
+```text
+B33ReferenceComparison.GeneratesAuthoritativeHdf5AndComparisonEvidence
+referenceBefore.size() = 5, expected = 4
+```
+
+MITC4 변경으로 B33 reference가 바뀐 것이 아니라, 해당 worktree의
+`reference/cantilever beam/`에 pre-existing `cantilever beam.h5`가 남아 있었다.
+`.gitignore`가 모든 `.h5`를 무시하므로 일반 `git status`는 이 파일을 보여주지 않았다
+(`.gitignore:20`). B33 test는 reference tree를 snapshot하고 정확히 네 파일만 있어야
+한다고 검사한다 (`tests/reference/b33_reference_comparison_test.cpp:73`, `:178-191`).
+
+### 8.2 해결
+
+Reference artifact를 삭제하거나 수정하지 않았다. ignored HDF5를 다음 복구 가능한 위치로
+이동했다.
+
+```text
+C:\git\FESADev\.harness\quarantine\preexisting-reference-artifacts\cantilever beam.h5
+SHA-256: 233DF10D6A13941A477BC5133A0D686D939FEF598B3748B6DE69D2684320E01F
+```
+
+이동 뒤 focused B33 test `1/1`, full CTest `144/144`, Harness pytest `7/7`을 다시 실행했다.
+Tracked reference path에는 변경이 없었다.
+
+### 8.3 교훈
+
+- clean worktree 감사에는 `git status`뿐 아니라 reference directory의 ignored file inventory도
+  포함해야 한다.
+- 테스트가 exact artifact count를 요구하면 build/output extension이 ignore되어 있는지
+  함께 확인해야 한다.
+- 사용자 또는 이전 실행이 만든 ignored file은 바로 삭제하지 말고 hash를 기록해 workspace
+  내부 quarantine으로 이동하는 것이 안전하다.
+
+## 9. 재사용할 개발 체크리스트
+
+### 9.1 Requirements와 Numerical Review
+
+- [ ] 외부 solver의 input label, internal algorithm과 observable reference quantity를
+      분리했는가?
+- [ ] readiness blocker가 실제 수치 판정에 필요한 정보인지 확인했는가?
+- [ ] optional metadata, provenance, bundle naming을 자동으로 blocking gate로 올리지 않았는가?
+- [ ] future nonlinear 식과 현재 executable scope를 명확히 분리했는가?
+
+### 9.2 Shell kernel
+
+- [ ] physical DOF와 numerical stabilization DOF의 transform, energy와 output을 분리했는가?
+- [ ] translation/rotation 혼합 단위의 raw diagonal 또는 spectrum으로 계수를 정하지 않는가?
+- [ ] normal/director reduction order와 invalid orientation predicate가 deterministic한가?
+- [ ] reference 전에 rigid mode, rank, energy congruence와 independent patch를 통과하는가?
+
+### 9.3 Parser와 reference comparison
+
+- [ ] identity가 `(kind, scope, source label)`을 모두 포함하는가?
+- [ ] source format의 case/whitespace 규칙을 comparator key에만 정확히 적용하는가?
+- [ ] missing, extra, duplicate, nonfinite row를 tolerance 전에 거부하는가?
+- [ ] source type 지원과 그 source type의 Abaqus artifact consumption을 별도 계약으로
+      판단하는가?
+- [ ] tolerance 변경 전에 authoritative HDF5와 kernel invariant를 확인했는가?
+
+### 9.4 State, HDF5와 Harness
+
+- [ ] complete candidate를 검증한 뒤 state를 한 번만 commit하는가?
+- [ ] HDF5 temporary file을 close/reopen/self-check한 뒤 final을 교체하는가?
+- [ ] Agent는 Executor가 선택한 Step 하나만 수행하고 Executor-owned 상태를 쓰지 않는가?
+- [ ] process exit code와 structured diagnostic의 fatal error를 모두 검사하는가?
+- [ ] 병합 전후 reference directory에 ignored generated artifact가 없는가?
+
+## 10. 최종 결과와 남은 한계
+
+최종 release readiness는 `ready-for-release`다
+(`docs/releases/linear-static-mitc4-shell-release.md:250`). 근거는 다음과 같다.
+
+- clean MSVC x64 Debug build와 compiler/linker warning `0`;
+- full CTest `144/144`, Harness pytest `7/7`;
+- Harness Step `0-13` 완료와 output `14/14` exit code `0`;
+- S4 reference U `147/147` pass, UR `147/147` 비교와 warning `0`;
+- exact 294 comparison rows, invalid row `0`;
+- physics equilibrium, direction, symmetry, recovery와 energy sanity pass
+  (`docs/releases/linear-static-mitc4-shell-release.md:168-181`).
+
+다만 이 결과가 다음을 의미하지는 않는다.
+
+- Abaqus S4/S4R 내부 정식화 동등성;
+- reduced integration 또는 hourglass control 지원;
+- S4R Abaqus reference acceptance;
+- curved/distorted/thin-thick mesh 전체의 convergence 보장;
+- geometric-nonlinear global 24 DOF tangent 구현 완료.
+
+이 한계는 release 문서에 승인된 boundary로 남아 있다
+(`docs/releases/linear-static-mitc4-shell-release.md:201-209`). 이번 작업의 가장 중요한
+결론은 “Abaqus처럼 작동하게 만들기”가 아니라, FESA의 독립 정식화와 외부 observable
+comparison 사이의 경계를 먼저 고정하고 각 계층의 invariant로 결함을 좁혀야 한다는
+점이다.

docs/PRD.md

@@ -1,9 +1,15 @@
 # PRD: FESA 구조해석 솔버
 
 ## 목표
-FESA는 Abaqus `.inp` keyword subset을 입력으로 받아 유한요소법 기반 구조해석을 수행하고, step/frame 단위 결과를 `results.h5` HDF5로 저장하며, Abaqus reference CSV rows와 비교 가능한 C++17/MSVC 솔버를 제공한다.
+FESA는 Abaqus `.inp` keyword subset을 입력으로 받아 자체 유한요소 정식화로 구조해석을
+수행하고, step/frame 단위 결과를 `results.h5` HDF5로 저장하며, 기능이 지정한 Abaqus
+reference CSV 수치와 비교 가능한 C++17/MSVC 솔버를 제공한다. Abaqus의 요소 알고리즘,
+적분법, stabilization 또는 내부 결과 생성 절차를 재현하는 것은 목표가 아니다.
 
-이 프로젝트의 성공 기준은 단순 실행 성공이 아니다. 기능은 요구조건, 정식화, I/O 계약, C++ 테스트, reference comparison, physics sanity, release readiness를 모두 통과해야 완료된다.
+이 프로젝트의 성공 기준은 단순 실행 성공이 아니다. 기능 구현은 요구조건, 정식화,
+I/O 계약, C++ build/test와 기능별 blocking reference comparison을 통과해야 완료된다.
+Physics sanity와 release readiness는 구현 완료 뒤 별도 배포 판단을 제공하며 Abaqus 내부
+동작 동등성을 요구하지 않는다.
 
 ## 사용자
 - Solver developer: C++17/MSVC/CMake/CTest 환경에서 요소, 재료, 해석 절차, solver backend를 구현한다.
@@ -15,41 +21,78 @@ FESA는 Abaqus `.inp` keyword subset을 입력으로 받아 유한요소법 기
 1. Abaqus `.inp` keyword subset parser와 내부 `Domain` semantic model 생성
 2. `AnalysisModel`, `DofManager`, `AnalysisState` 기반의 step별 equation system 구성
 3. 선형 정적 해석을 시작점으로 하는 `Analysis` procedure 계층
-4. 요소, 재료, 경계조건, 하중의 runtime-polymorphic base interface
+4. Stable source identity를 보존하는 concrete V0 node, B33 element, material, section, boundary, load record
 5. sparse matrix pattern 생성, 전역 행렬/벡터 조립, 제약조건 적용
-6. `LinearSolver` adapter를 통한 MKL PARDISO backend와 향후 iterative solver 확장
-7. HDF5 기반 `ResultStep` -> `ResultFrame` -> `FieldOutput`/`HistoryOutput` 저장
+6. `LinearSolver`, `ParallelFor`, `ResultsWriter` interface를 통한 MKL PARDISO, oneTBB, HDF5 backend 격리
+7. HDF5 기반 versioned step/frame field-result 저장과 향후 history-output 확장 경계
 8. FESA HDF5 rows와 `reference/<model-id>/` 아래 Abaqus reference CSV rows의 직접 비교
-9. CMake/MSVC/x64/Debug, CTest, Harness validation, TDD guard 기반 개발 검증
+9. CMake/MSVC/x64/Debug, CTest 기반 개발 검증
+
+Element/material 계층의 일반적인 runtime polymorphism, iterative solver, history output은 장기 확장 방향이다. 현재 제품 계약으로 간주하지 않으며, 실제 사용 사례와 성능·수명 요구가 승인되기 전에 추상 base class를 미리 추가하지 않는다.
+
+## 사용자 관점 제품 흐름
+
+1. 사용자는 승인된 Abaqus `.inp` subset으로 모델과 단일 analysis step을 기술한다.
+2. FESA는 syntax를 읽은 뒤 semantic mapping과 model validation을 수행한다. 지원하지 않는 모델 의미는 구조화된 diagnostic과 안정된 exit code로 거부한다.
+3. 해석 procedure는 active model view, DOF/equation map과 sparse system을 만들고, essential constraint elimination을 적용해 선형계를 factorize하고 substitution한다.
+4. FESA는 full displacement를 복구하고 equilibrium residual/reaction과 element 결과를 계산한다.
+5. 성공 시 output request와 무관한 mandatory 결과, metadata와 diagnostic을 versioned `results.h5`에 기록한다. 실패 시 불완전한 최종 결과 파일을 정상 결과처럼 남기지 않는다.
+6. 검증 workflow는 기능이 지정한 HDF5 quantity를 기존 Abaqus CSV의 source identity와
+   component에 대응시켜 tolerance를 판정하고, 별도로 equilibrium과 물리적 타당성을
+   검토한다. Reference bundle naming이나 provenance는 수치 비교 gate가 아니다.
+
+Parser keyword, element kernel, solver backend 또는 output dataset 중 하나만 추가된 상태는 end-to-end 제품 기능이 아니다. 같은 기능의 입력 의미부터 외부 결과와 검증까지 연결되어야 한다.
 
 ## V0 범위
-- 선형 정적 해석 골격
-- 첫 end-to-end 기능 후보: 1D truss/bar element
+- 선형 정적 해석 파이프라인 구현
+- 승인된 첫 end-to-end 기능: 2절점 3D Euler–Bernoulli beam, Abaqus `TYPE=B33`
+- 입력 파일당 하나의 `*STEP, *STATIC`
+- 절점당 자유도 `[UX, UY, UZ, URX, URY, URZ]`
+- 축, 두 방향 굽힘, Saint-Venant 비틀림 및 선형 등방 탄성
 - 최소 Abaqus keyword subset:
   - `*HEADING`
-  - `*NODE`
-  - `*ELEMENT`
-  - `*NSET`
-  - `*ELSET`
+  - `*PART`, `*END PART`
+  - `*NODE`, `*ELEMENT, TYPE=B33`
+  - `*NSET`, `*ELSET`, including `GENERATE`
   - `*MATERIAL`
   - `*ELASTIC`
-  - section keyword
+  - `*BEAM GENERAL SECTION, SECTION=GENERAL`
+  - `*SECTION POINTS`
+  - `*ASSEMBLY`, `*END ASSEMBLY`
+  - `*INSTANCE`, `*END INSTANCE`
   - `*BOUNDARY`
   - `*CLOAD`
-  - `*STEP`
-  - `*STATIC`
-  - output request subset
-- displacement 중심의 최소 `AnalysisState`
+  - `*STEP`, `*STATIC`, `*END STEP`
+- `*PREPRINT`, `*RESTART`, `*TRANSVERSE SHEAR STIFFNESS`, `*OUTPUT, FIELD`,
+  `*OUTPUT, HISTORY`, `*NODE OUTPUT`, `*ELEMENT OUTPUT`, `*CONTACT OUTPUT`과 그에 속한
+  미지원 variable data는 warning 후 no-op 처리
+- 같은 part의 여러 identity instance와 stable source label mapping
+- nonzero prescribed displacement를 포함한 free/constrained partition
+- formulation의 constant local line-load equivalent nodal vector kernel. V0 parser와 CLI는
+  `*DLOAD`를 지원하거나 이 kernel을 호출하지 않음
+- deterministic COO-to-CSR stiffness assembly
+- MKL PARDISO 기반 sparse direct solver
+- stiffness factorization과 load-vector substitution 분리
+- displacements, reactions, equilibrium end actions, section resultants, generalized results,
+  axial `S11` output
 - HDF5 result schema v0
-- FESA HDF5 to Abaqus reference CSV comparison 계약
+- `fesa.exe <model.inp> --output <results.h5>` CLI
+- 승인된 `reference/cantilever beam/` B33 결과와 displacement, reaction, section resultant
+  comparison; beam stress reference comparison은 N/A
 
-## V1 범위
-- 2D plane stress/plane strain element
-- 3D solid element
-- MKL PARDISO 기반 sparse direct solve
-- TBB element-local computation 병렬화
-- reference model portfolio 확장
-- nonlinear static, dynamic, frequency, heat transfer 해석을 위한 interface 확장점
+## 신규 기능의 제품 완료 정의
+
+새로운 element, load, constraint, material, analysis procedure 또는 output quantity는 다음 조건을 모두 만족할 때 FESA 제품 기능으로 취급한다.
+
+1. 지원 범위와 제외 범위, 실패 category, solver output의 units/coordinates/identity,
+   blocking reference quantity와 tolerance가 요구조건과 I/O 계약에 명시되어 있다.
+2. 필요한 FEM 정식화와 recovery/sign convention이 검토되었고, 수치 위험과 검증 문제를 numerical review가 다룬다.
+3. Syntax와 semantic mapping이 내부 모델에 안정된 source identity로 연결되며 잘못된 입력을 fail-closed로 거부한다. Kernel만 제공하는 기능은 parser/CLI 지원 여부를 별도로 표시한다.
+4. DOF, sparse pattern, assembly, constraint, solver lifecycle과 mutable state ownership이 기존 아키텍처에 연결되거나 승인된 새 procedure 경계를 가진다.
+5. Mandatory HDF5 schema와 diagnostic, CLI 실패 의미가 정의되고 failure path가 기존 state 또는 최종 output을 오염시키지 않는다.
+6. Unit test가 local 수식과 validation을, integration test가 orchestration과 외부 계약을,
+   required reference comparison이 기능별 blocking quantity의 외부 수치 acceptance를
+   각각 증명한다. Reference가 N/A이면 그 이유와 대체 evidence를 명시한다.
 
 ## 기능 요구조건
 | ID | 요구조건 | Acceptance Criteria | Verification Method |
@@ -58,38 +101,61 @@ FESA는 Abaqus `.inp` keyword subset을 입력으로 받아 유한요소법 기
 | FESA-PRD-002 | FESA는 입력 모델을 `Domain`으로 변환해야 한다. | nodes, elements, materials, properties, sets, loads, boundary conditions, step definitions가 semantic model에 보존된다. | parser integration test |
 | FESA-PRD-003 | FESA는 현재 step의 실행 view를 `AnalysisModel`로 구성해야 한다. | active elements, loads, boundary conditions, properties/materials가 Domain 복사 없이 참조 또는 id view로 연결된다. | analysis model unit test |
 | FESA-PRD-004 | FESA는 equation numbering과 constraint/free mapping을 `DofManager`에 집중해야 한다. | Node/Element 내부에 equation id를 분산 저장하지 않는다. | code review, DofManager unit test |
-| FESA-PRD-005 | FESA는 해석 중 변하는 물리량을 `AnalysisState`에 저장해야 한다. | displacement, force, residual, increment/iteration 상태가 step/frame 출력과 연결된다. | state unit test, integration test |
-| FESA-PRD-006 | FESA는 solver 결과를 HDF5 authoritative output `results.h5`로 저장해야 한다. | step/frame, field/history, metadata, diagnostics가 schema version과 함께 저장된다. | HDF5 schema test |
-| FESA-PRD-007 | FESA는 Abaqus reference CSV rows와 비교 가능한 deterministic row mapping을 제공해야 한다. | displacement, reaction, internal force, stress 등 검증 물리량의 row identity와 tolerance source가 명확하다. | reference comparison report |
-| FESA-PRD-008 | FESA의 production C++ 변경은 테스트를 먼저 작성하고 실패를 확인한 뒤 구현해야 한다. | 관련 C++ test file이 있고 Harness TDD guard를 통과한다. | hook test, CTest |
+| FESA-PRD-005 | FESA는 해석 중 변하는 물리량을 `AnalysisState`에 저장해야 한다. | V0 displacement, external/internal force, residual, constrained reaction, step/frame identity와 element recovery rows가 출력에 연결되고 velocity, acceleration, temperature, iteration history는 할당하지 않는다. | state unit test, integration test |
+| FESA-PRD-006 | FESA는 solver 결과를 HDF5 authoritative output `results.h5`로 저장해야 한다. | V0 step/frame field results, metadata, diagnostics가 schema version과 함께 저장된다. | HDF5 schema test |
+| FESA-PRD-007 | FESA는 기능이 지정한 Abaqus reference CSV quantity와 비교 가능한 deterministic source-row/component mapping을 제공해야 한다. | Required source IDs/components는 일대일 대응되고 missing/extra/duplicate/nonfinite row는 tolerance 전에 실패한다. Canonical naming, README, metadata, provenance 또는 CSV schema version은 요구하지 않는다. | reference comparison report |
+| FESA-PRD-008 | FESA의 production C++ 변경은 테스트를 먼저 작성하고 실패를 확인한 뒤 구현해야 한다. | 관련 C++ test file, RED 실패와 후속 GREEN 성공 증거가 있고 Stop의 전체 MSVC build/test가 통과한다. | implementation report, Hook guardrail, CTest |
 | FESA-PRD-009 | FESA는 외부 라이브러리 API를 solver core에 직접 노출하지 않아야 한다. | MKL, TBB, HDF5 의존은 adapter module에 제한된다. | architecture review, dependency review |
-| FESA-PRD-010 | FESA 기능 완료는 reference comparison과 physics sanity 통과를 요구해야 한다. | 수치 tolerance와 물리 검토가 모두 pass이고 known limitation이 기록된다. | verification report, physics evaluation report |
+| FESA-PRD-010 | FESA 기능 구현 완료는 build/test와 기능별 blocking reference comparison 통과를 요구해야 한다. | Required CTest가 통과하고 선언된 blocking quantity가 승인 tolerance 안에 있다. Physics sanity와 release readiness는 별도 후속 gate다. | build/test report, reference verification report |
+| FESA-PRD-011 | V0는 입력 파일당 하나의 linear static step과 Abaqus B33 3D Euler beam만 해석해야 한다. | 단일 B33 model은 해석되고, B31과 두 번째 step은 구조화된 unsupported diagnostic으로 거부된다. | parser/semantic unit test, CLI integration test |
+| FESA-PRD-012 | V0는 Part/Assembly/Instance wrapper와 source identity를 보존해야 한다. | 여러 identity instance의 node/element/set label이 stable internal ID로 deterministic하게 매핑되고 transform 또는 nested assembly는 거부된다. | semantic mapping unit test |
+| FESA-PRD-013 | Output-request allowlist는 해석 의미를 변경하지 않아야 한다. | 승인 keyword와 variable data는 warning 후 no-op이고, allowlist 밖 model-affecting keyword는 오류이며 기본 결과는 output request와 무관하게 생성된다. | parser diagnostic test, HDF5 integration test |
+| FESA-PRD-014 | 선형 정적 pipeline은 stiffness factorization과 load substitution을 분리해야 한다. | `Kff` factorization이 load vector assembly보다 먼저 수행되고, `rhs=Ff-Kfc*dc` substitution으로 full displacement를 복구한다. | orchestration test, solver-adapter test |
+| FESA-PRD-015 | FESA는 V0 결과와 diagnostic을 안정된 외부 계약으로 출력해야 한다. | CLI가 `0=success`, `2=usage`, `3=input`, `4=model`, `5=solver`, `6=HDF5` exit code를 사용하고 diagnostic field가 계약과 일치하며 HDF5가 displacement, reaction, end force, section resultant, generalized strain/resultant, axial `S11`을 포함하고 실패 시 불완전한 최종 파일을 남기지 않는다. | CLI integration test, HDF5 schema/atomicity test |
+| FESA-PRD-016 | Dense와 sparse math storage 및 backend 경계를 분리해야 한다. | `Vector`는 contiguous, `Matrix`는 row-major contiguous storage와 MKL CBLAS를 사용하고 `SparseMatrix`는 별도 0-based CSR 타입이며 MKL 타입이 public core API에 노출되지 않는다. | math unit test, dependency review |
+| FESA-PRD-017 | B33 reference comparison은 component-scale 혼합 tolerance를 사용해야 한다. | 모든 matched row가 `abs_error <= absolute_floor + 1e-6 * reference_scale`을 만족하고 missing/extra/nonfinite row는 comparison 전에 실패한다. | reference comparison unit/integration test, verification report |
+| FESA-PRD-018 | 승인된 B33 reference artifact는 현재 경로의 read-only baseline으로 유지해야 한다. | `reference/cantilever beam/` 파일을 rename, rewrite 또는 보정하지 않고 기능이 선언한 exact path에서 읽는다. | artifact inventory, Git diff review |
+| FESA-PRD-019 | B33 beam section과 local axis를 Abaqus 의미에 맞게 매핑해야 한다. | `n1 -> local y`, `t x n1 -> local z`, `Iy=I11`, `Iz=I22`, `I12=0`을 적용하고 nonpositive property, zero-length element, tangent-parallel guide vector를 구조화된 model diagnostic으로 거부한다. | section-mapping unit test, element geometry test |
 
 ## 비기능 요구조건
 - MSVC x64 Debug 환경에서 configure, build, CTest를 검증한다.
 - reference test 결과는 deterministic해야 한다.
 - HDF5 schema는 versioned contract로 관리한다.
-- tolerance policy는 absolute, relative, norm-based 기준을 구분한다.
+- B33 reference tolerance는 model, step/frame, quantity, component별 Abaqus scale만 사용한다.
+- 승인된 SI B33 bundle의 absolute floor는 displacement/rotation `1e-9`, force/moment
+  `1e-3`이며 relative coefficient는 `1e-6`이다.
+- MITC4 U/UR comparison은 고정 절대오차 `1.0e-5`를 사용한다. `U1/U2/U3`만
+  blocking이고 `UR1/UR2/UR3` 초과는 warning-only다. B33의 component-scale 혼합
+  tolerance는 별도 기존 계약으로 유지한다.
 - parser, solver, HDF5 writer는 실패 원인을 구조화된 diagnostic으로 보고한다.
 - oneMKL, oneTBB, HDF5는 CMake에서 명시 탐지하고 실패 원인을 분류한다.
-- 대규모 모델 성능 최적화보다 Phase 1 명확성, 테스트 가능성, 검증 traceability를 우선한다.
+- 대규모 모델 성능 최적화보다 V0의 명확성, 테스트 가능성, 검증 traceability를 우선한다.
 
 ## Acceptance Gates
 1. Requirements approved: 기능 범위, 제외 범위, 입력, 출력, tolerance, 검증 물리량이 정의되어 있다.
 2. Research evidence complete: 정식화와 benchmark 근거가 신뢰도와 한계와 함께 정리되어 있다.
 3. Formulation reviewed: 약형, shape function, B matrix, constitutive contract, 수치적분, output recovery가 검토되어 있다.
-4. I/O contract approved: Abaqus keyword subset, internal model mapping, HDF5 result contract, reference CSV comparison row contract가 승인되어 있다.
-5. Tests fail before implementation: 구현 전 실패해야 하는 C++/integration/reference test가 준비되어 있다.
+4. I/O contract approved: Abaqus keyword subset, internal model mapping, HDF5 result contract,
+   required reference quantity의 최소 source-ID/component matching이 승인되어 있다.
+5. Tests fail before implementation: C++/integration/reference test를 제품 코드보다 먼저 작성하고 같은 Step 안에서 RED 실패와 후속 GREEN 성공을 확인한다.
 6. CMake/CTest pass: MSVC/x64/Debug 기준 configure, build, test가 통과한다.
-7. Reference comparison pass: FESA `results.h5` rows와 Abaqus reference CSV rows가 documented IDs, components, units, coordinate system, step/frame identity, tolerance 기준 안에 있다.
-8. Physics sanity pass: equilibrium, reaction consistency, displacement direction, symmetry, stress sanity가 검토되어 있다.
+7. Reference comparison pass: 기능이 blocking으로 선언한 FESA `results.h5` quantity가
+   선언된 Abaqus CSV와 source identity/component별로 대응되고 승인된 tolerance 안에 있다.
+8. Physics sanity pass: equilibrium, reaction consistency, displacement direction, symmetry, section-force consistency와 normalized residual이 검토되어 있다.
 9. Release readiness pass: acceptance traceability, known limitations, release notes draft가 준비되어 있다.
 
 ## 제외 사항
 - Abaqus full parser 호환
+- Abaqus B31/Timoshenko beam
+- 다중 analysis step과 step 간 load/BC propagation
+- instance translation/rotation, nested assembly 및 dependent/independent mesh semantics
+- `I12 != 0`, taper, offset, release, curved beam, warping
+- Abaqus `*DLOAD` 입력과 Domain distributed-load object
+- 기하·재료비선형, dynamics, contact, thermal effects
+- transverse shear stress와 torsional shear stress recovery
+- beam stress에 대한 Abaqus reference comparison
 - Abaqus, Nastran 또는 reference solver 직접 실행 자동화
 - Agent가 Abaqus reference CSV 파일을 임의 생성 또는 수정하는 작업
 - GUI 또는 postprocessor
 - Visual Studio `.sln`/`.vcxproj` 전용 MSBuild workflow
-- Explicit dynamics, contact, plasticity, shell end-to-end 구현
-- JavaScript/TypeScript fallback 유지
+- plasticity와 shell end-to-end 구현

docs/SOLVER_AGENT_DESIGN.md

@@ -9,9 +9,29 @@
 - 기능 요구조건, 이론 정식화, 코드 구현, 검증, 배포 역할을 분리한다.
 - 실행 가능성만으로 성공을 판단하지 않고, 레퍼런스 결과와 물리량을 비교해 기능 완료를 판정한다.
 - 테스트는 구현 전에 준비한다. 개발 대상 솔버 테스트와 레퍼런스 솔버 결과 비교 테스트를 함께 사용한다.
-- Abaqus나 Nastran을 Agent가 직접 실행하지 않는다. `reference/<model-id>/`에 저장된 `model.inp`, `metadata.json`, Abaqus reference CSV files를 검증 기준으로 사용한다.
+- Abaqus나 Nastran을 Agent가 직접 실행하지 않는다. 기능이 선언한 기존 `.inp`와 실제
+  비교에 필요한 Abaqus CSV만 read-only 검증 기준으로 사용한다. Canonical naming,
+  README, metadata, version 또는 provenance는 기본 readiness 조건이 아니다.
+- FESA는 Abaqus와 독립적인 solver다. Agent는 Abaqus 내부 formulation, integration,
+  stabilization 또는 recovery equivalence를 요구하거나 추론하지 않는다.
 - 기본 개발 환경은 C++17 이상, MSVC, CMake, CTest이다.
 - 모든 기능은 tolerance 기준을 명시하고, 기준을 만족할 때만 배포 후보가 된다.
+- Harness 운영은 `docs/HARNESS_WORKFLOW.md`의 계획, 독립 Step 실행, PreToolUse/Stop 검증 계층을 따른다.
+
+## Harness Step 실행 계약
+
+계획과 구현 Agent는 작업 전 `docs/HARNESS.md`와 `docs/HARNESS_WORKFLOW.md`를 읽는다.
+Implementation Planning Agent는 multi-Step 초안을 사용자에게 승인받은 뒤 planning files만
+materialize하며 Step을 선택하거나 실행하지 않는다. Executor는 별도의 명시적 사용자 요청으로
+`scripts/execute.py`를 실행할 때 branch, pending Step 선택, retry, timestamps, commits, Step
+advancement와 phase status를 소유한다.
+
+Implementation Agent는 approved plan, materialized phase files, Executor-selected current
+`stepN.md`만 사용해 `RED -> observed failure -> minimal GREEN -> focused/full VERIFY`를 완료하고
+다음 Step을 시작하지 않는다. Agent가 쓸 수 있는 Harness metadata는 current Step의 `status`와
+`summary`, `error_message`, `blocked_reason` payload뿐이다. `.codex/hooks.json`이 PreToolUse
+interception과 Stop whole-project validation을 자동 실행하므로 hook entry point를 수동 실행해
+대체하지 않는다. 세부 schema와 recovery 절차는 `docs/HARNESS_WORKFLOW.md`를 따른다.
 
 ## 전체 Agent 구성
 
@@ -110,12 +130,13 @@
 - 단위와 좌표계 규약
 
 ### Reference Model Agent
-TDD와 검증에 사용할 테스트 모델을 준비하는 Agent이다.
+TDD와 검증에 사용할 기존 reference case를 inventory하는 Agent이다.
 
 책임:
-- 개발 대상 기능을 검증할 최소 모델, benchmark 모델, 회귀 모델을 설계한다.
-- `reference/<model-id>/`에 보관할 Abaqus input file, metadata, Abaqus reference CSV 요구사항을 정의한다.
-- 레퍼런스 결과에 포함될 물리량과 tolerance를 명시한다.
+- 기능이 요구할 때만 테스트 모델 목적을 구분하고, 기본적으로 기존 case를 사용한다.
+- 기존 reference case의 목적, exact input/required CSV path, blocking/warning quantity와
+  tolerance를 inventory한다.
+- FESA HDF5 quantity와 source ID/component matching을 명시한다.
 - 테스트 모델이 요구조건을 실제로 검증하는지 확인한다.
 
 중요 제약:
@@ -123,18 +144,17 @@ TDD와 검증에 사용할 테스트 모델을 준비하는 Agent이다.
 - Abaqus 해석 결과 CSV는 사람이 생성하거나 별도 승인된 절차로 생성해 `reference/<model-id>/`에 저장한다.
 - Agent는 저장된 reference artifact만 사용해 비교한다.
 
-권장 reference 구조:
+최소 reference case 구조:
 ```text
 reference/
-  <model-id>/
-    model.inp
-    metadata.json
-    <model-id>_displacements.csv
-    <model-id>_reactions.csv
-    <model-id>_internalforces.csv
-    <model-id>_stresses.csv
+  <case-dir>/
+    <declared-input>.inp
+    <declared-required-quantity>.csv
 ```
 
+Directory와 filename은 제공된 값을 그대로 사용한다. Reference Model Agent는 canonical
+이름, README, metadata, provenance 또는 비교하지 않는 quantity CSV를 요구하지 않는다.
+
 ### Implementation Planning Agent
 코드 구현 전에 작업 단위와 테스트 순서를 설계하는 Agent이다.
 
@@ -149,15 +169,33 @@ reference/
 - 테스트 우선순위
 - 변경 파일 후보
 - acceptance checklist
+- 사용자 승인 전 multi-Step Harness 초안
+- 승인 후 `phases/index.json`, `phases/<task-name>/index.json`, 자기완결적 `stepN.md`
+
+필수 절차:
+- 구현 계획 요청에서 project-local `$harness` skill을 사용한다.
+- `docs/HARNESS.md`와 `docs/HARNESS_WORKFLOW.md`를 읽고 multi-Step 초안만 사용자에게
+  제시한다.
+- 한 Step은 하나의 layer/module만 다루고 각 Step에 prerequisite file, TDD
+  RED/GREEN/VERIFY, 정확한 MSVC/CMake/CTest command와 금지사항을 포함한다.
+- Step 초안을 먼저 사용자에게 제시한다. 승인 전에는 `phases/` 파일을 생성하지 않는다.
+- 승인 후에는 planning files만 materialize하고 Step 선택/실행은 하지 않는다. Harness executor
+  실행은 별도 사용자 요청이 있을 때만 수행한다.
 
 ### Implementation Agent
 C++ 코드를 구현하는 Agent이다.
 
 책임:
+- `docs/HARNESS.md`, `docs/HARNESS_WORKFLOW.md`, materialized phase files와
+  Executor-selected current `stepN.md`를 읽고 현재 Step만 수행한다.
 - 테스트를 먼저 작성하고 실패를 확인한다.
 - 정식화와 I/O schema에 맞춰 최소 구현을 작성한다.
 - C++17 이상, MSVC, CMake, CTest 환경에서 동작하도록 구현한다.
 - 불필요한 일반화나 speculative abstraction을 피한다.
+- current Step의 `status`와 `summary`, `error_message`, `blocked_reason`만 기록한다.
+  branch, retry, timestamp, commit, advancement는 Executor에 맡긴다.
+- `.codex/hooks.json`으로 자동 등록된 PreToolUse와 Stop을 사용하며 hook script를 수동
+  검증 대체물로 실행하지 않는다.
 
 주요 산출물:
 - C++ source/header 변경
@@ -168,15 +206,20 @@ C++ 코드를 구현하는 Agent이다.
 빌드와 테스트를 실행하는 Agent이다.
 
 책임:
-- Harness validation을 실행한다.
+- `.harness/config.json` 또는 자동 감지 결과에 맞는 MSVC build/test 명령을 실행한다.
 - MSVC x64 Debug CMake configure/build/CTest 결과를 수집한다.
 - 실패 로그를 요약하고 Correction Agent에 전달한다.
 
-기본 검증 명령:
+기본 CMake 검증 명령:
 ```powershell
-python scripts/validate_workspace.py
+cmake -S . -B .harness/build -A x64
+cmake --build .harness/build --config Debug
+ctest --test-dir .harness/build -C Debug --show-only=json-v1
+ctest --test-dir .harness/build -C Debug --output-on-failure
 ```
 
+Preset 또는 직접 MSBuild 프로젝트는 `.harness/config.json`에 선언된 명령을 따른다.
+
 검증 대상:
 - CMake configure
 - MSVC Debug build
@@ -245,7 +288,7 @@ python scripts/validate_workspace.py
 | 2. 연구자료 조사 | Research Agent | 자료 요약, benchmark 후보 |
 | 3. 유한요소 정식화 | Formulation Agent, Numerical Review Agent | 정식화 문서, 리뷰 결과 |
 | 4. 입출력 데이터 정의 | I/O Definition Agent | 입력/출력 schema |
-| 5. TDD 테스트모델 작성 | Reference Model Agent, Implementation Planning Agent | 테스트 모델, reference artifact 요구사항 |
+| 5. Reference case 준비 | Reference Model Agent, Implementation Planning Agent | 기존 input/required CSV inventory, 비교 mapping, tolerance |
 | 6. 코드 구현 | Implementation Agent | C++ 코드, 테스트 |
 | 7. 레퍼런스 결과 비교 검증 | Reference Verification Agent, Physics Evaluation Agent | 비교 리포트, 물리 검토 |
 | 8. tolerance 만족 시 완료 | Coordinator Agent | 기능 완료 승인 |
@@ -269,8 +312,7 @@ flowchart TD
   L --> I
   K -- "예" --> M["Reference Verification Agent"]
   M --> N{"tolerance 만족?"}
-  N -- "아니오" --> O["Physics Evaluation Agent"]
-  O --> L
+  N -- "아니오" --> L
   N -- "예" --> P["Physics Evaluation Agent"]
   P --> Q{"물리 검토 통과?"}
   Q -- "아니오" --> L
@@ -294,20 +336,22 @@ flowchart TD
 ### Gate 3: 테스트 준비 승인
 통과 조건:
 - 구현 전 실패해야 하는 테스트가 정의되어 있다.
-- `reference/<model-id>/` artifact 요구사항이 명확하다.
-- 최소 모델, benchmark 모델, 회귀 모델의 목적이 구분되어 있다.
+- 기능이 요구하는 기존 input/CSV pair와 blocking/warning quantity가 명확하다.
+- 필요한 source ID/component matching과 tolerance가 정의되어 있다.
 
 ### Gate 4: 구현 검증
 통과 조건:
 - CMake/MSVC/CTest validation이 통과한다.
 - 단위 테스트와 통합 테스트가 통과한다.
-- Harness TDD guard를 만족한다.
+- 관련 C++ test file이 있고 같은 구현 Step 안에 RED 실패와 후속 GREEN 성공 증거가 있다.
+- Stop의 전체 MSVC build/test 검증이 통과한다.
 
 ### Gate 5: 레퍼런스 검증
 통과 조건:
-- Abaqus reference CSV 결과와 구현 solver HDF5 결과가 tolerance 안에 있다.
-- 절점 변위, 반력, 요소 내력, 응력 비교 결과가 리포트로 남아 있다.
-- 실패한 물리량이 없거나 승인된 known limitation으로 기록되어 있다.
+- 기능이 blocking으로 선언한 Abaqus CSV quantity와 구현 solver HDF5 quantity가
+  tolerance 안에 있다.
+- Warning-only quantity는 결과와 경고가 리포트에 남고 pass/fail을 바꾸지 않는다.
+- Required source row/component의 누락, 추가, 중복 또는 nonfinite 값이 없다.
 
 ### Gate 6: 배포 승인
 통과 조건:
@@ -352,17 +396,20 @@ Coordinator Agent는 분류 결과에 따라 Requirement, Formulation, I/O Defin
 ## 초기 적용 우선순위
 
 1. 선형 정적 해석의 최소 골격
-2. 1D truss 또는 bar element
-3. 2D plane stress/plane strain element
-4. 3D solid element
-5. material model 확장
-6. nonlinear 또는 dynamic analysis 확장
+2. Isoparametric 3D Euler beam element
+3. 1D truss 또는 bar element
+4. 2D plane stress/plane strain element
+5. 3D solid element
+6. material model 확장
+7. nonlinear 또는 dynamic analysis 확장
 
 각 단계는 요구조건, 정식화, 테스트모델, 구현, 레퍼런스 비교, 배포 Gate를 독립적으로 통과해야 한다.
 
 ## 운영 메모
 
 - Agent 산출물은 가능한 한 문서, 테스트, 비교 리포트 형태로 남긴다.
-- 사람이 생성한 Abaqus reference artifact의 출처와 생성 조건을 `metadata.json`에 기록한다.
+- 사람이 제공한 Abaqus reference artifact는 현재 path/name 그대로 read-only로 사용한다.
+  별도 provenance, README 또는 metadata가 없다는 이유로 gate를 차단하지 않는다.
 - reference artifact가 바뀌면 기능 구현 변경과 같은 수준으로 검토한다.
-- 기능 완료 판정은 코드 실행 성공이 아니라 reference validation과 physics evaluation 통과를 기준으로 한다.
+- 기능 구현 완료 판정은 build/test와 기능별 blocking reference validation 통과를 기준으로
+  한다. Physics evaluation과 release readiness는 별도 후속 배포 gate다.

docs/SOLVER_SKILL_DESIGN.md

@@ -15,7 +15,8 @@ Agent는 역할과 책임 단위이고, skill은 여러 Agent가 반복적으로
 - Abaqus, Nastran 또는 reference solver 실행은 skill 범위에 포함하지 않는다.
 - Abaqus reference CSV 파일 생성/수정은 skill 범위에 포함하지 않는다.
 - C++ 구현 관련 skill은 C++17 이상, MSVC, CMake, CTest, TDD 원칙을 따른다.
-- 기본 workspace validation 명령은 `python scripts/validate_workspace.py`이다.
+- C++ 검증 명령은 `.harness/config.json` 또는 `docs/HARNESS.md`의 자동 감지 기본값을 따른다.
+- Harness Python 변경은 `uv run --with pytest python -m pytest -v -rs`로 검증한다.
 
 ## Skill 구성
 
@@ -34,15 +35,18 @@ Agent는 역할과 책임 단위이고, skill은 여러 Agent가 반복적으로
 
 ## 개발 과정별 사용 예
 
-예시 기능: `linear-truss-1d`
+예시 기능: `isoparametric-3d-euler-beam`
 
 1. Requirement Agent는 `fesa-requirements-baseline`을 사용해 기능 범위, 제외 범위, 입력, 출력, 검증 물리량, tolerance, `Requirement Verification Matrix`를 작성한다.
-2. Research Agent는 `fesa-research-evidence`를 사용해 truss/bar element 이론, benchmark 후보, source reliability, applicability limits를 정리한다.
+2. Research Agent는 `fesa-research-evidence`를 사용해 3D Euler beam element 이론, benchmark 후보, source reliability, applicability limits를 정리한다.
 3. Formulation Agent는 `fesa-formulation-spec`을 사용해 strong form, weak form, shape functions, B matrix, element stiffness, output recovery를 정리한다.
 4. Numerical Review Agent는 `fesa-numerical-review`를 사용해 rigid body modes, patch test, stiffness symmetry, Jacobian, locking 위험을 검토하고 `pass-for-implementation-planning` 여부를 판단한다.
 5. I/O Definition Agent는 `fesa-io-contract`를 사용해 지원할 Abaqus `.inp` keyword subset, `results.h5` schema, reference CSV comparison row schema를 정의한다.
-6. Reference Model Agent는 `fesa-reference-models`를 사용해 `reference/<model-id>/` artifact bundle 계약과 coverage matrix를 작성한다.
-7. Implementation Planning Agent와 Implementation Agent는 `fesa-cpp-msvc-tdd`를 사용해 테스트 작성, 실패 확인, 최소 구현, CMake/CTest 등록, validation을 수행한다.
+6. Reference Model Agent는 `fesa-reference-models`를 사용해 기존 input/required CSV
+   reference-case inventory와 비교 mapping을 작성한다.
+7. Implementation Planning Agent는 먼저 project-local `harness`를 사용해 사용자 승인용
+   multi-Step 초안을 만들고, 승인 후 phase files를 생성한다. 그 뒤 Implementation Agent와
+   함께 `fesa-cpp-msvc-tdd` 계약에 따라 RED/GREEN/VERIFY를 수행한다.
 8. Reference Verification Agent는 `fesa-reference-comparison`을 사용해 구현 solver `results.h5` rows와 Abaqus reference CSV rows를 tolerance 기준으로 비교한다.
 9. Physics Evaluation Agent는 `fesa-physics-sanity`를 사용해 global equilibrium, reaction consistency, displacement direction, symmetry, model coverage를 검토한다.
 10. Release Agent는 `fesa-release-readiness`를 사용해 gate evidence, acceptance traceability, known limitations, release notes draft를 작성한다.
@@ -76,6 +80,8 @@ Agent는 역할과 책임 단위이고, skill은 여러 Agent가 반복적으로
 - dimensions, signs, DOF ordering, coordinate transforms, Jacobian, integration rule, stiffness symmetry, rigid body modes, patch test, hourglass, locking을 확인한다.
 - `pass-for-implementation-planning`은 구현 계획 가능 상태만 의미한다.
 - 정식화 문서를 직접 수정하지 않는다.
+- 이후 Reference Model 문서, artifact naming, README, metadata, provenance 또는 portfolio가
+  없다는 이유로 formulation verdict를 실패시키지 않는다.
 
 ### `fesa-io-contract`
 
@@ -86,10 +92,11 @@ Agent는 역할과 책임 단위이고, skill은 여러 Agent가 반복적으로
 
 ### `fesa-reference-models`
 
-- smoke, analytical, patch test, benchmark, regression, negative/invalid-input 모델을 구분한다.
-- `reference/<model-id>/` artifact bundle 계약을 정의한다.
-- `model.inp`, `metadata.json`, `<model-id>_displacements.csv`, `<model-id>_reactions.csv`, `<model-id>_internalforces.csv`, `<model-id>_stresses.csv`를 기준 artifact로 둔다.
-- required Abaqus reference CSV가 없으면 완료 상태가 아니라 `needs-reference-artifacts`로 둔다.
+- 기능이 실제로 사용하는 기존 reference case를 inventory한다.
+- Exact input/required CSV path, case purpose, blocking/warning quantity, HDF5 projection,
+  source ID/component matching과 tolerance만 정의한다.
+- Required comparison file이 없을 때만 `needs-reference-artifacts`로 둔다. Canonical naming,
+  README, metadata, provenance와 비교하지 않는 quantity CSV는 요구하지 않는다.
 
 ### `fesa-cpp-msvc-tdd`
 
@@ -98,18 +105,37 @@ Agent는 역할과 책임 단위이고, skill은 여러 Agent가 반복적으로
 - 기본 검증 명령:
 
 ```powershell
-python -m unittest discover -s scripts -p "test_*.py"
-python scripts/validate_workspace.py
-ctest -C Debug -R <feature-or-label>
+cmake -S . -B .harness/build -A x64
+cmake --build .harness/build --config Debug
+ctest --test-dir .harness/build -C Debug -R <feature-or-label> --output-on-failure
+ctest --test-dir .harness/build -C Debug --output-on-failure
+```
+
+Preset 또는 직접 MSBuild 프로젝트는 `.harness/config.json`의 설정을 사용한다. Harness
+Python, Hook, agent config를 변경한 경우에는 다음 명령도 실행한다.
+
+```powershell
+uv run --with pytest python -m pytest -v -rs
 ```
 
 - 실패는 `configure | compile | link | test | reference-comparison | harness | environment | upstream-contract`로 분류한다.
 - 요구조건, 정식화, I/O 계약, reference artifact, tolerance policy를 바꾸지 않는다.
 
+### project-local `harness`
+
+- Implementation Planning Agent가 구현 요청을 여러 독립 Step으로 분해할 때 사용한다.
+- 한 Step은 하나의 layer/module만 소유하고 prerequisite file, TDD RED/GREEN/VERIFY,
+  exact acceptance command와 구체적 금지사항을 포함한다.
+- 사용자에게 Step 초안을 먼저 제시한다. 승인 후에만 `phases/index.json`,
+  `phases/<task-name>/index.json`, `phases/<task-name>/stepN.md`를 생성한다.
+- 계획 작성과 executor 실행을 구분하며, `scripts/execute.py`는 별도 사용자 요청 없이
+  실행하지 않는다.
+
 ### `fesa-reference-comparison`
 
 - `ARTIFACT CHECK -> COMPARE -> CLASSIFY -> REPORT` 순서로 수행한다.
-- `metadata.json`, `model.inp`, `results.h5`, Abaqus reference CSV files, schema version, units, coordinate system, step/frame identity, ID matching, output location, tolerance source를 확인한다.
+- 선언된 input, required Abaqus CSV, `results.h5`, source ID/component mapping과 tolerance를
+  확인한다. Missing/extra/duplicate/nonfinite required row는 비교 전에 실패한다.
 - max absolute error, max relative error, RMS error, norm error, missing rows, extra rows를 보고한다.
 - Reference pass는 physics validation이나 release readiness를 의미하지 않는다.
 
@@ -138,7 +164,7 @@ ctest -C Debug -R <feature-or-label>
 | Numerical Review Agent | `fesa-numerical-review` |
 | I/O Definition Agent | `fesa-io-contract` |
 | Reference Model Agent | `fesa-reference-models` |
-| Implementation Planning Agent | `fesa-formulation-spec`, `fesa-reference-models`, `fesa-cpp-msvc-tdd` |
+| Implementation Planning Agent | project-local `harness`, `fesa-formulation-spec`, `fesa-reference-models`, `fesa-cpp-msvc-tdd` |
 | Implementation Agent | `fesa-cpp-msvc-tdd` |
 | Build/Test Executor Agent | `fesa-cpp-msvc-tdd` |
 | Correction Agent | `fesa-cpp-msvc-tdd` |
@@ -148,7 +174,8 @@ ctest -C Debug -R <feature-or-label>
 
 ## 검증 기준
 
-Skill 구성 검증은 `scripts/test_fesa_solver_skills.py`가 담당한다.
+Skill 구성은 실제 `.codex/skills/` 파일을 source of truth로 삼아 정적 계약과 repository
+pytest suite로 검증한다.
 
 검증 항목:
 
@@ -163,15 +190,11 @@ Skill 구성 검증은 `scripts/test_fesa_solver_skills.py`가 담당한다.
 검증 명령:
 
 ```powershell
-python -m unittest discover -s scripts -p "test_*.py"
-python scripts/validate_workspace.py
+uv run --with pytest python -m pytest -v -rs
 ```
 
-Skill 구조 검증:
-
-```powershell
-python C:\Users\user\.codex\skills\.system\skill-creator\scripts\quick_validate.py .codex\skills\<skill-name>
-```
+개별 skill schema를 점검할 때는 현재 Codex 설치에 포함된 `skill-creator` validator를
+사용하되 사용자 홈을 하드코딩한 경로를 프로젝트 계약으로 두지 않는다.
 
 ## v1 범위
 

docs/archive/ProjectInitialPlanNote.md

@@ -1,5 +1,11 @@
 # FESA 초기 문서 완성 계획 노트
 
+> **Historical / Superseded:** 이 문서는 2026-06-10 시점의 초기 조사와 실행 기록이다.
+> 현재 제품 범위는 `docs/PRD.md`, Harness 운영 계약은 `docs/HARNESS_WORKFLOW.md`와
+> `docs/HARNESS.md`를 따른다. 아래의 구형 스킬명, 검증 명령, 기능 우선순위는 현재
+> 지침으로 사용하지 않는다. 아래의 `metadata.json` 필수 provenance 문구도 ADR-010의
+> 선택-artifact 정책으로 대체되었다.
+
 ## 메타데이터
 - 작성일: 2026-06-10
 - 목적: `AGENTS.md`, `docs/PRD.md`, `docs/ARCHITECTURE.md`를 유한요소법 기반 구조해석 솔버 개발 프로젝트 문서로 완성하기 위한 조사 내용과 실행 계획 정리

docs/build-test-reports/README.md

@@ -2,16 +2,17 @@
 
 이 디렉터리는 Build/Test Executor Agent가 작성하거나 제안하는 기능별 build/test 실행 리포트를 보관하는 위치다.
 
-Build/Test Executor Agent는 Implementation Agent 이후 독립적으로 C++/MSVC/CMake/CTest 검증을 실행하고, 실패를 분류해 다음 agent로 handoff한다. 이 agent는 source code, tests, CMake files, requirements, formulations, I/O contracts, reference artifacts, tolerance policies를 수정하지 않는다. build artifacts와 test outputs는 `build/` 아래 생성될 수 있다.
+Build/Test Executor Agent는 Implementation Agent 이후 독립적으로 C++/MSVC/CMake/CTest 검증을 실행하고, 실패를 분류해 다음 agent로 handoff한다. 이 agent는 source code, tests, CMake files, requirements, formulations, I/O contracts, reference artifacts, tolerance policies를 수정하지 않는다. 기본 build artifact는 `.harness/build/` 아래 생성된다.
 
 기본 문서명은 `docs/build-test-reports/<feature-id>-build-test.md` 형식을 사용한다.
 
 ## Build/Test Executor Agent 역할
 
 수행한다:
-- `python scripts/validate_workspace.py`를 기본 검증 명령으로 실행한다.
-- implementation plan/report에 명시된 경우 harness self-test와 feature-specific CTest를 실행한다.
-- `HARNESS_VALIDATION_COMMANDS`, `CMakePresets.json`의 `msvc-debug`, 기본 CMake/MSVC x64 Debug 경로 중 어떤 검증 경로가 사용되었는지 기록한다.
+- `.harness/config.json`과 프로젝트 자동 감지 결과를 확인하고 같은 build/test 경로를 독립 실행한다.
+- implementation plan/report에 명시된 feature-specific CTest를 전체 검증 전에 실행한다.
+- Harness Python, Hook, agent config 변경이 포함되면 `uv run --with pytest python -m pytest -v -rs`를 실행한다.
+- CMake preset, 직접 MSBuild, 기본 CMake/MSVC x64 Debug 중 어떤 검증 경로가 사용되었는지 기록한다.
 - configure, compile, link, test, reference-comparison, harness, environment, upstream-contract 실패를 구분한다.
 - command, exit code, duration, stdout/stderr tail, failed test name을 요약한다.
 - 실패 원인에 따라 Implementation Agent, Correction Agent, Reference Verification Agent, Implementation Planning Agent 중 handoff 대상을 제안한다.
@@ -28,29 +29,43 @@ Build/Test Executor Agent는 Implementation Agent 이후 독립적으로 C++/MSV
 
 ## 실행 순서
 
-기본 순서는 implementation plan/report에 따라 다음 중 필요한 항목만 실행한다.
+기본 순서는 implementation plan/report에 따라 다음 중 필요한 항목을 실행한다.
 
 ```powershell
-python -m unittest discover -s scripts -p "test_*.py"
-ctest -C Debug -R <feature-or-label>
-python scripts/validate_workspace.py
+cmake -S . -B .harness/build -A x64
+cmake --build .harness/build --config Debug
+ctest --test-dir .harness/build -C Debug -R <feature-or-label> --output-on-failure
+ctest --test-dir .harness/build -C Debug --show-only=json-v1
+ctest --test-dir .harness/build -C Debug --output-on-failure
 ```
 
-`scripts/validate_workspace.py`의 command discovery 우선순위는 다음과 같다.
+Harness Python, Hook, agent config 변경이 검증 범위에 포함되면 다음 명령을 먼저 실행한다.
 
-1. `HARNESS_VALIDATION_COMMANDS`
-2. `CMakePresets.json`의 `msvc-debug`
-3. 기본 CMake/MSVC x64 Debug 명령
-4. `CMakeLists.txt`가 없고 override도 없으면 안내 메시지와 함께 성공 종료
+```powershell
+uv run --with pytest python -m pytest -v -rs
+```
+
+프로젝트 선택 우선순위는 다음과 같다.
+
+1. `.harness/config.json`의 명시적 `projectType`
+2. 루트의 CMake metadata
+3. 루트의 단일 `.sln`
+4. 루트의 단일 `.vcxproj`
 
 기본 CMake/MSVC x64 Debug 명령은 다음과 같다.
 
 ```powershell
-cmake -S . -B build/msvc-debug -G "Visual Studio 17 2022" -A x64
-cmake --build build/msvc-debug --config Debug
-ctest --test-dir build/msvc-debug --output-on-failure -C Debug
+cmake -S . -B .harness/build -A x64
+cmake --build .harness/build --config Debug
+ctest --test-dir .harness/build -C Debug --show-only=json-v1
+ctest --test-dir .harness/build -C Debug --output-on-failure
 ```
 
+CMake preset을 사용하면 configure/build/test preset과 `binaryDir`를 모두
+`.harness/config.json`에 지정한다. 직접 MSBuild는 solution/project와
+`msbuild.testCommand`를 지정한다. C/C++와 build metadata가 모두 없으면 검증 대상이
+없으므로 통과하지만, C/C++ 파일만 있고 build metadata가 없으면 오류다.
+
 ## 문서 템플릿
 
 ```markdown
@@ -69,17 +84,19 @@ ctest --test-dir build/msvc-debug --output-on-failure -C Debug
 - generator: Visual Studio 17 2022 | <observed generator>
 - platform: x64 | <observed platform>
 - config: Debug | <observed config>
-- build_dir: build/msvc-debug | <observed build dir>
-- active_override_env_vars: HARNESS_VALIDATION_COMMANDS | HARNESS_CMAKE_GENERATOR | HARNESS_CMAKE_PLATFORM | HARNESS_CMAKE_CONFIG | HARNESS_BUILD_DIR | none
-- command_discovery_path: HARNESS_VALIDATION_COMMANDS | CMakePresets.json msvc-debug | default CMake/MSVC x64 Debug | no-CMake informational success
+- build_dir: .harness/build | <configured/observed build dir>
+- harness_config: .harness/config.json | absent-defaults
+- project_selection: configured cmake | configured msbuild | auto CMake | auto MSBuild | no C/C++ project
+- command_discovery_path: CMake preset | direct MSBuild | default CMake/MSVC x64 Debug | no C/C++ project
 
 ## Command Log Summary
 
 | order | command | exit_code | duration | stdout_stderr_tail |
 | --- | --- | --- | --- | --- |
-| 1 | python -m unittest discover -s scripts -p "test_*.py" | <code> | <duration> | <tail summary> |
-| 2 | ctest -C Debug -R <feature-or-label> | <code> | <duration> | <tail summary> |
-| 3 | python scripts/validate_workspace.py | <code> | <duration> | <tail summary> |
+| 1 | uv run --with pytest python -m pytest -v -rs (when applicable) | <code or skipped> | <duration> | <tail summary> |
+| 2 | <config-resolved configure/build commands> | <code> | <duration> | <tail summary> |
+| 3 | <feature-specific test command when applicable> | <code or skipped> | <duration> | <tail summary> |
+| 4 | <config-resolved test discovery/full test commands> | <code> | <duration> | <tail summary> |
 
 ## Validation Results
 
@@ -137,7 +154,7 @@ ctest --test-dir build/msvc-debug --output-on-failure -C Debug
 - 모든 실행 명령과 exit code를 기록해야 한다.
 - 실패 로그는 전체 원문을 복제하지 않고 마지막 핵심 구간과 실패 원인을 요약한다.
 - configure, compile, link, test, reference-comparison, harness, environment, upstream-contract 실패를 구분한다.
-- no-CMake 상황은 `scripts/validate_workspace.py` 정책대로 안내 메시지와 성공 종료로 기록한다.
+- C/C++와 build metadata가 모두 없는 상황만 `no C/C++ project` 성공으로 기록한다. C/C++ 파일이 있는데 build metadata가 없으면 `environment` 또는 `configure` 실패로 기록한다.
 - 성공 판정은 build/test 통과까지만 의미한다.
 - reference tolerance, physics validation, release readiness는 판정하지 않는다.
 - upstream 계약 문제는 Implementation Agent에 임의 수정으로 넘기지 않고 적절한 upstream agent로 handoff한다.

docs/build-test-reports/linear-static-3d-euler-beam.md

@@ -0,0 +1,238 @@
+# Linear Static 3D Euler Beam Build/Test Report
+
+## Metadata
+
+- feature_id: `linear-static-3d-euler-beam`
+- source_commit: `400db191ce9f766ca6b34e5b609eaa13c54ccfa3`
+- source_implementation_report: `docs/implementation-plans/linear-static-3d-euler-beam-implementation-report.md`
+- source_implementation_plan: `docs/implementation-plans/linear-static-3d-euler-beam.md`
+- status: `pass-for-reference-verification`
+- owner_agent: `build-test-executor-agent`
+- date: `2026-08-09`
+- evidence_window: `2026-08-09T23:16:20.8670416+09:00` through `2026-08-09T23:20:15.7264584+09:00`
+
+## Verdict
+
+Fresh Visual Studio 18 2026/MSVC x64 Debug configuration, a clean full rebuild,
+the exact Step 25 configure/build commands, nonzero JSON discovery, the feature-label
+CTest run, and the full CTest run all passed. CTest discovered the expected 83 tests
+and both executed suites passed 83/83. The clean rebuild emitted no compiler or linker
+warning line, and generated FESA product projects retain Level 4 plus warnings-as-errors.
+
+The build/test gate therefore passes for handoff to Step 26 Reference Verification.
+This verdict does not approve reference tolerance, physics sanity, or release readiness.
+
+## Execution Environment
+
+- os: `Microsoft Windows 11 Home 10.0.26200 build 26200; 64-bit`
+- source_head: `400db191ce9f766ca6b34e5b609eaa13c54ccfa3`
+- generator: `Visual Studio 18 2026`
+- Visual Studio: `Community 18.8.2` (`18.8.12023.21`)
+- MSBuild: `18.8.2+ce25c0108`
+- compiler: `MSVC 19.51.36252.0`
+- compiler_architecture: `x64`
+- Windows SDK: `10.0.26100.0`
+- language: `C++17`, required, extensions disabled
+- config: `Debug`
+- build_dir: `.harness/build`
+- harness_config: absent; repository auto-CMake defaults plus Step 25 explicit cache values
+- project_selection: auto CMake from root `CMakeLists.txt`
+- command_discovery_path: default CMake/MSVC x64 Debug with explicit local dependency paths
+- CMake / CTest: `4.4.0 / 4.4.0`
+
+### Dependency Revisions
+
+| dependency | resolved revision or version | evidence |
+| --- | --- | --- |
+| GoogleTest | `04ee1b4f2aefdffb0135d7cf2a2c519fe50dabe4` | clean `C:/git/googletest` checkout HEAD |
+| Intel oneMKL | `2026.1.0` | `MKLConfigVersion.cmake`; configure reported `MKL_VERSION: 2026.1.0`, dynamic ILP64, Intel threading |
+| Intel oneTBB | `2023.1.0` | `TBBConfigVersion.cmake` from the configured `2023.1` package |
+| HDF5 | `2.1.1` | `hdf5-config-version.cmake` from the configured `2.1.1` package |
+
+## Freshness and Configuration Resolution
+
+The ignored generated build tree already existed. Fresh evidence was obtained without
+reusing its cache or products by running CMake `--fresh` with the generator explicitly
+fixed to Visual Studio 18 2026, then running the generated `clean` target before the
+full build. The literal no-`--fresh`, no-`-G` configure command from Step 25 was then
+run against that resolved VS18 cache and followed by the literal build, discovery,
+feature-label, and full-test commands.
+
+Post-configure metadata recorded:
+
+- `CMAKE_GENERATOR=Visual Studio 18 2026`
+- `CMAKE_GENERATOR_PLATFORM=x64`
+- `CMAKE_CXX_COMPILER_ID=MSVC`
+- `CMAKE_CXX_COMPILER_VERSION=19.51.36252.0`
+- `CMAKE_CXX_COMPILER_ARCHITECTURE_ID=x64`
+
+## Command Log Summary
+
+| order | command | start / end | exit code | duration | verdict and stdout/stderr tail |
+| ---: | --- | --- | ---: | ---: | --- |
+| 1 | `cmake --fresh -S . -B .harness/build -G "Visual Studio 18 2026" -A x64 -DFESA_GTEST_SOURCE_DIR=C:/git/googletest "-DMKL_DIR=C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl" "-DTBB_DIR=C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb" "-DHDF5_DIR=C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"` | `23:16:20.867+09:00` / `23:16:27.706+09:00` | 0 | `6.836 s` | pass; MKL 2026.1.0 and required runtime libraries resolved; `Configuring done`, `Generating done`, build files written to `.harness/build` |
+| 2 | `cmake --build .harness/build --config Debug --target clean` | `23:16:37.194+09:00` / `23:16:37.914+09:00` | 0 | `0.716 s` | pass; generated VS18 clean target completed |
+| 3 | `cmake --build .harness/build --config Debug` | `23:16:47.054+09:00` / `23:18:01.769+09:00` | 0 | `74.713 s` | pass; clean compile/link produced `fesa.exe` and all three test executables; warning scan count `0` |
+| 4 | `cmake -S . -B .harness/build -A x64 -DFESA_GTEST_SOURCE_DIR=C:/git/googletest "-DMKL_DIR=C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl" "-DTBB_DIR=C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb" "-DHDF5_DIR=C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"` | `23:19:10.210+09:00` / `23:19:10.861+09:00` | 0 | `0.649 s` | pass; exact Step 25 command selected Windows SDK 10.0.26100.0, retained VS18/x64, and completed configure/generate |
+| 5 | `cmake --build .harness/build --config Debug` | `23:19:25.404+09:00` / `23:19:28.969+09:00` | 0 | `3.562 s` | pass; exact Step 25 build confirmed `fesa_solver`, `fesa.exe`, and all test executables; warning scan count `0` |
+| 6 | `ctest --test-dir .harness/build -C Debug --show-only=json-v1` | `23:19:45.728+09:00` / `23:19:45.798+09:00` | 0 | `0.065 s` | pass; JSON kind `ctestInfo` version 1.0; 83 tests; every test has the feature label |
+| 7 | `ctest --test-dir .harness/build -C Debug -L linear-static-3d-euler-beam --output-on-failure` | `23:20:00.199+09:00` / `23:20:04.163+09:00` | 0 | `3.961 s` | pass; `100% tests passed out of 83`; real test time `3.92 s` |
+| 8 | `ctest --test-dir .harness/build -C Debug --output-on-failure` | `23:20:11.899+09:00` / `23:20:15.726+09:00` | 0 | `3.825 s` | pass; `100% tests passed out of 83`; real test time `3.79 s` |
+
+An initial post-clean discovery/feature/full smoke was also run before the literal
+configure replay: discovery exit 0 in `0.068 s` with 83 tests, feature-label CTest
+exit 0 in `4.244 s` with 83/83, and full CTest exit 0 in `4.011 s` with 83/83.
+Rows 4 through 8 are the final canonical Step 25 acceptance chain.
+
+## Validation Results
+
+| validation_stage | result | evidence |
+| --- | --- | --- |
+| harness self-test | skipped | No Harness Python, Hook, or agent-config file is part of HEAD `400db19` verification scope. |
+| fresh configure | pass | Explicit VS18/x64 `--fresh` configure exit 0, followed by clean target exit 0. |
+| exact configure | pass | Literal Step 25 configure exit 0; generated metadata is MSVC/x64. |
+| clean full build | pass | Exit 0 after clean; all source and test translation units compiled and linked. |
+| exact build | pass | Exit 0; product and three test executables confirmed. |
+| compiler/warning policy | pass | `fesa_solver` and `fesa_cli` generated projects have `Level4` and `TreatWarningAsError=true`; clean and exact build scans found zero warning lines. |
+| CTest discovery | pass | Exit 0; 83 tests, greater than zero and equal to the expected inventory. |
+| feature-specific tests | pass | Label `linear-static-3d-euler-beam`: 83/83 passed. |
+| full CTest | pass | 83/83 passed with zero failed tests. |
+| reference immutability | pass | Pre/post `git diff --exit-code -- reference/` exit 0, status empty, and four exact SHA-256 values unchanged. |
+| source worktree before report | pass | `git status --short` empty at HEAD `400db19`. |
+
+## CTest Inventory
+
+### Label Inventory
+
+| label | count |
+| --- | ---: |
+| `linear-static-3d-euler-beam` | 83 |
+| `unit` | 73 |
+| `integration` | 5 |
+| `reference` | 5 |
+
+### Suite Inventory and Step Trace
+
+| implementation Step | CTest suite or suites | count | cumulative count | Step 7-24 report evidence audit |
+| ---: | --- | ---: | ---: | --- |
+| 7 | `BuildInfo` | 2 | 2 | pass |
+| 8 | `CoreDiagnostics` | 3 | 5 | pass |
+| 9 | `DenseMath` | 2 | 7 | pass |
+| 10 | `DomainModel` | 3 | 10 | pass |
+| 11 | `InpSyntax` | 4 | 14 | pass |
+| 12 | `InpDomainMapping` | 5 | 19 | pass |
+| 13 | `AnalysisModel` | 3 | 22 | pass |
+| 14 | `DofManager` | 4 | 26 | pass |
+| 15 | `AnalysisState` | 3 | 29 | pass |
+| 16 | `EulerBeam3D` | 10 | 39 | pass |
+| 17 | `ParallelFor` | 3 | 42 | pass |
+| 18 | `SparseAssembly` | 5 | 47 | pass |
+| 19 | `EssentialConstraints` | 4 | 51 | pass |
+| 20 | `MklPardisoSolver` | 6 | 57 | pass |
+| 21 | `LoadAssembly` | 5 | 62 | pass |
+| 22 | `ResultRecovery` | 6 | 68 | pass |
+| 23 | `Hdf5ResultsWriter` | 5 | 73 | pass |
+| 24 | `LinearStaticCli` (5), `ReferenceComparisonContract` (4), `B33ReferenceComparison` (1) | 10 | 83 | pass |
+
+The JSON inventory contains every exact test name registered by GoogleTest discovery.
+No duplicate CTest name was observed; the label partition is exactly 73 unit + 5
+integration + 5 reference = 83.
+
+## Step 7-24 Implementation Evidence Audit
+
+The cumulative implementation report was checked block-by-block against the implementation
+plan and the phase index summaries. All 18 Step blocks are present and each records:
+
+- its matching `TASK-07` through `TASK-24`, `status: completed`, changed files,
+  requirement IDs, and test IDs;
+- at least one implementation-owned nonzero RED command with the expected missing API
+  or named behavioral failure;
+- a zero-exit GREEN build/test for the Step's targeted CTest suite;
+- zero-exit MSVC x64 configure/build, nonzero JSON discovery, and zero-failure full CTest;
+- `/W4 /WX` or equivalent generated warning-policy evidence and reference-tree
+  immutability evidence.
+
+Step 20 and Step 22 additionally retain valid behavioral RED/GREEN correction evidence.
+Step 23 records its environment link incident separately from the valid missing-API RED,
+so the environment incident was not counted as TDD evidence. The cumulative counts in the
+implementation report and the Step 7-24 phase summaries progress exactly to the freshly
+discovered 83-test inventory above.
+
+The implementation report's cumulative header still says `in-progress`; the audited
+step-local evidence contract and phase index nevertheless mark every implementation Step
+7-24 `completed`. This stale aggregate header is not a missing Step block, missing test,
+or failed build/test gate and was not modified by the independent executor.
+
+## `/W4 /WX` and Warning Audit
+
+- `src/fesa/CMakeLists.txt` applies `/W4 /WX` privately to `fesa_solver` and `fesa_cli`.
+- Generated `fesa_solver.vcxproj` and `fesa_cli.vcxproj` contain
+  `<WarningLevel>Level4</WarningLevel>` and
+  `<TreatWarningAsError>true</TreatWarningAsError>` for Debug and the other generated
+  configurations.
+- The clean 74.713-second build recompiled the product and all test translation units;
+  its compiler/linker warning scan found `0` lines.
+- The exact post-configure build also exited 0 and found `0` warning lines.
+
+Result: no product warning was emitted, and any MSVC product warning would have failed
+the build under `/WX`.
+
+## Reference Read-Only Audit
+
+The following SHA-256 values were identical before and after all configure/build/test
+commands, while both reference diff checks exited 0 and both reference status checks
+were empty:
+
+| exact approved legacy path | SHA-256 |
+| --- | --- |
+| `reference/cantilever beam/cantilever beam.inp` | `E406EA9560321B791DB829E03BD24593B9875E0195D35B86BD931EDA122EF3` |
+| `reference/cantilever beam/cantilever beam displacements.csv` | `7B3312FBC8848E81D9A0FD4FF2B56BC1954636A2C14B5C1CBB269CB9477D3C31` |
+| `reference/cantilever beam/cantilever beam reactions.csv` | `BF30CDB0CD50106885DE14D63492737736C587426EBD787DE4F7EE6AA86DAA23` |
+| `reference/cantilever beam/cantilever beam elemental forces.csv` | `E5E77FEC0FA9482AE018DBF296E74D396335C7C711BD2E9AA2315247A34290BA` |
+
+## Failure Classification
+
+- classification: `N/A`
+- primary_failure: `N/A`
+- first_failed_command: `N/A`
+- evidence_tail: All required configure, build, discovery, feature-label, and full-test
+  commands exited 0; no failed test exists.
+- correction_handoff: `N/A`; no implementation-owned, environment, harness, or
+  upstream-contract failure requires correction.
+
+## Failed Test Inventory
+
+None. Feature-label CTest and full CTest both passed 83/83.
+
+## Handoff Recommendation
+
+| target_agent | reason | required_input |
+| --- | --- | --- |
+| Reference Verification Agent | Step 25 build/test gate is `pass-for-reference-verification`. | This report, HEAD `400db19`, `.harness/build/tests/Debug/fesa_reference_tests.exe`, and the unchanged exact legacy bundle. |
+
+The build-local Step 24 evidence exists at
+`.harness/build/reference/cantilever-beam-b33/results.h5` and
+`.harness/build/reference/cantilever-beam-b33/comparison.json`; the JSON is 128,118 bytes
+with SHA-256
+`258347AEA791D981AEA9B2BCAD85DE5344D4859ECA3692DC5E7AA01A848F8E0D`.
+Step 26 must independently rerun and inspect the approved comparison evidence. Its
+presence and CTest success here are not a reference-verification verdict.
+
+## No-Change Assertion
+
+- source_files_modified: `false`
+- test_files_modified: `false`
+- cmake_files_modified: `false`
+- requirements_or_upstream_contracts_modified: `false`
+- reference_artifacts_modified: `false`
+- tolerance_policies_modified: `false`
+- owned_report_modified: `true`
+- phase_index_step25_modified: `true`
+- notes: Before report/index creation the worktree was clean at the audited HEAD. Final
+  scope validation is limited to this report and the Step 25 fields in the phase index.
+
+## Open Issues
+
+- None blocking Reference Verification.
+- The implementation report aggregate `in-progress` header is noted above but does not
+  contradict its 18 completed Step blocks, the phase index, or the fresh build/test result.

docs/build-test-reports/linear-static-mitc4-shell-build-test.md

@@ -0,0 +1,193 @@
+# Linear Static MITC4 Shell Build/Test Report
+
+## Metadata
+
+- feature_id: `linear-static-mitc4-shell`
+- source_commit: `820ba30c717b3d0e113775608e20dfd5fbc05d53`
+- source_implementation_report: `N/A`; Harness completion evidence is recorded in
+  `phases/linear-static-mitc4-shell/index.json`
+- source_implementation_plan:
+  `docs/implementation-plans/linear-static-mitc4-shell-implementation-plan.md`
+- status: `pass-for-reference-verification`
+- owner_agent: `build-test-executor-agent`
+- date: `2026-08-13`
+
+## Verdict
+
+The formal build/test gate passes. A fresh Visual Studio 18 2026/MSVC x64 Debug
+configuration, clean full rebuild, three implementation-plan-focused CTest runs,
+nonzero JSON discovery, full CTest regression, and the required Harness Python
+self-test all completed successfully.
+
+- clean full rebuild: exit `0`; compiler/linker warning scan `0`; error scan `0`
+- focused kernel/model/assembly/recovery regex: `87/87` passed
+- focused linear-static lifecycle regex: `10/10` passed
+- focused MITC4 reference-test regex: `8/8` passed
+- CTest discovery: `144` tests, including `32` names containing `Mitc4`
+- full CTest after clean rebuild: `144/144` passed
+- Harness Python self-test: `7/7` passed
+- failed tests: `0`
+- required S4 reference hash mismatches or Git changes: `0`
+
+This verdict authorizes handoff to Reference Verification only. It does not approve
+reference tolerance results, physics sanity, or release readiness.
+
+## Execution Environment
+
+- os: `Microsoft Windows 11 Home 10.0.26200 build 26200`
+- branch: `feat-linear-static-mitc4-shell`
+- source_head: `820ba30c717b3d0e113775608e20dfd5fbc05d53`
+- generator: `Visual Studio 18 2026`
+- MSBuild: `18.8.2+ce25c0108`
+- compiler: `MSVC 19.51.36252.0`
+- compiler_architecture: `x64`
+- Windows SDK: `10.0.26100.0`
+- language/config: `C++17 / Debug`
+- CMake: `4.4.0`
+- build_dir: `.harness/build`
+- harness_config: absent
+- project_selection: auto CMake from root `CMakeLists.txt`
+- command_discovery_path: default CMake/MSVC x64 Debug with implementation-plan
+  generator and dependency paths
+- resolved dependencies: GoogleTest `C:/git/googletest`; oneMKL `2026.1.0`;
+  oneTBB package path `2023.1`; HDF5 package path `2.1.1`
+
+The generated compiler metadata at
+`.harness/build/CMakeFiles/4.4.0/CMakeCXXCompiler.cmake` independently confirms
+`CMAKE_CXX_COMPILER_ID=MSVC` and version `19.51.36252.0`.
+
+## Command Log Summary
+
+All durations below are wall-clock durations measured for the command. The initial
+green chain was retained as corroborating evidence; the later clean-rebuild chain is
+the canonical acceptance evidence.
+
+| order | command | exit_code | duration | relevant stdout/stderr tail |
+| ---: | --- | ---: | ---: | --- |
+| 1 | `git status --short --branch; git rev-parse HEAD` | 0 | `0.8 s` | Clean `feat-linear-static-mitc4-shell`; HEAD matched `820ba30...`. |
+| 2 | Required dependency `Test-Path` precheck from the implementation plan | 0 | `0.215 s` | All four GoogleTest/MKL/TBB/HDF5 paths returned `True`. |
+| 3 | `cmake --fresh -S . -B .harness/build -G "Visual Studio 18 2026" -A x64 "-DFESA_GTEST_SOURCE_DIR=C:/git/googletest" "-DMKL_DIR=C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl" "-DTBB_DIR=C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb" "-DHDF5_DIR=C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"` | 0 | `8.684 s` | MSVC `19.51.36252.0`, MKL `2026.1.0`; `Configuring done`, `Generating done`. The failed pthread probes were normal CMake feature probes; `Found Threads: TRUE`. |
+| 4 | `cmake --build .harness/build --config Debug` | 0 | `4.382 s` | Initial incremental build produced `fesa.exe` and all three test executables; warning/error scan `0/0`. |
+| 5 | `ctest --test-dir .harness/build -C Debug -R "DomainModel|InpDomainMapping|Mitc4Geometry|Mitc4Shell|DofManager|EssentialConstraints|SparseAssembly|LoadAssembly|ResultRecovery|Hdf5ResultsWriter" --output-on-failure` | 0 | `5.743 s` | `100% tests passed out of 87`; failed `0`. |
+| 6 | `ctest --test-dir .harness/build -C Debug -R "LinearStaticCli|Mitc4ShellCli" --output-on-failure` | 0 | `1.442 s` | `100% tests passed out of 10`; failed `0`. |
+| 7 | `ctest --test-dir .harness/build -C Debug -R "Mitc4ReferenceComparison|Mitc4S4Reference" --output-on-failure` | 0 | `1.377 s` | `100% tests passed out of 8`; failed `0`. |
+| 8 | `ctest --test-dir .harness/build -C Debug --show-only=json-v1` | 0 | `0.208 s` | Discovered `144` tests; `32` test names contained `Mitc4`. |
+| 9 | `ctest --test-dir .harness/build -C Debug --output-on-failure` | 0 | `9.789 s` | Initial full regression: `144/144` passed; failed `0`. |
+| 10 | First environment/reference audit helper | 1 | `0.9 s` | Non-gating report-generation error: it hardcoded nonexistent CMake internal directory `CMakeFiles/4.3.0`; both S4 hashes had already matched before the helper stopped. No build or test failed. |
+| 11 | Corrected dynamic environment/reference audit helper | 0 | `0.583 s` | Located `CMakeFiles/4.4.0/CMakeCXXCompiler.cmake`; confirmed MSVC/version, both S4 hashes, no S4 diff, and clean worktree. |
+| 12 | `cmake --build .harness/build --config Debug --target clean` | 0 | `1.251 s` | Generated Visual Studio clean target completed. |
+| 13 | `cmake --build .harness/build --config Debug` | 0 | `94.616 s` | Canonical clean rebuild compiled/linked the solver, CLI, and all test executables; `89` output lines, warning scan `0`, error scan `0`. |
+| 14 | `cmake --build .harness/build --config Debug --target fesa_unit_tests` | 0 | `1.943 s` | `fesa_solver`, GoogleTest, and `fesa_unit_tests.exe` confirmed. |
+| 15 | Focused kernel/model/assembly/recovery regex from order 5 | 0 | `4.863 s` | Canonical focused run: `87/87` passed; failed `0`. |
+| 16 | `cmake --build .harness/build --config Debug --target fesa_integration_tests` | 0 | `1.712 s` | `fesa_solver`, GoogleTest, and `fesa_integration_tests.exe` confirmed. |
+| 17 | Focused lifecycle regex from order 6 | 0 | `1.531 s` | Canonical focused run: `10/10` passed; failed `0`. |
+| 18 | `cmake --build .harness/build --config Debug --target fesa_reference_tests` | 0 | `1.769 s` | `fesa_solver`, GoogleTest, and `fesa_reference_tests.exe` confirmed. |
+| 19 | Focused reference regex from order 7 | 0 | `1.511 s` | Canonical focused run: `8/8` passed; failed `0`; S4 end-to-end tests were included. |
+| 20 | `ctest --test-dir .harness/build -C Debug --show-only=json-v1` | 0 | `0.080 s` | Canonical discovery: `144` total, `32` MITC4-named; unit/integration/reference labels `121/10/13`. |
+| 21 | `ctest --test-dir .harness/build -C Debug --output-on-failure` | 0 | `9.669 s` | Canonical full regression: `100% tests passed out of 144`; failed `0`; CTest real time `9.62 s`. |
+| 22 | Full `reference/` Git scope and worktree audit | 0 | `0.362 s` | `reference_diff_count=0`, `reference_status_count=0`; branch and HEAD unchanged. |
+| 23 | `git merge-base dev HEAD` plus changed-file scope audit | 0 | `0.321 s` | Merge base `a058ef7...`; detected `scripts/execute.py`, so Harness Python self-test was required. |
+| 24 | `uv run --with pytest python -m pytest -v -rs` | 0 | `4.651 s` | Python `3.11.15`, pytest `9.1.1`; `7 passed in 0.11s`; failed `0`. |
+
+## Validation Results
+
+| validation_stage | result | evidence |
+| --- | --- | --- |
+| clean baseline | pass | Branch and HEAD matched the requested baseline; worktree was clean before report creation. |
+| dependency precheck | pass | All four implementation-plan dependency paths existed. |
+| fresh configure | pass | VS18/x64 configure exit `0`; compiler metadata is MSVC x64. |
+| clean full build | pass | Exit `0`; solver, CLI, unit, integration, and reference targets compiled/linked. |
+| compiler warning policy | pass | Clean rebuild emitted zero warning lines and zero compiler/linker error lines; product CMake uses warnings-as-errors. |
+| feature-specific tests | pass | Approved focused regexes passed `87/87`, `10/10`, and `8/8`. |
+| CTest discovery | pass | Nonzero inventory: `144` tests, including `32` MITC4-named tests. |
+| full CTest | pass | `144/144` passed after the clean rebuild. |
+| Harness self-test | pass | Required because `scripts/execute.py` differs from the `dev` merge base; `7/7` passed. |
+| reference immutability | pass | Required S4 SHA-256 values match; entire `reference/` tree has no Git diff or status entry. |
+
+## CTest Inventory
+
+| inventory | count |
+| --- | ---: |
+| all discovered tests | 144 |
+| unit label | 121 |
+| integration label | 10 |
+| reference label | 13 |
+| test names containing `Mitc4` | 32 |
+| failed tests | 0 |
+
+The `32` MITC4-named tests comprise `30` tests in `Mitc4*` suites plus
+`DomainModel.Mitc4ShellRecordsPreserveSourceAndInternalIdentity` and
+`InpDomainMapping.MapsS4AndS4rThroughOneMitc4Identity`. The broader focused regex
+also exercises shared Domain, DOF, constraints, assembly, recovery, and HDF5 seams.
+
+CTest currently applies the target-wide legacy label
+`linear-static-3d-euler-beam` to all `144` tests and has no separate MITC4 label.
+The approved implementation plan explicitly permits exact suite regex filtering,
+which was used here, so this labeling limitation is nonblocking.
+
+## Warning and Failure Audit
+
+- Clean rebuild warning lines: `0`.
+- Clean rebuild compiler/linker error lines: `0`.
+- Focused CTest failures: `0`.
+- Full CTest failures: `0`.
+- Harness Python failures: `0`.
+- Configure probes for POSIX pthread symbols reported expected negative probe
+  results on MSVC before CMake resolved `Threads: TRUE`; this is not a configure
+  warning or failure.
+- One report-generation helper failed because it assumed a CMake internal versioned
+  directory. The corrected dynamic lookup passed. This incident did not affect
+  configure, compile, link, test, reference artifacts, or the gate verdict.
+
+## Reference Read-Only Audit
+
+| exact approved path | observed SHA-256 | expected match |
+| --- | --- | --- |
+| `reference/shell/shell.inp` | `4005851E1AB22FD3A16AC17A8D5DA3E051233F69F37419079F3553AD134ECFCF` | yes |
+| `reference/shell/shell displacements.csv` | `C81D94E0B4A849F87AA0F79C83A79B94D5661AC79E44ED826919AB432C87746B` | yes |
+
+The post-test audit found zero changed paths anywhere under `reference/`. No Abaqus
+or other reference solver was run.
+
+## Failure Classification
+
+- classification: `N/A`
+- primary_failure: `N/A`
+- first_failed_build_or_test_command: `N/A`
+- failed_target_or_test: `N/A`
+- correction_handoff: `N/A`
+- non_gating_incident: report-only environment metadata lookup used the wrong CMake
+  internal directory and was rerun successfully; no product correction is required
+
+## Failed Test Inventory
+
+None. All focused, full CTest, and Harness Python tests passed.
+
+## Handoff Recommendation
+
+| target_agent | reason | required_input |
+| --- | --- | --- |
+| Reference Verification Agent | Build/test status is `pass-for-reference-verification`. | This report, source HEAD `820ba30...`, `.harness/build/tests/Debug/fesa_reference_tests.exe`, and the unchanged declared S4 input/CSV pair. |
+
+The focused reference CTest generated/used build-local comparison evidence, but the
+Build/Test Executor does not interpret that evidence as the formal reference
+tolerance verdict. Reference Verification must independently inspect and report it.
+
+## No-Change Assertion
+
+- source_files_modified: `false`
+- test_files_modified: `false`
+- cmake_files_modified: `false`
+- requirements_formulation_io_numerical_reference_documents_modified: `false`
+- phase_files_modified: `false`
+- tolerance_policies_modified: `false`
+- reference_artifacts_modified: `false`
+- owned_report_modified: `true`
+- notes: The worktree was clean at the requested source HEAD before this report was
+  created. Build products remained under the ignored `.harness/build/` directory.
+
+## Open Issues
+
+- None blocking Reference Verification.
+- The target-wide legacy CTest label prevents a precise MITC4 label count; exact
+  implementation-plan suite regexes provide the approved focused test entry point.

docs/coordination/README.md

@@ -53,7 +53,7 @@ INTAKE -> STATE AUDIT -> GATE DECISION -> HANDOFF PACKAGE -> STATUS REPORT
 - Reference Verification Agent report
 - Physics Evaluation Agent report
 - Release Agent report
-- validation command evidence: `python scripts/validate_workspace.py`
+- Build/Test report의 `.harness/config.json` 또는 자동 감지 기반 MSVC build/test command evidence
 
 ## 문서 템플릿
 
@@ -158,7 +158,8 @@ INTAKE -> STATE AUDIT -> GATE DECISION -> HANDOFF PACKAGE -> STATUS REPORT
 - `needs-formulation`: Formulation Agent가 FEM 정식화를 작성하거나 수정해야 한다.
 - `needs-numerical-review`: Numerical Review Agent가 정식화를 검토하거나 재검토해야 한다.
 - `needs-io-definition`: I/O Definition Agent가 Abaqus input/output 계약을 정의하거나 수정해야 한다.
-- `needs-reference-model`: Reference Model Agent가 reference model artifacts를 정의하거나 수정해야 한다.
+- `needs-reference-model`: Reference Model Agent가 lightweight reference-case inventory,
+  required input/CSV presence, source-ID/component matching 또는 tolerance를 정의해야 한다.
 - `needs-implementation-plan`: Implementation Planning Agent가 TDD implementation plan을 작성하거나 수정해야 한다.
 - `ready-for-implementation`: implementation plan이 준비되었고 downstream 구현을 막는 upstream gate가 없다.
 - `needs-build-test`: 구현 이후 독립 Build/Test Executor 검증이 필요하다.
@@ -184,6 +185,6 @@ INTAKE -> STATE AUDIT -> GATE DECISION -> HANDOFF PACKAGE -> STATUS REPORT
 
 ## 검증 기준
 
-- Coordinator Agent config와 문서 템플릿 검증은 Python unittest로 수행한다.
-- workspace 검증은 `python scripts/validate_workspace.py`를 사용한다.
-- 현재 repository에 CMake 프로젝트가 없으면 harness 정책에 따라 no-CMake validation 경로가 성공으로 기록될 수 있다.
+- Coordinator Agent config와 문서 템플릿에 자동화된 Python 검증이 있으면 `uv run --with pytest python -m pytest -v -rs`로 실행한다.
+- C++ build/test evidence는 `.harness/config.json` 또는 Harness 자동 감지 기본값에 따른 Build/Test report에서 확인한다.
+- C/C++ 파일과 build metadata가 모두 없을 때만 `no C/C++ project` 성공을 허용한다. C/C++ 파일만 있고 build metadata가 없으면 통과 evidence로 사용하지 않는다.

docs/corrections/README.md

@@ -12,8 +12,8 @@ Correction Agent는 Build/Test Executor Agent, Reference Verification Agent, Phy
 - 실패 로그와 implementation report를 읽고 failure classification을 먼저 확정한다.
 - configure, compile, link, test, reference-comparison, harness, environment, upstream-contract 실패를 구분한다.
 - implementation-owned failure에 한해 source/header/test/CMake를 최소 수정한다.
-- 수정 후 targeted command를 먼저 실행하고 `python scripts/validate_workspace.py`를 실행한다.
-- harness, hook, agent config 관련 수정에서는 `python -m unittest discover -s scripts -p "test_*.py"`도 실행한다.
+- 수정 후 targeted command를 먼저 실행하고 `.harness/config.json` 또는 자동 감지 기본값에 따른 전체 MSVC build/test를 실행한다.
+- Harness Python, Hook, agent config 관련 수정에서는 `uv run --with pytest python -m pytest -v -rs`도 실행한다.
 - 반복 실패 또는 upstream 계약 문제를 Coordinator Agent나 관련 upstream agent로 handoff한다.
 
 수행하지 않는다:
@@ -40,11 +40,16 @@ TRIAGE -> MINIMAL FIX -> VERIFY -> REPORT
 
 ```powershell
 <targeted command that reproduced the failure>
-python scripts/validate_workspace.py
-python -m unittest discover -s scripts -p "test_*.py"
+cmake -S . -B .harness/build -A x64
+cmake --build .harness/build --config Debug
+ctest --test-dir .harness/build -C Debug --show-only=json-v1
+ctest --test-dir .harness/build -C Debug --output-on-failure
 ```
 
-`python -m unittest discover -s scripts -p "test_*.py"`는 harness, hook, agent config, Python validation behavior가 correction 범위에 포함될 때 실행한다.
+Preset 또는 직접 MSBuild 프로젝트는 `.harness/config.json`의 설정을 따른다. Harness
+Python, Hook, agent config, Python validation behavior가 correction 범위에 포함될 때는
+`uv run --with pytest python -m pytest -v -rs`도 실행한다. Stop 검증은 응답 종료 전에
+같은 전체 프로젝트 검증을 다시 수행한다.
 
 ## Failure Classification
 
@@ -53,7 +58,7 @@ python -m unittest discover -s scripts -p "test_*.py"
 - `link`: linker, symbol resolution, target dependency 실패
 - `test`: CTest, unit, integration, parser/I/O, ordinary regression test 실패
 - `reference-comparison`: 저장된 reference artifact와 deterministic comparison 실패
-- `harness`: Python harness self-test, TDD guard, hook, validation script 실패
+- `harness`: Python Harness test, PreToolUse/Stop Hook, config loading, discovery, adapter validation 실패
 - `environment`: MSVC, CMake, Python, path, permission, generator, local dependency 문제
 - `upstream-contract`: requirements, formulation, I/O, reference artifact, tolerance, implementation plan 불일치 또는 누락
 
@@ -104,8 +109,8 @@ Excluded files:
 | order | command | exit_code | result | evidence |
 | --- | --- | --- | --- | --- |
 | 1 | <targeted command> | <code> | pass | fail | <summary> |
-| 2 | python scripts/validate_workspace.py | <code> | pass | fail | <summary> |
-| 3 | python -m unittest discover -s scripts -p "test_*.py" | <code or skipped> | pass | fail | skipped | <summary> |
+| 2 | <config-resolved full MSVC build/test commands> | <code> | pass | fail | <summary> |
+| 3 | uv run --with pytest python -m pytest -v -rs | <code or skipped> | pass | fail | skipped | <summary> |
 
 ## Traceability
 

docs/implementation-plans/README.md

@@ -2,7 +2,24 @@
 
 이 디렉터리는 Implementation Planning Agent가 작성하거나 제안한 기능별 구현계획 문서를 보관하는 위치다.
 
-Implementation Planning Agent는 승인된 요구조건, 연구 브리프, 정식화, 수치 리뷰, I/O 정의, reference model 계약을 C++/MSVC 구현 전 TDD 작업계획으로 변환한다. Agent는 코드, 테스트, CMake 파일을 작성하지 않고, Abaqus/Nastran을 실행하지 않으며, Abaqus reference CSV 생성 또는 수정이나 solver 결과 비교, release readiness 승인도 하지 않는다.
+Implementation Planning Agent는 승인된 요구조건, 연구 브리프, 정식화, 수치 리뷰, I/O
+정의와 lightweight reference-case inventory를 C++/MSVC 구현 전 TDD 작업계획으로
+변환한다. Project-local `$harness`를 사용해 multi-Step 초안을 먼저 제시하고 사용자가
+승인한 뒤에만 `phases/` planning files를 생성한다. 계획과 구현 전에
+`docs/HARNESS.md`와 `docs/HARNESS_WORKFLOW.md`를 읽는다.
+
+## Harness 실행 handoff
+
+Planning Agent는 draft -> explicit user approval -> planning files만 수행하며 Step을
+선택하거나 실행하지 않는다. 별도의 명시적 사용자 요청이 있어야 Executor
+(`scripts/execute.py`)가 branch, pending Step, retry, timestamps, commits, advancement와 phase
+status를 소유한다.
+
+Implementation Agent는 approved plan, materialized phase indexes, Executor-selected current
+`stepN.md` 하나만 사용한다. current Step에서 `RED -> observed failure -> minimal GREEN ->
+focused/full VERIFY`를 완료하고 다음 Step을 시작하지 않는다. Agent는 current Step의 `status`
+및 `summary`, `error_message`, `blocked_reason` payload만 쓴다. `.codex/hooks.json`의
+PreToolUse와 Stop은 자동으로 실행되며 hook entry point를 수동 실행해 대체하지 않는다.
 
 기본 파일명은 `docs/implementation-plans/<feature-id>-implementation-plan.md` 형식을 사용한다. 각 문서는 Implementation Agent가 먼저 작성해야 할 실패 테스트, 최소 구현 순서, CMake/CTest 등록 계획, acceptance traceability를 제공해야 한다.
 
@@ -15,7 +32,12 @@ Implementation Planning Agent는 승인된 요구조건, 연구 브리프, 정
 - CMake/CTest target, `add_test`, label, `ctest -C Debug` 검증 계획을 정의한다.
 - candidate source/header/test/CMake 파일과 ownership boundary를 제안한다.
 - requirement, task, test, reference model, acceptance criterion을 Acceptance Traceability Matrix로 연결한다.
-- `python scripts/validate_workspace.py`를 포함한 validation command를 명시한다.
+- `.harness/config.json` 또는 자동 감지 기본값에서 해석되는 MSVC build/test 명령과 feature-specific command를 명시한다.
+- 한 Step을 하나의 layer/module로 제한하고 prerequisite files, RED/GREEN/VERIFY, exact
+  acceptance commands와 구체적 금지사항을 포함한다.
+- 사용자 승인 전에는 `phases/` 파일을 만들지 않고, 승인 뒤에도 planning files만
+  materialize한다. 별도 요청 없이는 `scripts/execute.py`를 실행하지 않으며 Step을
+  선택하거나 실행하지 않는다.
 
 수행하지 않는다:
 - C++ 코드를 구현하지 않는다.
@@ -80,8 +102,8 @@ Implementation Planning Agent는 승인된 요구조건, 연구 브리프, 정
 - add_test_needs: <CTest registration needs>
 - labels: unit | integration | reference | parser | io
 - msvc_config: Debug
-- expected_feature_command: ctest -C Debug -R <feature-or-label>
-- workspace_validation: python scripts/validate_workspace.py
+- expected_feature_command: ctest --test-dir .harness/build -C Debug -R <feature-or-label> --output-on-failure
+- full_validation_source: .harness/config.json | Harness auto detection
 
 ## Candidate Files and Ownership
 
@@ -96,8 +118,8 @@ Implementation Planning Agent는 승인된 요구조건, 연구 브리프, 정
 1. Abaqus `.inp` input follows docs/io-definitions/<feature-id>-io.md.
 2. Parser/I/O path maps model data and history data into the internal semantic model.
 3. Solver path produces authoritative `results.h5` with displacement, reaction, internal force, stress, or feature-specific result datasets.
-4. Reference artifacts are Abaqus-generated CSV files under `reference/<model-id>/`.
-5. Reference comparison tests compare FESA `results.h5` rows against `reference/<model-id>/<model-id>_*.csv` rows.
+4. Reference inputs and required CSV files use exact existing paths declared by the feature.
+5. Reference comparison tests compare only blocking/warning quantities by source ID/component.
 
 ## Acceptance Traceability Matrix
 
@@ -107,11 +129,17 @@ Implementation Planning Agent는 승인된 요구조건, 연구 브리프, 정
 
 ## Validation Commands
 ```powershell
-python -m unittest discover -s scripts -p "test_*.py"
-python scripts/validate_workspace.py
-ctest -C Debug -R <feature-or-label>
+cmake -S . -B .harness/build -A x64
+cmake --build .harness/build --config Debug
+ctest --test-dir .harness/build -C Debug -R <feature-or-label> --output-on-failure
+ctest --test-dir .harness/build -C Debug --output-on-failure
 ```
 
+Preset 또는 직접 MSBuild 프로젝트는 `.harness/config.json`에 해석 가능한 명령을 적는다.
+Harness Python, Hook, agent config 변경이 계획 범위에 포함되면
+`uv run --with pytest python -m pytest -v -rs`도 추가한다. Stop 검증은 Step 종료 전 전체
+MSVC build/test를 다시 확인하며, 구현 보고서의 RED 실패 증거를 대체하지 않는다.
+
 ## Risks and Downstream Handoff
 
 ### Implementation Agent
@@ -124,17 +152,40 @@ ctest -C Debug -R <feature-or-label>
 - <likely failure classifications and upstream rollback guidance>
 
 ### Reference Verification Agent
-- <planned HDF5/CSV view comparison tests, reference model ids, tolerance mapping, ID matching assumptions>
+- <planned HDF5/CSV comparison tests, exact case paths, tolerance mapping, source-ID/component matching>
+
+## Harness Step Draft
+
+| step | name | owned layer/module | prerequisite files | RED/GREEN/VERIFY | acceptance commands | stop condition |
+| ---: | --- | --- | --- | --- | --- | --- |
+| 0 | <kebab-case> | <one scope> | <exact paths> | <test-first sequence> | <exact commands> | <condition> |
+
+User approval is required before materializing this draft under `phases/`.
+
+## Executor Handoff
+
+- Executor authorization: separate explicit user request for `scripts/execute.py`.
+- implementation input: approved plan, materialized phase indexes, and Executor-selected current
+  `stepN.md`.
+- implementation recipe: `RED -> observed failure -> minimal GREEN -> focused/full VERIFY`.
+- metadata ownership: Implementation Agent records only the current Step `status` plus `summary`,
+  `error_message`, or `blocked_reason`; Executor records branch, pending-Step selection, retry,
+  timestamps, commits, advancement, and phase status.
+- hooks: `.codex/hooks.json` automatically invokes PreToolUse and Stop; never manually run hook
+  entry points as substitutes.
 
 ## Open Issues
-- <requirement, formulation, I/O, reference artifact, tolerance, or architecture issue>
+- <requirement, formulation, I/O, required comparison file/mapping, tolerance, or architecture issue>
 ```
 
 ## 품질 기준
 
 - 모든 `must` requirement는 최소 하나의 task와 test에 연결되어야 한다.
 - C++ production 변경마다 선행 테스트 파일 또는 테스트 추가 계획이 있어야 한다.
-- reference artifact가 필요한 기능은 `reference/<model-id>/`와 FESA HDF5-to-reference-CSV 비교 테스트 계획을 가져야 한다.
+- reference comparison이 필요한 기능은 exact existing input/required CSV path와 FESA
+  HDF5-to-reference-CSV source-ID/component mapping test 계획을 가져야 한다.
+- Implementation Planning Agent는 Harness Step 초안을 사용자에게 승인받은 뒤에만 phase
+  index와 step files를 생성하며 executor는 자동 실행하지 않는다.
 - CMake/CTest 계획은 MSVC x64 Debug 검증 경로와 호환되어야 한다.
 - 구현 계획은 테스트 작성, 실패 확인, 최소 구현, validation 순서를 명시해야 한다.
 - upstream 문서가 불완전하면 값을 임의로 채우지 않고 `needs-upstream-decision` 또는 `blocked`로 표시한다.

docs/implementation-plans/linear-static-mitc4-shell-implementation-plan.md

@@ -0,0 +1,921 @@
+# Linear Static MITC4 Shell Implementation Plan
+
+> **For agentic implementation workers:** 이 문서는 사용자 승인 전 `draft`다. 승인 후
+> Implementation Planning Agent가 같은 내용으로 Harness phase planning files만
+> materialize한다. Implementation Agent는 승인된 phase의 pending Step을
+> `docs/HARNESS.md`와 `docs/HARNESS_WORKFLOW.md`에 따라 하나씩 실행해야 하며,
+> Harness hook/runner lifecycle을 우회해서는 안 된다.
+
+## 1. Metadata
+
+- feature_id: `linear-static-mitc4-shell`
+- document_type: `implementation-plan`
+- status: `ready-for-implementation`
+- approval_state: `harness-step-draft-approved-2026-08-12`
+- owner_agent: `implementation-planning-agent`
+- date: `2026-08-13`
+- source_requirement: `docs/requirements/linear-static-mitc4-shell.md`
+- source_research: `docs/research/linear-static-mitc4-shell-research.md`
+- source_formulation: `docs/formulations/mitc4-shell-formulation.md`
+- source_numerical_review:
+  `docs/numerical-reviews/linear-static-mitc4-shell-review.md`
+- source_io_definition:
+  `docs/io-definitions/linear-static-mitc4-shell-io.md`
+- source_reference_models:
+  `docs/reference-models/linear-static-mitc4-shell-reference-models.md`
+- target_platform: `Windows x64 / MSVC / C++17`
+- build_system: `CMake + CTest`
+- execution_infrastructure: `Python Harness`
+- current_numerical_verdict: `pass-for-implementation-planning`
+- harness_task_name_candidate: `linear-static-mitc4-shell`
+- implementation_authorized: `true-user-requested-2026-08-12`
+- harness_execution_authorized: `true-user-requested-2026-08-12`
+- phase_files_authorized: `true-user-approved-2026-08-12`
+
+### Goal
+
+승인된 Abaqus `.inp` subset의 `S4` 및 `S4R` source element를 하나의 FESA
+`FESA-MITC4` 선형 정적 shell formulation으로 해석하고, 물리적으로 분리된 fixed
+drilling stabilization, deterministic sparse assembly, mandatory HDF5 shell results,
+sole declared S4 displacement reference case를 end-to-end로 연결한다.
+
+### Architecture
+
+기존 B33 경로를 파괴하거나 speculative common element hierarchy를 만들지 않는다.
+Domain에 shell semantic records를 추가하고, 별도 concrete `Mitc4Shell` kernel과
+shell-specific recovery를 만든다. 기존 `Analysis` lifecycle, six-DOF nodal
+load/constraint, sparse COO reduction, `LinearSolver`, generic `ResultsWriter` 경계,
+HDF5 temporary/self-check/atomic replacement는 재사용한다.
+
+### Tech Stack
+
+- C++17, MSVC `/W4 /WX`
+- CMake 3.25+, Visual Studio 18 2026 generator, x64 Debug
+- GoogleTest/CTest
+- Intel oneAPI MKL and TBB
+- HDF5 schema version 0
+- Python 3 Harness runner and repository hooks
+
+### Global Constraints
+
+1. 모든 production behavior는 같은 Step 안에서 `RED -> observed failure ->
+   minimal GREEN -> focused VERIFY -> full VERIFY`를 닫는다.
+2. production C++ 파일 변경은 관련 C++ test와 함께 수행한다.
+3. public solver headers에 MKL, TBB, HDF5, Win32/vendor type을 노출하지 않는다.
+4. Node/Element에 equation ID를 저장하지 않고 `DofManager`만 numbering, scatter,
+   constrained/free mapping 및 sparse pattern을 소유한다.
+5. `S4`와 `S4R`은 같은 FESA numerical path를 사용하며 source metadata만 다르다.
+6. physical 20-DOF kernel과 four numerical drilling coordinates를 recovery/output에서
+   분리한다.
+7. reference files를 생성, 수정, rename, repair, normalize하지 않으며 Abaqus를
+   실행하지 않는다.
+8. future geometrically nonlinear residual/tangent, distributed loads, mixed beam-shell
+   models, reduced integration/hourglass, drilling calibration/energy output,
+   `NR-O03`/`NR-O04`는 구현 범위 밖이다.
+9. 이 `draft`의 승인은 phase planning files 작성만 허용한다. Harness 실행은 별도의
+   명시적 사용자 요청이 있어야 한다.
+
+## 2. Readiness Check
+
+| gate | evidence | status | planning consequence |
+| --- | --- | --- | --- |
+| Requirements | `docs/requirements/linear-static-mitc4-shell.md`, 001-072 approved | pass | 모든 must를 task/test에 추적 |
+| Research | `docs/research/linear-static-mitc4-shell-research.md` | pass | source-backed MITC4 tying/director/drilling 경계 유지 |
+| Formulation | `docs/formulations/mitc4-shell-formulation.md`, `approved-for-implementation-planning` | pass | linear sections만 구현; Section 15 future nonlinear 제외 |
+| Numerical Review | `docs/numerical-reviews/linear-static-mitc4-shell-review.md` | pass | critical blocker 없음; planning authorized |
+| I/O | `docs/io-definitions/linear-static-mitc4-shell-io.md`, `approved-for-implementation-planning` | pass | keyword, diagnostic, HDF5 schema를 그대로 구현 |
+| Reference Model | `docs/reference-models/linear-static-mitc4-shell-reference-models.md` | pass | sole S4 input/CSV pair만 read-only acceptance input으로 사용 |
+| Repository seams | parser/model, element/analysis, result/reference 영역 read-only 조사 | pass | candidate files와 current signatures 확인 |
+| Toolchain paths | GoogleTest/MKL/TBB/HDF5 config directories 존재 | pass | Section 10의 exact configure command 사용 가능 |
+
+Toolchain path evidence was resolved in this workspace on `2026-08-12`with
+`Test-Path -LiteralPath`returning `True`for all four literal directories used in
+Sections 10 and 12. They are environment-resolved paths, not placeholders. Each Step
+copies the fail-fast path precheck before CMake so a changed machine configuration
+stops before RED/GREEN evidence is recorded.
+
+Declared read-only reference inventory:
+
+| case | source | displacement CSV | SHA-256 |
+| --- | --- | --- | --- |
+| S4 | `reference/shell/shell.inp` | `reference/shell/shell displacements.csv` | input `4005851E1AB22FD3A16AC17A8D5DA3E051233F69F37419079F3553AD134ECFCF`; CSV `C81D94E0B4A849F87AA0F79C83A79B94D5661AC79E44ED826919AB432C87746B` |
+
+README, `metadata.json`, Abaqus provenance/version, canonical naming 및 추가 portfolio는
+readiness gate가 아니다. 현재 열린 product/numerical 결정은 없다. 남은 승인 항목은
+Section 12의 multi-Step Harness draft뿐이다.
+
+## 3. Implementation Scope
+
+### Included behavior
+
+- exactly one `*STEP, *STATIC`, small displacement/small rotation
+- four-node `S4`/`S4R` parsing and one internal `FESA-MITC4` identity
+- stable source instance/label/type and four-node source ordering
+- homogeneous isotropic `E,nu` and centered single-layer constant `t`
+- deterministic positive-thickness nodal directors and right-handed frames
+- six global nodal DOFs; 24-entry shell scatter
+- physical membrane, bending, transverse shear with MITC edge-midpoint tying
+- common `2x2x2` Gauss integration for S4 and S4R
+- fixed `k_d=10^-3 min(R+)` drilling stabilization from the eight physical
+  tangent-rotation diagonals only
+- nodal BC and global CLOAD; aggregate director-parallel moment rejection
+- deterministic global stiffness, constrained partition, factorize-before-load,
+  effective RHS, solve, full residual/reaction
+- physical-only shell recovery, energy/equilibrium/verification metrics
+- exact mandatory HDF5 model/result schema and failure-atomic finalization
+- direct HDF5-to-Abaqus-displacement comparison: U blocking, UR warning-only
+
+### Non-goals
+
+- Abaqus `S4`/`S4R` algorithm equivalence
+- B31 mapping, mixed B33/MITC4 model execution or common public element hierarchy
+- `*DLOAD`, pressure, gravity, body/edge/follower load
+- composite, offsets, variable thickness, explicit normal/orientation
+- reduced integration, hourglass control, MITC4+
+- nonlinear state, finite director update, nonlinear residual/tangent execution
+- drilling physical strain/load/result/stress/energy, coefficient sweep or calibration
+- `NR-O03` smooth-angle and `NR-O04` warp/distortion threshold sweeps
+- extra shell benchmarks as a completion gate
+- Abaqus execution or reference artifact mutation
+
+## 4. Work Breakdown
+
+Tasks are ordered by implementation dependency. Harness executes Steps 0-13 in strict
+order even when the minimal dependency set below is smaller.
+
+| task | depends on |
+| --- | --- |
+| TASK-00 | none |
+| TASK-01 | TASK-00 |
+| TASK-02 | TASK-01 |
+| TASK-03 | TASK-02 |
+| TASK-04 | TASK-03 |
+| TASK-05 | TASK-04 |
+| TASK-06 | TASK-00; executed after TASK-05 |
+| TASK-07 | TASK-04, TASK-06 |
+| TASK-08 | TASK-02, TASK-07 |
+| TASK-09 | TASK-05, TASK-08 |
+| TASK-10 | TASK-05, TASK-09 |
+| TASK-11 | TASK-09, TASK-10 |
+| TASK-12 | TASK-01, TASK-07, TASK-08, TASK-10, TASK-11 |
+| TASK-13 | TASK-11, TASK-12 |
+| TASK-14 | TASK-13 |
+| TASK-15 | TASK-01, TASK-07, TASK-11 |
+| TASK-16 | TASK-00 through TASK-15 |
+
+### TASK-00: `shell-semantic-model`
+
+- Own only model semantic records and immutable Domain access.
+- Candidate additions: `Mitc4ShellDefinition`, `ShellSection`, source type enum/value,
+  internal formulation identity, four-node indices, material/section indices, node
+  director/frame storage.
+- Preserve current B33 records and stable source/internal identity; reject mixed models
+  at mapping rather than designing a heterogeneous solver hierarchy.
+- Tests: `MITC4-MODEL-001`, `MITC4-MODEL-002`.
+
+### TASK-01: `shell-domain-mapping`
+
+- Extend `AbaqusDomainMapper::map(const ParsedInput&)`; keep `AbaqusInputReader`
+  syntax-only.
+- Accept exact S4/S4R and single-layer SHELL SECTION grammar, resolve ELSET/material,
+  identity wrappers and six-DOF BC/CLOAD.
+- Fail closed with exact I/O diagnostic classes for connectivity, assignment,
+  unsupported option/procedure/mixed model/distributed load.
+- Tests: `MITC4-MAP-001` through `MITC4-MAP-004`.
+
+### TASK-02: `shell-director-geometry`
+
+- Add deterministic geometry preprocessing after instance expansion: element normal
+  candidates, area-weighted nodal director, pairwise orientation validation and nodal
+  frame tie-break.
+- Validate center, eight stiffness points, four tying points and committed recovery
+  points for finite bases, nonzero surface measure and positive finite Jacobian.
+- Do not introduce calibrated angle, warp or distortion thresholds.
+- Tests: `MITC4-GEO-001` through `MITC4-GEO-004`.
+
+### TASK-03: `mitc4-kinematics-constitutive`
+
+- Create concrete candidate `Mitc4Shell` without a public base hierarchy.
+- Implement shape identities, local frames, `T_p`/`T_d` channel maps, direct
+  membrane/bending terms, all four covariant MITC tying samples/interpolation,
+  engineering-shear factors, `C_ps/C_5/A/D/A_s` and fixed point order.
+- Keep all intermediate physical coordinates at 20 DOFs.
+- Tests: `MITC4-KIN-001` through `MITC4-KIN-005`.
+
+### TASK-04: `mitc4-stiffness-drilling`
+
+- Form physical `K20` with common `2x2x2` integration and embed by congruence.
+- Build `R+` only from the eight physical tangent-rotation diagonals, use exact
+  `k_d=10^-3 min(R+)` and `T_d^T(k_d I4)T_d`; fail empty/nonfinite `R+`.
+- Tests: `MITC4-KERNEL-001` through `MITC4-KERNEL-006`.
+
+### TASK-05: `mitc4-physical-recovery`
+
+- Add only the element-kernel physical recovery seam for generalized strain/resultant,
+  bottom/middle/top stress and physical element energy.
+- Prove pure numerical drill action contributes zero to every physical recovery value.
+- Tests: `MITC4-KERNEL-007`, `MITC4-PHYSREC-001`.
+
+### TASK-06: `shell-dof-scatter`
+
+- Retain six per-node full DOFs and add typed 24-entry shell scatter/pattern access;
+  preserve existing 12-entry B33 behavior.
+- Preserve stable full/free/constrained numbering and all-constrained `0x0 Kff`.
+- Tests: `MITC4-DOF-001` through `MITC4-DOF-003`.
+
+### TASK-07: `shell-sparse-assembly`
+
+- Dispatch shell topology to `Mitc4Shell::globalStiffness()`.
+- Emit 576 element-local COO entries with stable `elementOrder`/`localOrder` into
+  worker-owned buffers; preserve canonical fixed reduction and diagonal slots.
+- Tests: `MITC4-ASM-001` through `MITC4-ASM-003`.
+
+### TASK-08: `shell-load-validation`
+
+- Reuse global six-DOF `LoadAssembler` and existing constraint partition.
+- Aggregate CLOAD deterministically before testing exact-zero or
+  `rho_M=abs(dot(d,M))/norm(M)<=1e-12`; rejected moments never reach stabilization.
+- Preserve force/moment units and factorization-before-load lifecycle.
+- Tests: `MITC4-LOAD-001` through `MITC4-LOAD-004`.
+
+### TASK-09: `shell-analysis-state`
+
+- Add shell result rows to `AnalysisState` and `result_records.hpp`: four fixed
+  midsurface locations, local frames, eight generalized strains/resultants,
+  bottom/middle/top stress, physical energy, equilibrium and verification metrics.
+- Preserve stable row order and expose candidate-owned containers only; perform no
+  element calculation in this task.
+- Tests: `MITC4-STATE-001` through `MITC4-STATE-003`.
+
+### TASK-10: `shell-result-recovery`
+
+- Recover full residual `K*d-F` for nodal reaction/equilibrium evidence but call the
+  kernel physical-only recovery for shell quantities.
+- Validate candidates fully before committing state; keep stable row order.
+- Tests: `MITC4-REC-001` through `MITC4-REC-005`.
+
+### TASK-11: `shell-hdf5-output`
+
+- Extend `Hdf5ResultsWriter` behind the unchanged generic `ResultsWriter::write`
+  boundary.
+- Add exact schema paths/shapes/component attributes from the I/O contract without
+  changing B33 dataset meaning.
+- Reuse temporary write, finite/schema self-check, close/reopen and atomic replace.
+- Tests: `MITC4-H5-001` through `MITC4-H5-004`.
+
+### TASK-12: `shell-linear-static-flow`
+
+- Route a shell Domain through the existing eight-hook `Analysis::run()` lifecycle.
+- Preserve assemble/partition, factorize, load/effective RHS, substitute,
+  reconstruct, full residual/recover, atomic write order and single factorization.
+- Validate nonzero prescribed values, singular support and valid all-constrained solve.
+- Tests: `MITC4-FLOW-001` through `MITC4-FLOW-004`.
+
+### TASK-13: `shell-reference-comparison`
+
+- Add a test-only MITC4 comparator rather than widening beam-specific assumptions.
+- Consume exactly one declared input and displacement CSV per case; map instance,
+  source node and six displacement components directly to HDF5.
+- Precheck header/row set/duplicates/nonfinite/schema/identity before numeric work.
+- Apply fixed absolute `1.0e-5` to every U/UR row without a scale-dependent decision
+  term; U blocks, UR only emits deterministic warning; record all required metrics
+  and worst row.
+- Tests: `MITC4-REF-001` through `MITC4-REF-006`.
+
+### TASK-14: `shell-s4-end-to-end`
+
+- This is declared-case sub-work owned by TASK-13/Step 13's test-only reference module,
+  not an independent production-module Step.
+- Run the declared S4 deck through CLI, authoritative HDF5, schema checks and
+  read-only comparator.
+- Assert source type `S4`, internal `FESA-MITC4` and U pass/UR report behavior.
+- Tests: `MITC4-E2E-S4-001`, `MITC4-E2E-S4-002`.
+
+### TASK-15: `shell-s4r-common-path-verification`
+
+- This is non-reference coverage distributed across the existing domain-mapping,
+  sparse-assembly and HDF5 tests; Step 13 does not consume an S4R Abaqus artifact.
+- Assert S4R selects the same FESA-MITC4 integration/kernel/assembly path as an
+  otherwise identical S4 semantic fixture while preserving only source metadata.
+- Tests: `InpDomainMapping.MapsS4AndS4rThroughOneMitc4Identity`,
+  `SparseAssembly.S4AndS4rSemanticFixturesAssembleIdenticalStiffness`, and the
+  existing shell HDF5 source-type metadata coverage.
+
+### TASK-16: `mitc4-full-verification`
+
+- Run MSVC x64 Debug full build, CTest discovery, focused feature suites and full CTest.
+- Audit warnings, deterministic repeat evidence, required HDF5 inventory, reference
+  immutability and git diff scope.
+- Produce only downstream implementation evidence; do not claim reference verification,
+  physics sanity or release readiness.
+- Tests/audits: `MITC4-VERIFY-001` through `MITC4-VERIFY-004`.
+
+## 5. TDD Test Plan
+
+| test id | initial RED assertion | minimal GREEN behavior | focused verification |
+| --- | --- | --- | --- |
+| MITC4-MODEL-001 | four-node S4/S4R records/director/source identity do not exist | immutable shell records preserve source and internal identity | `DomainModel.*` |
+| MITC4-MODEL-002 | shell section/material/thickness ownership unavailable | one resolved centered homogeneous assignment per element | `DomainModel.*` |
+| MITC4-MAP-001 | valid S4/S4R and SHELL SECTION reject | both source types map to FESA-MITC4 | `InpDomainMapping.*` |
+| MITC4-MAP-002 | duplicate/unresolved/conflicting section cases lack exact errors | exact assignment/material validation | `InpDomainMapping.*` |
+| MITC4-MAP-003 | excluded shell options/mixed models may be ignored | exact fail-closed diagnostics | `InpDomainMapping.*` |
+| MITC4-MAP-004 | second/nonstatic/NLGEOM/DLOAD cases lack shell boundary tests | exact procedure/load rejection; no-op output unchanged | `InpDomainMapping.*` |
+| MITC4-GEO-001 | planar/rotated/warped directors unavailable | deterministic unit director and right-handed frame | `Mitc4Geometry.*` |
+| MITC4-GEO-002 | incident orientation/tie-break is untested | stable area-weighted result across repeated order | `Mitc4Geometry.*` |
+| MITC4-GEO-003 | duplicate/bow-tie/zero/reversed/nonfinite geometry may pass | exact geometry failures | `Mitc4Geometry.*` |
+| MITC4-GEO-004 | required-point Jacobian inventory absent | every required point finite and positive | `Mitc4Geometry.*` |
+| MITC4-KIN-001 | shape/derivative identities unavailable | partition/unity/derivative identities | `Mitc4ShellKinematics.*` |
+| MITC4-KIN-002 | frame/T transforms unavailable | orthonormal/right-handed frames and channel selection | `Mitc4ShellKinematics.*` |
+| MITC4-KIN-003 | tying values/weights unavailable | four hand-computed covariant tying values | `Mitc4ShellKinematics.*` |
+| MITC4-KIN-004 | constitutive/section matrices unavailable | exact coefficients, symmetry, positivity, unit rescaling | `Mitc4ShellConstitutive.*` |
+| MITC4-KIN-005 | quadrature order not fixed | exact common 2x2x2 points/weights | `Mitc4ShellKinematics.*` |
+| MITC4-KERNEL-001 | no 24x24 shell stiffness | finite symmetric 24x24 stiffness | `Mitc4ShellKernel.*` |
+| MITC4-KERNEL-002 | energy congruence unavailable | 20/24 virtual work and energy equal within 1e-12 | `Mitc4ShellKernel.*` |
+| MITC4-KERNEL-003 | rigid/rank checks fail | six physical rigid modes, physical rank 14, stabilized rank 18 | `Mitc4ShellKernel.*` |
+| MITC4-KERNEL-004 | deformation energy/patch fields unavailable | positive membrane/bending/shear/twist modes | `Mitc4ShellPatch.*` |
+| MITC4-KERNEL-005 | R+ membership/coefficient not implemented | exact rotational-only min and 1e-3 factor | `Mitc4ShellDrilling.*` |
+| MITC4-KERNEL-006 | empty R+ and pure drill behavior unspecified | deterministic failure; pure drill stabilized | `Mitc4ShellDrilling.*` |
+| MITC4-KERNEL-007 | drilling contaminates recovery/energy | physical recovery/energy exact zero for pure drill | `Mitc4ShellDrilling.*` |
+| MITC4-PHYSREC-001 | kernel recovery contract is not independently callable | exact physical strain/resultant/stress/energy for hand field | `Mitc4ShellPhysicalRecovery.*` |
+| MITC4-DOF-001 | shell scatter fixed at 12 | stable 24-entry scatter in node/component order | `DofManager.*` |
+| MITC4-DOF-002 | shell pattern unavailable | sorted unique pattern with all diagonals | `DofManager.*` |
+| MITC4-DOF-003 | constraint roundtrip lacks shell-sized system | no/mixed/all constraints and nonzero values roundtrip | `DofManager.*; EssentialConstraints.*` |
+| MITC4-ASM-001 | assembler rejects four-node element | 576 stable local contributions assemble | `SparseAssembly.*` |
+| MITC4-ASM-002 | thread/repetition may reorder | serial/TBB/repeated CSR bytes and values match | `SparseAssembly.*` |
+| MITC4-ASM-003 | S4/S4R could branch numerically | identical semantic fixtures produce identical K | `SparseAssembly.*` |
+| MITC4-LOAD-001 | shell force/moment fixture unavailable | six global components aggregate stably | `LoadAssembly.*` |
+| MITC4-LOAD-002 | director-parallel exact-zero branch untested | zero aggregate moment accepted | `LoadAssembly.*` |
+| MITC4-LOAD-003 | rho boundary/rejection untested | <=1e-12 accepted; >1e-12 exact diagnostic | `LoadAssembly.*` |
+| MITC4-LOAD-004 | rejected moment might enter drill channel | failure occurs before RHS/substitution | `LoadAssembly.*` |
+| MITC4-STATE-001 | AnalysisState has no shell row containers | exact shell row/component/location types are owned | `AnalysisState.*` |
+| MITC4-STATE-002 | physical energy/equilibrium/metrics are absent | finite candidate global evidence is stored | `AnalysisState.*` |
+| MITC4-STATE-003 | shell candidate rollback is unavailable | invalid candidate leaves prior state unchanged | `AnalysisState.*` |
+| MITC4-REC-001 | shell row types absent | four ordered location/frame/strain/resultant rows | `ResultRecovery.*` |
+| MITC4-REC-002 | bottom/middle/top stress absent | direct S11/S22/S12 recovery in fixed order | `ResultRecovery.*` |
+| MITC4-REC-003 | energy may include drilling | physical strain energy excludes stabilization | `ResultRecovery.*` |
+| MITC4-REC-004 | reaction/equilibrium semantics may diverge | full residual, force/moment balance, normalized metrics | `ResultRecovery.*` |
+| MITC4-REC-005 | invalid partial rows may commit | nonfinite/inventory failure preserves old state | `ResultRecovery.*` |
+| MITC4-H5-001 | shell metadata/model schema missing | exact metadata, elements, director/frame, material/section | `Hdf5ResultsWriter.*` |
+| MITC4-H5-002 | mandatory shell result paths missing | exact displacement/reaction/frame/strain/resultant/stress/global rows | `Hdf5ResultsWriter.*` |
+| MITC4-H5-003 | output request could filter or drilling paths appear | inventory unconditional; forbidden paths absent | `Hdf5ResultsWriter.*` |
+| MITC4-H5-004 | invalid shell candidate may replace final file | self-check failure preserves prior final | `Hdf5ResultsWriter.*` |
+| MITC4-FLOW-001 | shell cannot traverse Analysis lifecycle | exact hook order and one factorization | `LinearStaticCli.*` |
+| MITC4-FLOW-002 | prescribed shell RHS/reconstruction absent | Ff-Kfc*dc and full displacement correct | `LinearStaticCli.*` |
+| MITC4-FLOW-003 | singular/all-constrained behavior unproven | singular fails; 0x0 Kff succeeds | `LinearStaticCli.*` |
+| MITC4-FLOW-004 | failed output may commit state | candidate state/output commits only after validation | `LinearStaticCli.*` |
+| MITC4-REF-001 | six-column CSV header unsupported | exact MITC4 header maps instance/node/U/UR | `Mitc4ReferenceComparison.*` |
+| MITC4-REF-002 | invalid row inventory may be ignored | missing/extra/duplicate/nonfinite/schema mismatch fails first | `Mitc4ReferenceComparison.*` |
+| MITC4-REF-003 | tolerance could remain scale-dependent or clamp/row-normalize | exact fixed absolute `1.0e-5` for every U/UR row | `Mitc4ReferenceComparison.*` |
+| MITC4-REF-004 | UR may block verdict | U blocks; UR only warns | `Mitc4ReferenceComparison.*` |
+| MITC4-REF-005 | report metrics/order incomplete | row decisions, max, normalized, RMS, vector, worst row deterministic | `Mitc4ReferenceComparison.*` |
+| MITC4-REF-006 | comparator may require administrative files | only declared input/CSV/HDF5 required | `Mitc4ReferenceComparison.*` |
+| MITC4-E2E-S4-001 | S4 deck cannot produce valid shell HDF5 | CLI succeeds with exact S4 metadata/schema | `Mitc4S4Reference.*` |
+| MITC4-E2E-S4-002 | S4 U comparison unavailable | all U rows pass; UR fully reported | `Mitc4S4Reference.*` |
+| MITC4-VERIFY-001 | feature tests not discoverable | all planned suites discovered/labeled | CTest JSON inventory |
+| MITC4-VERIFY-002 | warnings/regressions unknown | MSVC Debug full build passes /W4 /WX | full build |
+| MITC4-VERIFY-003 | nondeterminism unknown | repeated focused/full tests pass | full CTest |
+| MITC4-VERIFY-004 | artifact governance unknown | reference hashes/path and git diff unchanged | read-only audit |
+
+Numerical thresholds are fixed: frame/symmetry/transformation-energy `<=1e-12`;
+rigid action, linear residual and global equilibrium `<=1e-10`. Patch tests compare
+against independently hand-computed analytical fields and signs, not the production
+routine itself.
+
+## 6. CMake/CTest Plan
+
+### Existing topology to preserve
+
+- production library: `fesa_solver`
+- CLI: `fesa_cli`
+- unit: `fesa_unit_tests`
+- integration: `fesa_integration_tests`
+- reference: `fesa_reference_tests`
+- aggregate: `fesa_tests`
+
+No new executable target is required. New kernel/test/comparator source files are
+explicitly registered in existing source lists. Add `linear-static-mitc4-shell` as an
+additive CTest label without removing the B33 label. Because
+`gtest_discover_tests()` currently applies target-wide labels, focused Step
+verification uses exact suite regexes; label-based MITC4 filtering is enabled only
+if per-test labeling can be added without relabeling unrelated B33 tests.
+
+Candidate registrations:
+
+- `src/fesa/CMakeLists.txt`: candidate `model/shell_geometry.cpp`,
+  `elements/mitc4_shell.cpp` and any separate shell recovery implementation.
+- `tests/CMakeLists.txt`: candidate `shell_geometry_test.cpp`,
+  `mitc4_shell_test.cpp`, optional focused shell recovery/HDF5 tests, and MITC4
+  reference comparator/test sources.
+- Preserve existing runtime staging for MKL/TBB/HDF5 on all three test executables.
+
+CTest discovery must show every suite named in Section 5 before implementation is
+considered verified.
+
+## 7. Candidate Files and Ownership
+
+All signatures in this section are candidates for the Implementation Agent to confirm
+against the approved contracts during the owning Step; they are not new approved APIs.
+
+| owner/module | candidate files | candidate interface/direction |
+| --- | --- | --- |
+| model | `include/fesa/model/model_types.hpp`, `include/fesa/model/domain.hpp`, `src/fesa/model/domain.cpp` | separate shell records/accessors; no equation IDs |
+| shell semantic geometry | candidate new `include/fesa/model/shell_geometry.hpp`, `src/fesa/model/shell_geometry.cpp` | director/frame and required-point geometry validation without parser/kernel dependency |
+| Abaqus semantic map | `include/fesa/io/abaqus/domain_mapper.hpp`, `src/fesa/io/abaqus/domain_mapper.cpp` | keep `map(const ParsedInput&) -> Result<Domain>` |
+| analysis view | `include/fesa/analysis/analysis_model.hpp`, `src/fesa/analysis/analysis_model.cpp` | non-owning active shell view only if record representation requires |
+| shell kernel | new `include/fesa/elements/mitc4_shell.hpp`, `src/fesa/elements/mitc4_shell.cpp` | concrete create/stiffness/physical-recover API |
+| DOF | `include/fesa/fem/dof_manager.hpp`, `src/fesa/fem/dof_manager.cpp` | typed `array<size_t,24>` shell scatter beside B33 scatter |
+| sparse assembly | `src/fesa/assembly/sparse_assembler.cpp` | topology dispatch; unchanged public assemble signature |
+| load | `src/fesa/assembly/load_assembler.cpp` only if aggregate director projection cannot live in semantic validation | reuse full six-DOF assembly |
+| state/results | `include/fesa/analysis/analysis_state.hpp`, `src/fesa/analysis/analysis_state.cpp`, `include/fesa/results/result_records.hpp` | additive shell rows/global metrics |
+| recovery | `include/fesa/results/result_recovery.hpp`, `src/fesa/results/result_recovery.cpp` or new shell-specific cpp | candidate-then-commit; physical/drill split |
+| HDF5 | `src/fesa/io/hdf5/hdf5_results_writer.cpp` | generic public writer unchanged |
+| lifecycle | `src/fesa/analysis/linear_static_analysis.cpp` | preserve existing hook order |
+| app | `tests/integration/app/fesa_application_test.cpp`; production app only if feature dispatch needs it | CLI syntax unchanged |
+| reference tests | new `tests/reference/mitc4_reference_comparison.hpp/.cpp` and tests | test-only direct HDF5/CSV comparator |
+| build graph | `src/fesa/CMakeLists.txt`, `tests/CMakeLists.txt` | explicit additive source/test registration |
+
+Candidate kernel seam:
+
+```cpp
+class Mitc4Shell {
+public:
+    static Result<Mitc4Shell> create(
+        std::array<const Node*, 4> nodes,
+        std::array<Vector3, 4> initialDirectors,
+        const ShellSection& section,
+        const LinearElasticMaterial& material);
+
+    [[nodiscard]] Matrix physicalLocalStiffness20() const;
+    [[nodiscard]] Matrix globalStiffness24() const;
+    [[nodiscard]] Result<ShellRecovery> recoverPhysical(
+        const Vector& globalElementDisplacement24) const;
+};
+```
+
+This candidate explicitly avoids returning drill energy/results and avoids a common
+public `Element` hierarchy. Exact value/reference ownership and math types are decided
+inside TASK-03 after compiling the first RED test.
+
+## 8. Data Flow Contract
+
+```text
+.inp bytes
+  -> AbaqusInputReader (syntax/source locations only)
+  -> AbaqusDomainMapper (approved semantics, S4/S4R provenance, section/material)
+  -> geometry/director preprocessing
+  -> immutable Domain
+  -> non-owning AnalysisModel
+  -> DofManager (6 DOF/node, 24-entry shell scatter, free/constrained maps)
+  -> Mitc4Shell physical K20 + fixed drill embedding -> global K24
+  -> worker-local COO -> stable SparseMatrix reduction
+  -> Kff/Kfc/Kcf/Kcc partition -> Kff factorize
+  -> aggregate CLOAD/director check -> Ff-Kfc*dc
+  -> substitute -> full displacement
+  -> full residual K*d-F
+  -> physical-only shell recovery + global evidence
+  -> validated candidate AnalysisState
+  -> temporary results.h5 -> schema self-check -> atomic finalization
+
+authoritative results.h5
+  -> test-only MITC4 HDF5 projection
+  -> exact source instance/node/component row-set precheck
+  -> read-only declared Abaqus displacement CSV
+  -> U blocking / UR warning-only deterministic report
+```
+
+Invariants:
+
+- Domain outlives AnalysisModel; no Domain copying.
+- Source labels/instances/types never become equation indices.
+- `S4`/`S4R` source type is metadata; both call the same kernel/quadrature.
+- full residual uses stabilized global K; shell strain/resultant/stress/physical energy
+  use physical recovery only.
+- HDF5 `nodal/reaction` is full residual; constraint mask decides reaction versus free
+  residual evidence.
+- result rows use fixed GP1..GP4 and BOTTOM/MIDDLE/TOP identity; no averaging or Abaqus
+  integration-point relabeling.
+- state/output mutation occurs only after complete validation.
+
+## 9. Acceptance Traceability Matrix
+
+The inclusive ranges below cover every must requirement `001` through `072` exactly
+once without gap or overlapping requirement range.
+
+| requirement range | owning tasks | test/evidence id | reference model id | acceptance |
+| --- | --- | --- | --- | --- |
+| 001 | TASK-01, TASK-12 | MAP-004, FLOW-001 | N/A | one static step only; deterministic rejection otherwise |
+| 002-004 | TASK-00, TASK-01, TASK-11, TASK-14, TASK-15 | MODEL-001, MAP-001, H5-001, S4 E2E plus S4R common-path tests | `shell-s4` for reference; S4R N/A | S4/S4R one kernel; distinct stable source identity |
+| 005 | TASK-00, TASK-06, TASK-11 | MODEL-001, DOF-001/003, H5-001/002 | N/A | exact six-component order; no distributed equation ownership |
+| 006-010 | TASK-00, TASK-01 | MODEL-002, MAP-002/003 | N/A | finite E,nu,t; one assignment; unsupported meanings fail |
+| 011-016 | TASK-02, TASK-03 | GEO-001..004, KIN-002 | N/A | deterministic unit directors; exact geometry predicates |
+| 017-020 | TASK-01, TASK-08 | MAP-004, LOAD-001..004 | N/A | six-DOF BC/CLOAD; drilling/distributed load fails |
+| 021-023 | TASK-01 | MAP-001..004 and existing no-op regression | N/A | approved parser subset/identity wrappers/no-op policy |
+| 024-030 | TASK-00, TASK-06, TASK-07, TASK-09, TASK-10, TASK-12, TASK-16 | MODEL, DOF, ASM, STATE, REC, FLOW, VERIFY suites | N/A | ownership, deterministic assembly, lifecycle, residual reaction |
+| 031-038 | TASK-03, TASK-04, TASK-05, TASK-07, TASK-10 | KIN, KERNEL, PHYSREC, ASM-003, REC-003 | N/A | physical 5-DOF embedding, exact drilling, same quadrature, invariants |
+| 039-048 | TASK-09, TASK-10, TASK-11, TASK-12 | STATE-001..003, REC-001..005, H5-001..004, FLOW-004 | N/A | mandatory finite schema/results and atomic commit |
+| 049 | TASK-00 through TASK-16 | every production Task records RED/failure/GREEN/focused/full VERIFY; VERIFY-001..003 | `shell-s4` where reference-dependent | TDD evidence, related C++ tests, MSVC Debug no-warning build and full CTest |
+| 050 | TASK-02 through TASK-05, TASK-07 | GEO-001/002, KIN-001/002, KERNEL-001..004, ASM-002 | N/A | frames, Jacobian, symmetry, transformation, six modes, positivity and repeatability |
+| 051 | TASK-02 through TASK-05, TASK-10, TASK-12 | GEO-001, KERNEL-001..003, REC-004, FLOW-002 | N/A | exact normalized 1e-12 and 1e-10 algebraic thresholds |
+| 052 | TASK-03 through TASK-05, TASK-10 | KIN-003/004, KERNEL-004, PHYSREC-001, REC-001/002 | N/A | independent membrane, bending, shear, twist fields and recovery signs/order |
+| 053 | TASK-04, TASK-05, TASK-14 | KERNEL-001..007, PHYSREC-001, declared S4 E2E suite | `shell-s4` | formulation invariants/patches and the S4 reference case pass |
+| 054 | TASK-02 | GEO-001..004 | N/A | exact valid/rejected geometry inventory; no NR-O03/O04 |
+| 055 | TASK-16 | VERIFY scope audit | N/A | extra benchmark portfolio is explicitly nonblocking and absent from completion gate |
+| 056 | TASK-04, TASK-05, TASK-07, TASK-10 | KERNEL-005..007, PHYSREC-001, ASM-001/002, REC-003 | N/A | exact fixed drilling, deterministic rank/action and physical-output exclusion |
+| 057 | TASK-10, TASK-12, downstream Physics Evaluation | REC-002..004, FLOW-002, later physics report | `shell-s4` | implementation exposes equilibrium/sign/energy evidence; physical plausibility verdict is downstream |
+| 058-060 | TASK-13, TASK-14 | REF-003 and S4 E2E comparison | `shell-s4` | exact fixed absolute U tolerance `1.0e-5` without scale/clamp |
+| 061-062 | TASK-13, TASK-14 | REF-004/005 and S4 E2E test | `shell-s4` | UR fixed absolute `1.0e-5`, deterministic warning only |
+| 063-064 | TASK-13 | REF-001/002/005 | `shell-s4` | schema/row failure before numeric comparison; full metrics |
+| 065-068 | TASK-13, TASK-14, TASK-15 | REF-001/002/006, S4 case precheck and S4R non-consumption/common-path evidence | `shell-s4` | exact two S4 paths; unique finite mapped rows; no S4R artifact consumption |
+| 069-071 | TASK-14, TASK-15 | S4 E2E suite and S4R common-path tests | `shell-s4` | S4 U blocks/UR warns; S4R mapping has no Abaqus equality gate |
+| 072 | TASK-13 through TASK-16 | REF-006, VERIFY-004 and git/hash audit | `shell-s4` | no reference solver run or artifact mutation |
+
+## 10. Validation Commands
+
+These commands are the environment-resolved Windows x64 Debug baseline. Planning does
+not execute build/tests. Each approved Harness Step first runs this literal path
+precheck and then repeats the relevant build/test subset after its RED and GREEN
+changes.
+
+```powershell
+$requiredBuildPaths = @(
+  "C:/git/googletest",
+  "C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl",
+  "C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb",
+  "C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"
+)
+foreach ($requiredBuildPath in $requiredBuildPaths) {
+  if (-not (Test-Path -LiteralPath $requiredBuildPath)) {
+    throw "Required configured build path is absent: $requiredBuildPath"
+  }
+}
+
+cmake --fresh -S . -B .harness/build -G "Visual Studio 18 2026" -A x64 `
+  "-DFESA_GTEST_SOURCE_DIR=C:/git/googletest" `
+  "-DMKL_DIR=C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl" `
+  "-DTBB_DIR=C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb" `
+  "-DHDF5_DIR=C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"
+
+cmake --build .harness/build --config Debug
+ctest --test-dir .harness/build -C Debug --show-only=json-v1
+ctest --test-dir .harness/build -C Debug --output-on-failure
+```
+
+Focused commands:
+
+```powershell
+cmake --build .harness/build --config Debug --target fesa_unit_tests
+ctest --test-dir .harness/build -C Debug -R "DomainModel|InpDomainMapping|Mitc4Geometry|Mitc4Shell|DofManager|EssentialConstraints|SparseAssembly|LoadAssembly|ResultRecovery|Hdf5ResultsWriter" --output-on-failure
+
+cmake --build .harness/build --config Debug --target fesa_integration_tests
+ctest --test-dir .harness/build -C Debug -R "LinearStaticCli|Mitc4ShellCli" --output-on-failure
+
+cmake --build .harness/build --config Debug --target fesa_reference_tests
+ctest --test-dir .harness/build -C Debug -R "Mitc4ReferenceComparison|Mitc4S4Reference" --output-on-failure
+```
+
+Planning-document verification:
+
+```powershell
+git diff --check -- docs/implementation-plans/linear-static-mitc4-shell-implementation-plan.md
+git status --short
+git diff --name-only
+```
+
+Reference immutability audit is read-only and fails on any mismatch:
+
+```powershell
+$expectedReferenceHashes = [ordered]@{
+  "reference/shell/shell.inp" = "4005851E1AB22FD3A16AC17A8D5DA3E051233F69F37419079F3553AD134ECFCF"
+  "reference/shell/shell displacements.csv" = "C81D94E0B4A849F87AA0F79C83A79B94D5661AC79E44ED826919AB432C87746B"
+}
+foreach ($referencePath in $expectedReferenceHashes.Keys) {
+  $actualHash = (Get-FileHash -Algorithm SHA256 -LiteralPath $referencePath).Hash
+  if ($actualHash -ne $expectedReferenceHashes[$referencePath]) {
+    throw "Reference artifact changed: $referencePath"
+  }
+}
+```
+
+Do not invoke `scripts/hooks/*.py` manually. Harness runner installs/uses the configured
+PreToolUse and Stop hooks automatically. Do not invoke `scripts/execute.py` until the
+user separately authorizes execution.
+
+## 11. Risks and Downstream Handoff
+
+| risk | controlling plan decision | stop condition |
+| --- | --- | --- |
+| beam-only ModelDefinition leaks through every layer | add shell semantic records first; preserve B33 access | stop if a Step requires unapproved mixed-model hierarchy |
+| fixed 12-DOF scatter breaks B33 | typed beam/shell scatter paths and B33 regressions | stop on any B33 focused/full regression |
+| drilling contaminates physical output | separate physical recovery from stabilized full K | stop if pure-drill recovery/energy is nonzero |
+| director/frame sign nondeterminism | source-order, area-weight and tie-break tests | stop on repeat/order/thread difference |
+| S4R accidentally selects reduced integration | one internal formulation and ASM/E2E equality tests | stop if source type reaches quadrature dispatch |
+| full residual confused with element resultants | keep reaction from Kd-F, physical recovery separately | stop if reaction is reconstructed from shell resultants |
+| writer expansion changes B33 schema | additive shell branches plus full B33 CTest | stop on B33 schema regression |
+| comparator inherits B33 four-file/Frame assumptions | dedicated test-only MITC4 comparator | stop if administrative files become required |
+| reference artifacts staged by Harness | clean isolated worktree, hash/diff audit | stop immediately on any reference path change |
+| future nonlinear equations enter production | scope and code review prohibition | stop if nonlinear state/tangent is allocated or called |
+
+### Implementation Agent
+
+- Read the approved implementation plan, `docs/HARNESS.md` and
+  `docs/HARNESS_WORKFLOW.md` before every Step.
+- Execute only the Harness-selected pending Step and use the repository hooks/scripts
+  through the documented runner lifecycle.
+- Never choose the next Step, edit executor-owned timestamps/statuses, batch multiple
+  Steps, or implement outside the Step's file ownership.
+- Record the RED command and observed failure before GREEN.
+
+### Build/Test Executor Agent
+
+- Use Section 10 exact CMake/MSVC/CTest baseline after implementation Steps finish.
+- Report new warnings, discovery gaps and exact failing test names without changing
+  upstream contracts.
+
+### Correction Agent
+
+- Apply only minimal failure-driven corrections inside approved file ownership.
+- Do not reinterpret MITC4 mathematics, I/O schema or tolerance.
+
+### Reference Verification Agent
+
+- Consume authoritative HDF5 and declared read-only CSV directly.
+- Create the separate reference-verification report; only U affects pass/fail and every
+  UR warning remains visible.
+
+### Physics Evaluation and Release Agents
+
+- Physics evaluates equilibrium, directions, symmetry, energy and result signs after
+  reference verification.
+- Release readiness remains blocked until implementation, build/test, reference and
+  physics gates all provide evidence.
+
+## 12. Harness Step Draft
+
+This approved draft is materialized under `phases/linear-static-mitc4-shell/`.
+Every Step is zero-based, kebab-case and closes RED/GREEN/VERIFY before the
+Executor advances it. TASK-14 is declared-case sub-work inside Step 13's single
+test-only reference module; TASK-15 is non-reference coverage already owned by
+Steps 1/7/11; TASK-16 is downstream Build/Test Executor evidence,
+not an Implementation Agent phase Step. During materialization, the exact required-reading
+paths, configure block, focused command and full VERIFY block shown here are copied
+verbatim into every `stepN.md`; a materialized Step never refers back to this draft or
+to an external conversation.
+
+Every materialized Step copies this mandatory reading inventory before its
+Step-specific paths:
+
+- `AGENTS.md`
+- `docs/PRD.md`, `docs/ARCHITECTURE.md`, `docs/ADR.md`
+- `docs/HARNESS.md`, `docs/HARNESS_WORKFLOW.md`
+- this approved implementation plan and all source contracts listed in Metadata
+- `.codex/hooks.json`
+- `phases/index.json`, `phases/linear-static-mitc4-shell/index.json` and its own
+  `phases/linear-static-mitc4-shell/stepN.md`
+- every path created/modified by prerequisite Steps and their step output/status
+
+If any mandatory or Step-specific path is missing or contradicts the approved plan,
+the Implementation Agent records `blocked` for the Executor-selected current Step and
+stops; it does not invent the missing contract.
+
+Step-specific path ledger copied into the corresponding materialized Step:
+
+| Step | exact source/prerequisite paths |
+| ---: | --- |
+| 0 | `include/fesa/model/model_types.hpp`; `include/fesa/model/domain.hpp`; `src/fesa/model/domain.cpp`; `tests/unit/model/model_types_test.cpp`; `tests/unit/model/domain_test.cpp` |
+| 1 | Step 0 paths; `include/fesa/io/abaqus/domain_mapper.hpp`; `src/fesa/io/abaqus/domain_mapper.cpp`; `tests/unit/io/abaqus/domain_mapper_test.cpp` |
+| 2 | Step 0-1 paths; candidate new `include/fesa/model/shell_geometry.hpp`; `src/fesa/model/shell_geometry.cpp`; `tests/unit/model/shell_geometry_test.cpp`; `src/fesa/CMakeLists.txt`; `tests/CMakeLists.txt` |
+| 3 | Step 2 paths; candidate new `include/fesa/elements/mitc4_shell.hpp`; `src/fesa/elements/mitc4_shell.cpp`; `tests/unit/elements/mitc4_shell_test.cpp`; `src/fesa/CMakeLists.txt`; `tests/CMakeLists.txt` |
+| 4 | Step 3 MITC4 kernel/header/test paths |
+| 5 | Step 3-4 MITC4 kernel/header/test paths |
+| 6 | Step 0 paths; `include/fesa/fem/dof_manager.hpp`; `src/fesa/fem/dof_manager.cpp`; `tests/unit/fem/dof_manager_test.cpp`; `tests/unit/constraints/essential_constraints_test.cpp` |
+| 7 | Steps 4/6 paths; `include/fesa/assembly/sparse_assembler.hpp`; `src/fesa/assembly/sparse_assembler.cpp`; `tests/unit/assembly/sparse_assembler_test.cpp` |
+| 8 | Steps 2/7 paths; `include/fesa/assembly/load_assembler.hpp`; `src/fesa/assembly/load_assembler.cpp`; `tests/unit/assembly/load_assembler_test.cpp` |
+| 9 | Step 5 paths; `include/fesa/results/result_records.hpp`; `include/fesa/analysis/analysis_state.hpp`; `src/fesa/analysis/analysis_state.cpp`; `tests/unit/results/result_records_test.cpp` |
+| 10 | Steps 5/9 paths; `include/fesa/results/result_recovery.hpp`; `src/fesa/results/result_recovery.cpp`; `tests/unit/results/result_recovery_test.cpp` |
+| 11 | Steps 9/10 paths; `include/fesa/io/hdf5/hdf5_results_writer.hpp`; `src/fesa/io/hdf5/hdf5_results_writer.cpp`; `tests/unit/io/hdf5/hdf5_results_writer_test.cpp` |
+| 12 | Steps 7-11 paths; `include/fesa/analysis/linear_static_analysis.hpp`; `src/fesa/analysis/linear_static_analysis.cpp`; `tests/integration/analysis/linear_static_analysis_test.cpp`; `tests/integration/app/fesa_application_test.cpp` |
+| 13 | Steps 11/12 paths; candidate new `tests/reference/mitc4_reference_comparison.hpp`, `tests/reference/mitc4_reference_comparison.cpp`, `tests/reference/mitc4_reference_comparison_test.cpp`, `tests/reference/mitc4_reference_cases_test.cpp`; `tests/CMakeLists.txt`; the two exact read-only S4 reference paths in Section 2 |
+
+The configure command copied before each Step's RED build is:
+
+```powershell
+$requiredBuildPaths = @(
+  "C:/git/googletest",
+  "C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl",
+  "C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb",
+  "C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"
+)
+foreach ($requiredBuildPath in $requiredBuildPaths) {
+  if (-not (Test-Path -LiteralPath $requiredBuildPath)) {
+    throw "Required configured build path is absent: $requiredBuildPath"
+  }
+}
+
+cmake --fresh -S . -B .harness/build -G "Visual Studio 18 2026" -A x64 `
+  "-DFESA_GTEST_SOURCE_DIR=C:/git/googletest" `
+  "-DMKL_DIR=C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl" `
+  "-DTBB_DIR=C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb" `
+  "-DHDF5_DIR=C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"
+```
+
+The full VERIFY block copied at the end of every Step is:
+
+```powershell
+cmake --build .harness/build --config Debug
+ctest --test-dir .harness/build -C Debug --show-only=json-v1
+ctest --test-dir .harness/build -C Debug --output-on-failure
+```
+
+### Step 0 — `shell-semantic-model`
+
+- Required reading: requirements 002-016/024, I/O Sections 3/5, architecture model
+  ownership, current `model_types.hpp`/`domain.*` and their tests.
+- Prerequisite: approved plan only; no production dependency on a prior Step.
+- RED: add MODEL-001/002 tests and CMake registration if needed; run:
+  `cmake --build .harness/build --config Debug --target fesa_unit_tests` then
+  `ctest --test-dir .harness/build -C Debug -R "DomainModel" --output-on-failure`.
+  Record the missing shell type/accessor failure. Unexpected pass is a stop.
+- GREEN: minimally add shell semantic records/Domain const access; no parser/kernel.
+- VERIFY: rerun the focused commands and common full VERIFY.
+- Prohibitions: no equation IDs, element hierarchy, mixed-model execution, parser edits.
+
+### Step 1 — `shell-domain-mapping`
+
+- Required reading: Step 0 outputs, requirements 001-010/017-023, I/O Sections 1-3/8-9,
+  current `domain_mapper.*` and parser/model tests.
+- Prerequisite: Step 0 `completed`.
+- RED: add MAP-001..004; build `fesa_unit_tests` and run
+  `ctest --test-dir .harness/build -C Debug -R "InpDomainMapping" --output-on-failure`.
+  Record valid S4/S4R rejection and exact negative diagnostic failures.
+- GREEN: minimally extend semantic mapping; keep `input_reader` syntax-only.
+- VERIFY: focused parser/model tests, then common full VERIFY.
+- Prohibitions: no element math, no silent unsupported keyword, no reference edits.
+
+### Step 2 — `shell-director-geometry`
+
+- Required reading: requirements 011-016, formulation Sections 4/9/17, Numerical Review
+  5.2/5.5/6.1, I/O 3.3/9, completed semantic model/mapping.
+- Prerequisite: Step 1 `completed`.
+- RED: add GEO-001..004; build unit target and run
+  `ctest --test-dir .harness/build -C Debug -R "Mitc4Geometry" --output-on-failure`.
+- GREEN: implement deterministic director/frame and exact geometry inventory validation.
+- VERIFY: focused geometry/mapping tests, then common full VERIFY.
+- Prohibitions: no calibrated angle/warp/distortion threshold; no NR-O03/O04.
+
+### Step 3 — `mitc4-kinematics-constitutive`
+
+- Required reading: formulation Sections 3-11/17, Numerical Review 5.1-5.6/6.1,
+  current math adapters and Euler kernel style.
+- Prerequisite: Step 2 `completed`.
+- RED: add KIN-001..005 in new `mitc4_shell_test.cpp`, register it, build unit target,
+  run `ctest --test-dir .harness/build -C Debug -R "Mitc4ShellKinematics|Mitc4ShellConstitutive" --output-on-failure`.
+- GREEN: minimally add concrete shell kernel kinematics/constitutive seams; no global
+  assembly or drilling.
+- VERIFY: focused kernel tests, then common full VERIFY.
+- Prohibitions: no public base hierarchy, no S4R branch, no nonlinear tangent code.
+
+### Step 4 — `mitc4-stiffness-drilling`
+
+- Required reading: formulation Sections 10-14/17, requirements 031-038/050-056,
+  Numerical Review 5.7/6.1-6.2, completed Step 3 kernel.
+- Prerequisite: Step 3 `completed`.
+- RED: add KERNEL-001..006; build unit target and run
+  `ctest --test-dir .harness/build -C Debug -R "Mitc4ShellKernel|Mitc4ShellPatch|Mitc4ShellDrilling" --output-on-failure`.
+- GREEN: implement K20, 20-to-24 congruence and exact fixed drilling only.
+- VERIFY: focused kernel suite, then common full VERIFY.
+- Prohibitions: translations in R+, coefficient sweep, recovery/result output, future nonlinear.
+
+### Step 5 — `mitc4-physical-recovery`
+
+- Required reading: formulation Sections 14/16, requirements 035/042-046/052/056,
+  I/O result component/location order, completed Step 4 kernel.
+- Prerequisite: Step 4 `completed`.
+- RED: add KERNEL-007 and PHYSREC-001; build unit target and run
+  `ctest --test-dir .harness/build -C Debug -R "Mitc4ShellDrilling|Mitc4ShellPhysicalRecovery" --output-on-failure`.
+- GREEN: minimally add kernel-local physical recovery and physical energy API only.
+- VERIFY: focused physical recovery/drilling tests, then common full VERIFY.
+- Prohibitions: no AnalysisState/global result rows, no drilling contribution or HDF5.
+
+### Step 6 — `shell-dof-scatter`
+
+- Required reading: requirements 005/025, architecture DofManager ownership, current
+  `dof_manager.*` and constraint tests, completed shell model.
+- Prerequisite: Step 5 `completed`.
+- RED: add DOF-001..003; build unit target and run
+  `ctest --test-dir .harness/build -C Debug -R "DofManager|EssentialConstraints" --output-on-failure`.
+- GREEN: minimally add typed 24-entry scatter/pattern while preserving 12-entry B33.
+- VERIFY: focused DOF/constraint tests, then common full VERIFY.
+- Prohibitions: no equation IDs in model, no constraint/load ownership move.
+
+### Step 7 — `shell-sparse-assembly`
+
+- Required reading: requirements 027/030/037, architecture deterministic COO rule,
+  current `sparse_assembler.cpp`/`sparse_matrix.cpp` tests, completed kernel/scatter.
+- Prerequisite: Step 6 `completed`.
+- RED: add ASM-001..003; build unit target and run
+  `ctest --test-dir .harness/build -C Debug -R "SparseAssembly" --output-on-failure`.
+- GREEN: minimally dispatch shell and emit stable 576-entry local buffers.
+- VERIFY: focused assembly tests, then common full VERIFY.
+- Prohibitions: no worker global CSR mutation, unordered reduction or S4R integration branch.
+
+### Step 8 — `shell-load-validation`
+
+- Required reading: requirements 017-020/028, formulation 8/13, I/O 4.2-4.3,
+  current `load_assembler.*` and constraint lifecycle.
+- Prerequisite: Step 7 `completed`.
+- RED: add LOAD-001..004; build unit target and run
+  `ctest --test-dir .harness/build -C Debug -R "LoadAssembly|EssentialConstraints" --output-on-failure`.
+- GREEN: minimally add aggregate nodal moment/director validation and reuse full DOF load.
+- VERIFY: focused load/constraint tests, then common full VERIFY.
+- Prohibitions: no distributed/equivalent/follower load; no drill load channel.
+
+### Step 9 — `shell-analysis-state`
+
+- Required reading: requirements 026/041-046/048, I/O 6.3-6.5,
+  current `analysis_state.*`/`result_records.hpp` and completed physical recovery types.
+- Prerequisite: Step 8 `completed`.
+- RED: add STATE-001..003; build unit target and run
+  `ctest --test-dir .harness/build -C Debug -R "AnalysisState" --output-on-failure`.
+- GREEN: minimally add candidate-owned shell row/global evidence containers and
+  validation/commit mechanics.
+- VERIFY: focused AnalysisState tests, then common full VERIFY.
+- Prohibitions: no element calculation, ResultRecovery orchestration or HDF5 writing.
+
+### Step 10 — `shell-result-recovery`
+
+- Required reading: requirements 029/035/041-046/048, formulation 14/16, I/O 6.3-6.5,
+  current `result_recovery.*` and completed Steps 5/9.
+- Prerequisite: Step 9 `completed`.
+- RED: add REC-001..005; build unit target and run
+  `ctest --test-dir .harness/build -C Debug -R "ResultRecovery" --output-on-failure`.
+- GREEN: minimally orchestrate full-residual evidence and physical shell recovery into
+  a fully validated candidate, then commit it.
+- VERIFY: focused recovery tests, then common full VERIFY.
+- Prohibitions: no new result record type, location averaging, drill recovery or writer edit.
+
+### Step 11 — `shell-hdf5-output`
+
+- Required reading: requirements 039-048, I/O Section 6 exact schema, ADR atomic output,
+  current HDF5 writer/self-check tests, completed recovery records.
+- Prerequisite: Step 10 `completed`.
+- RED: add H5-001..004; build unit target and run
+  `ctest --test-dir .harness/build -C Debug -R "Hdf5ResultsWriter" --output-on-failure`.
+- GREEN: add exact additive shell schema behind unchanged ResultsWriter boundary.
+- VERIFY: focused HDF5 tests, then common full VERIFY.
+- Prohibitions: no B33 schema reinterpretation, CSV solver output, partial final file.
+
+### Step 12 — `shell-linear-static-flow`
+
+- Required reading: requirements 024-030, architecture eight-hook lifecycle, I/O CLI
+  contract, current `linear_static_analysis.*`/application integration tests.
+- Prerequisite: Step 11 `completed`.
+- RED: add FLOW-001..004; build integration target and run
+  `ctest --test-dir .harness/build -C Debug -R "LinearStaticCli|Mitc4ShellCli" --output-on-failure`.
+- GREEN: minimally route shell through existing lifecycle; preserve one factorization.
+- VERIFY: focused integration tests, then common full VERIFY.
+- Prohibitions: no analysis lifecycle reorder, no 0x0 singular conversion, no early state commit.
+
+### Step 13 — `shell-reference-comparison`
+
+- Required reading: requirements 058-072, I/O Section 7, Reference Model contract,
+  the sole declared S4 paths and hashes, and current B33 comparator only as reusable
+  identity/report precedent.
+- Scope ownership: this one test-only reference module owns TASK-13 comparator behavior
+  plus TASK-14 declared-case tests; it owns no solver production module.
+- Prerequisite: Step 12 `completed` and valid MITC4 HDF5 fixture.
+- RED: update REF-003 first so the existing scale-dependent comparator fails against
+  literal fixed-boundary cases around `1.0e-5`; build the reference target and run
+  `ctest --test-dir .harness/build -C Debug -R "Mitc4ReferenceComparison|Mitc4S4Reference" --output-on-failure`.
+  Record the expected old-tolerance assertion failure.
+- GREEN: minimally replace only the MITC4 comparator decision value with fixed absolute
+  `1.0e-5`; keep reference scale as diagnostic report data only.
+- If a declared case exposes a production defect outside this reference-test module,
+  stop the Step and route a focused correction to the owning prior module; do not patch
+  unrelated production layers inside this Step.
+- VERIFY: focused comparator and the declared S4 tests, then common full VERIFY.
+- Prohibitions: no reference artifact writes/Abaqus run, no metadata/README gate, no UR
+  blocking, no B33 comparator change, and no scale/clamp substitution for fixed `1.0e-5`.
+
+After explicit approval, planning may create only:
+
+- `phases/index.json` with task status `pending` and no creation timestamp;
+- `phases/linear-static-mitc4-shell/index.json` with Steps 0-13 initially `pending` and
+  no executor-owned timestamps;
+- `phases/linear-static-mitc4-shell/stepN.md` containing the approved self-contained
+  directions.
+
+Approval does not authorize `python scripts/execute.py linear-static-mitc4-shell` or
+`--push`.
+
+## 13. Open Issues
+
+| id | item | blocking now | resolution owner |
+| --- | --- | --- | --- |
+| OI-001 | Section 12 multi-Step Harness draft was explicitly approved on 2026-08-12 and materialized. | resolved | user |
+| OI-002 | Candidate shell semantic representation and exact C++ value/reference types are not public API decisions. | no | owning RED test in Steps 0/3 |
+| OI-003 | Per-test MITC4 CTest label can be added without relabeling B33 tests인지 확인한다. Exact suite regex remains sufficient. | no | Step 0 and downstream TASK-14 CMake verification |
+
+No mathematical, I/O, reference-inventory or tolerance decision remains open for
+implementation planning. The user separately authorized implementation and Harness
+execution on 2026-08-12; the Executor still owns branch, Step selection, timestamps,
+commits and advancement.

docs/io-definitions/README.md

@@ -16,7 +16,7 @@ I/O Definition Agent는 Abaqus input file subset, 내부 solver model mapping, o
 - model data와 history data를 내부 solver 개념으로 매핑한다.
 - node, element, set, material, section, boundary condition, load, step, output request의 의미 계약을 정의한다.
 - `results.h5`의 authoritative HDF5 schema를 정의한다.
-- FESA HDF5 dataset을 `reference/<model-id>/` 아래 Abaqus reference CSV rows와 비교하기 위한 deterministic row schema를 정의한다.
+- 기능이 선언한 existing Abaqus CSV와 비교하기 위한 최소 source-ID/component mapping을 정의한다.
 
 수행하지 않는다:
 - parser를 구현하지 않는다.
@@ -123,58 +123,25 @@ I/O Definition Agent는 Abaqus input file subset, 내부 solver model mapping, o
 | element_force | /steps/<step>/frames/<frame>/field_outputs/element_forces | <nrow, ncomp> | float64 | component_names, element_ids, location | element | feature-dependent |
 | stress | /steps/<step>/frames/<frame>/field_outputs/S | <nrow, ncomp> | float64 | component_names, element_ids, integration_points | integration_point | feature-dependent |
 
-## FESA HDF5 to Reference CSV Comparison Schema
+## FESA HDF5 to Reference CSV Comparison Mapping
 
-FESA solver output은 `results.h5`이다. Comparison tooling reads required HDF5 datasets and maps them to deterministic row records that can be matched against Abaqus reference CSV files under `reference/<model-id>/`.
+FESA solver output은 `results.h5`이다. 기능이 blocking 또는 warning-only로 선언한
+quantity에 대해서만 existing CSV path와 다음 mapping을 정의한다.
 
-공통 규칙:
-- reference_root: `reference/<model-id>/`
-- hdf5_schema_version: <version>
-- reference_csv_schema_version: <version>
-- sort_order: step, frame, id, location, component
-- numeric_format: <precision and exponent policy>
-- missing_component_policy: 0 | N/A | omitted, feature-specific
-- hdf5_dataset_source: HDF5 dataset path를 각 row schema 또는 report에 기록한다.
+| field | contract |
+| --- | --- |
+| reference_input | exact existing `.inp` path |
+| reference_csv | exact existing required CSV path |
+| hdf5_dataset | authoritative FESA dataset path |
+| source_identity | node/element source label used for exact matching |
+| components | required CSV columns and corresponding HDF5 components |
+| row_precheck | missing/extra/duplicate/nonfinite required rows fail before tolerance |
+| behavior | blocking or warning-only |
+| tolerance | upstream-approved formula |
 
-### displacement rows / `<model-id>_displacements.csv`
-| column | type | description |
-| --- | --- | --- |
-| step | string | step name or index |
-| frame | integer | frame or increment id |
-| node_id | integer/string | Abaqus node label |
-| ux | float | displacement component |
-| uy | float | displacement component or 0/N/A |
-| uz | float | displacement component or 0/N/A |
-
-### reaction rows / `<model-id>_reactions.csv`
-| column | type | description |
-| --- | --- | --- |
-| step | string | step name or index |
-| frame | integer | frame or increment id |
-| node_id | integer/string | Abaqus node label |
-| rfx | float | reaction component |
-| rfy | float | reaction component or 0/N/A |
-| rfz | float | reaction component or 0/N/A |
-
-### internal force rows / `<model-id>_internalforces.csv`
-| column | type | description |
-| --- | --- | --- |
-| step | string | step name or index |
-| frame | integer | frame or increment id |
-| element_id | integer/string | Abaqus element label |
-| location | string | element/nodal/integration_point location |
-| component | string | force component name |
-| value | float | component value |
-
-### stress rows / `<model-id>_stresses.csv`
-| column | type | description |
-| --- | --- | --- |
-| step | string | step name or index |
-| frame | integer | frame or increment id |
-| element_id | integer/string | Abaqus element label |
-| integration_point | integer/string | integration point id or N/A |
-| component | string | stress component name |
-| value | float | stress value |
+Row order alone으로 대응하지 않는다. Canonical filename, reference CSV schema version,
+README, metadata, provenance 또는 single-step/final-frame case의 duplicated unit/coordinate/
+step-frame columns를 요구하지 않는다.
 
 ## Validation Rules
 - required_fields: <required input fields>
@@ -208,4 +175,5 @@ FESA solver output은 `results.h5`이다. Comparison tooling reads required HDF5
 - 내부 모델 계약은 semantic fields로 작성하고 C++ class/function/API를 확정하지 않는다.
 - `results.h5`가 authoritative solver output임을 명시해야 한다.
 - HDF5 schema는 dataset path, dtype/shape, required attributes, ID field, component naming, coordinate system, units, step/frame identity, quantity location을 포함해야 한다.
-- Reference CSV comparison row schema는 column name, stable sort order, ID field, component naming, coordinate system, units, step/frame identity, quantity location을 포함해야 한다.
+- Reference CSV comparison mapping은 exact path, source-ID column, required component columns,
+  HDF5 projection, row prechecks와 tolerance를 포함해야 한다.

docs/io-definitions/linear-static-3d-euler-beam-io.md

@@ -0,0 +1,473 @@
+# Linear Static 3D Euler Beam I/O Definition
+
+## Metadata
+
+- feature_id: `linear-static-3d-euler-beam`
+- source_requirement: `docs/requirements/linear-static-3d-euler-beam.md`
+- source_formulation: `docs/formulations/3d-isoparametric-euler-beam-formulation.md`
+- source_numerical_review: `docs/numerical-reviews/linear-static-3d-euler-beam-review.md`
+- source_research: `docs/research/linear-static-3d-euler-beam-research.md`
+- approved_design: `docs/superpowers/specs/2026-08-08-linear-static-3d-euler-beam-design.md`
+- status: `ready-for-implementation-planning`
+- owner_agent: `io-definition-agent`
+- date: `2026-08-09`
+- authoritative_output: `results.h5`
+- reference_baseline: `reference/cantilever beam/` at source commit `2b34d0b`
+
+이 문서는 승인된 V0의 semantic I/O contract만 정의한다. Parser, HDF5 writer,
+comparison tooling의 C++ API나 구현 구조는 정의하지 않으며 Abaqus full compatibility를
+주장하지 않는다.
+
+## Abaqus Input Scope
+
+- input_format: Abaqus input file (`.inp`)
+- supported_analysis: 입력 파일당 하나의 linear-static step과 `TYPE=B33` 2절점 3D
+  Euler–Bernoulli beam
+- ordinary_unit_system: user-consistent; `.inp`만 보고 SI를 추론하지 않음
+- compatibility_disclaimer: 아래 표의 위치, parameter, data grammar만 지원함
+
+`supported`는 해당 행의 정확한 subset만 의미한다. `warning no-op`은 syntax를 소비하고
+구조화된 warning을 기록하지만 Domain, AnalysisModel 또는 mandatory HDF5 output을
+변경하지 않는다는 뜻이다.
+
+| keyword | status and allowed location | required parameters and data grammar | purpose and semantic mapping | unsupported behavior |
+| --- | --- | --- | --- | --- |
+| `*HEADING` | supported; optional top-level first keyword | parameters 없음; 다음 keyword 전까지 0개 이상의 text data line | 원문 heading을 source metadata로 보존 | 중첩 위치 또는 parameter는 input error |
+| `*PART` / `*END PART` | supported; top-level model block | `NAME=<part-name>` 필수; `*END PART` data 없음 | part-local node, element, set, section 정의 범위 | 닫히지 않음, 중첩 part, duplicate part name은 error |
+| `*NODE` | supported; part 내부 | parameter 없음; 각 row `node_label, x, y, z` | positive integer source label과 finite global Cartesian 좌표 | 다른 arity, duplicate label, nonfinite 좌표는 error |
+| `*ELEMENT` | supported; part 내부 | `TYPE=B33` 필수; 각 row `element_label, node_1, node_2` | 2절점 straight Euler beam definition | `TYPE=B31`은 `unsupported-element-formulation`; 다른 type/arity와 dangling connectivity는 error |
+| `*NSET` | supported; part 또는 assembly 내부 | `NSET=<name>` 필수; optional `GENERATE`; assembly에서는 `INSTANCE=<instance-name>` 필수; explicit row는 하나 이상의 node label, generate row는 `first,last,increment` | part-local 또는 single-instance assembly node set | mixed-instance set, zero/negative increment, duplicate name, dangling member는 error |
+| `*ELSET` | supported; part 또는 assembly 내부 | `ELSET=<name>` 필수; optional `GENERATE`; assembly에서는 `INSTANCE=<instance-name>` 필수; explicit/generate grammar는 `*NSET`과 동일 | part-local 또는 single-instance assembly element set | mixed-instance set, invalid range, duplicate name, dangling member는 error |
+| `*MATERIAL` | supported; top-level model data | `NAME=<material-name>` 필수; data 없음 | 뒤따르는 단일 isotropic `*ELASTIC`을 소유 | duplicate name, missing/duplicate elasticity, 다른 material model은 error |
+| `*ELASTIC` | supported; 현재 material 내부 | parameter 없음; 정확히 한 row `E, nu` | homogeneous isotropic elasticity; `G=E/(2(1+nu))` | extra field/row, nonfinite value 또는 `E<=0`/`G<=0`은 model error |
+| `*BEAM GENERAL SECTION` | supported; part 내부 | `ELSET=<name>`, `MATERIAL=<name>`, `SECTION=GENERAL` 필수; 첫 row `A,I11,I12,I22,J`, 둘째 row `n1x,n1y,n1z` | section assignment, properties와 first section axis | 다른 `SECTION`, missing/dangling reference, `I12!=0`, invalid property/guide vector는 error |
+| `*SECTION POINTS` | supported; 바로 앞 general beam section에 종속 | parameter 없음; 하나 이상의 row `x1,x2` | 입력 순서의 stress recovery point; `x1=y`, `x2=z` | 선행 section 없음, 다른 arity, nonfinite 또는 duplicate point는 error |
+| `*ASSEMBLY` / `*END ASSEMBLY` | supported; 정확히 하나의 top-level assembly block | `NAME=<assembly-name>` 필수; `*END ASSEMBLY` data 없음 | identity instance와 assembly set 범위 | nested/duplicate assembly는 `unsupported-nested-assembly` |
+| `*INSTANCE` / `*END INSTANCE` | supported; assembly 내부 | `NAME=<instance-name>`, `PART=<part-name>` 필수; 두 keyword 사이 data 없음 | named identity copy; 같은 part의 여러 identity instance 허용 | translation/rotation data는 `unsupported-instance-transform`; duplicate/dangling instance는 error |
+| `*BOUNDARY` | supported; top-level model data 또는 sole step 내부 | parameter 없음; 각 row `target, first_dof, last_dof[, value]`; omitted value는 `0` | sole step의 prescribed displacement | invalid arity/range, unresolved target, conflicting expanded node/DOF value는 error |
+| `*CLOAD` | supported; sole step 내부 | parameter 없음; 각 row `target, dof, magnitude` | sole step의 global nodal concentrated load | invalid arity/DOF, nonfinite magnitude 또는 unresolved target은 error |
+| `*STEP` / `*END STEP` | supported; exactly one top-level history block | optional `NAME`; optional `NLGEOM=NO`; `*END STEP` data 없음 | canonical result identity `(Step-1, frame 0)` | second step은 `unsupported-multiple-step`; `NLGEOM=YES`는 `unsupported-nonlinear-geometry` |
+| `*STATIC` | supported; sole step 내부, exactly once | parameter 없음; exactly one row `initial_increment, time_period, minimum_increment, maximum_increment` | 승인 legacy row를 읽되 V0는 하나의 linear solve와 frame 0만 생성 | missing/extra/nonfinite/nonpositive field 또는 다른 procedure는 error |
+| `*PREPRINT` | warning no-op; top-level | 모든 parameter를 보존 후 무시; data 없음 | legacy generator control 수용 | semantic object를 만들지 않음 |
+| `*RESTART` | warning no-op; sole step | 모든 parameter를 보존 후 무시; data 없음 | legacy restart request 수용 | restart state를 만들지 않음 |
+| `*TRANSVERSE SHEAR STIFFNESS` | warning no-op; beam section context | keyword와 소속 data line을 보존 후 무시 | B33 legacy deck 수용 | Euler formulation/property를 변경하지 않음 |
+| `*OUTPUT, FIELD` | warning no-op; sole step | output parameter와 subordinate data를 보존 후 무시 | legacy field request root 수용 | mandatory FESA output을 선택·억제하지 않음 |
+| `*OUTPUT, HISTORY` | warning no-op; sole step | output parameter와 subordinate data를 보존 후 무시 | legacy history request root 수용 | history result를 생성하지 않음 |
+| `*NODE OUTPUT` | warning no-op; active output request 내부 | 모든 parameter와 다음 keyword 전 variable data를 무시 | legacy nodal variable request 수용 | requested variables로 HDF5 schema를 변경하지 않음 |
+| `*ELEMENT OUTPUT` | warning no-op; active output request 내부 | 모든 parameter와 다음 keyword 전 variable data를 무시 | legacy element variable request 수용 | requested variables로 HDF5 schema를 변경하지 않음 |
+| `*CONTACT OUTPUT` | warning no-op; active output request 내부 | 모든 parameter와 다음 keyword 전 variable data를 무시 | legacy contact variable request 수용 | contact model/result를 만들지 않음 |
+
+`*DLOAD`, `*INCLUDE` 및 표에 없는 model-affecting keyword는 no-op 대상이 아니며
+`unsupported-keyword` input error다. 특히 formulation-only constant local line-load
+kernel은 parser나 Domain의 distributed-load 지원을 뜻하지 않는다.
+
+### Nesting grammar
+
+```text
+input-file
+  := heading? part+ assembly material+ model-boundary* step EOF
+
+part
+  := *PART
+       node-block+ element-block+ (nset | elset)*
+       general-section+ section-points*
+     *END PART
+
+assembly
+  := *ASSEMBLY
+       instance+ assembly-set*
+     *END ASSEMBLY
+
+instance
+  := *INSTANCE *END INSTANCE
+
+step
+  := *STEP *STATIC step-boundary* cload* allowed-no-op* *END STEP
+```
+
+Top-level material과 model boundary는 step 전에만 나타난다. Part는 assembly 전에 모두
+닫혀야 하고 assembly 안에는 instance와 assembly-level set만 허용한다. Instance 안의
+node/element 재정의, nested assembly, dependent/independent mesh option은 지원하지 않는다.
+Sole step의 source `NAME` spelling은 metadata에 보존하지만 V0 HDF5와 comparison의
+canonical identity는 항상 `Step-1`, `frame 0`이다.
+
+## Syntax Policy
+
+- keyword line은 첫 non-whitespace character가 `*`이고 `**`가 아니어야 한다.
+- comment line은 `**`로 시작하며 의미 모델에서는 제외하되 file과 1-based line 위치를
+  유지한다.
+- keyword, parameter name, enumerated parameter value와 named-reference lookup은 ASCII
+  case-insensitive다. Part, instance, material, set의 원래 spelling과 numeric label lexeme는
+  외부 identity를 위해 그대로 보존한다.
+- keyword line은 comma-separated `KEY[=VALUE]` fields다. Data line도 comma-separated이며
+  field 양끝 whitespace를 제거한다. Required empty field, trailing empty optional value,
+  잘못된 numeric token은 input error다.
+- Keyword/data continuation, quoted/multiline name, include file 및 line continuation은 V0에서
+  지원하지 않는다. 한 logical keyword/data row는 한 physical line에 완결되어야 한다.
+- Node/element labels와 explicit set members는 positive base-10 integer다. Internal index로
+  바꾸어도 raw source label text를 잃지 않는다.
+- 모든 numeric value는 finite `double`이어야 한다. `NaN`, positive/negative infinity는
+  syntax/semantic validation에서 거부한다.
+- 각 parsed keyword, parameter, data row와 semantic entity는 `file`, 1-based `line`, raw
+  `keyword`, raw source label을 추적할 수 있어야 한다.
+- Output-request subordinate variable data는 직전의 allowlisted output keyword부터 다음
+  keyword까지에만 warning no-op이다. 그 밖의 예상되지 않은 data line은 input error다.
+
+### Duplicate and dangling-reference policy
+
+- Part, assembly, instance, material, set 이름은 각 semantic scope의 case-insensitive key로
+  unique해야 한다. Node/element numeric source label은 part scope에서 unique해야 한다.
+- 같은 part의 여러 identity instance는 duplicate가 아니다. 각 copy는 instance name으로
+  구분되는 별도 source identity를 가진다.
+- Element connectivity, set membership, instance `PART`, section `ELSET`/`MATERIAL`, assembly
+  set `INSTANCE`, boundary/load target은 Domain finalization 전에 모두 resolve되어야 한다.
+- Duplicate definition은 `duplicate-entity`; unresolved reference는 `unresolved-reference`로
+  진단하고 partial Domain을 해석에 넘기지 않는다.
+
+## Model Data Mapping
+
+### Stable source identity and instances
+
+Part-local node, element, set은 instance expansion 뒤 다음 identity를 갖는다.
+
+```text
+SourceEntityId { instance_name, source_label }
+```
+
+`instance_name`과 `source_label`은 원래 spelling을 보존한다. Case-insensitive lookup key와
+표시용 raw text는 별개다. Stable Domain internal index는 input declaration order,
+instance declaration order, part-local entity declaration order의 결정적 순서로 부여하며
+thread count나 hash iteration order에 의존하지 않는다. 같은 part의 두 identity instance는
+source label이 같아도 instance name이 다르므로 서로 merge하지 않는다.
+
+Assembly-level `*NSET`/`*ELSET`의 `INSTANCE`는 정확히 하나의 identity instance를
+지정하고 data의 label을 그 instance가 참조하는 part-local source label로 resolve한다.
+따라서 assembly set member도 `(instance_name, source_label)`로 결정된다. V0는 한 set에
+여러 instance의 member를 섞는 grammar를 제공하지 않는다.
+
+### Nodes, elements, sets, material, and section
+
+- Node는 global Cartesian coordinate `[X,Y,Z]`, stable internal node ID와 source identity를
+  가진다.
+- B33 element는 ordered connectivity `[node_1,node_2]`, stable internal element ID,
+  source identity, general-section assignment를 가진다. Connectivity order가 local tangent
+  `t=(X2-X1)/L`의 방향을 정한다.
+- Explicit set은 data order, generated set은 inclusive `first,last,increment` expansion
+  order를 보존한다. Membership은 internal ID에 연결되지만 source identity로 round-trip
+  가능해야 한다.
+- Material은 정확한 입력 `E,nu`를 보존하고 `G=E/(2(1+nu))`를 유도한다.
+- General section 첫 row는 정확히 `[A,I11,I12,I22,J]`다. V0는 `I12`의 exact numeric
+  zero만 허용하고 `Iy=I11`, `Iz=I22`로 매핑한다.
+- Guide vector `a=n1`을 tangent에 직교 투영·정규화하여 local `y`로, `t x n1`을 local
+  `z`로 둔다. `(x,y,z)`는 right-handed다.
+
+### Model validation
+
+모든 값은 finite여야 하고 다음 조건을 element calculation 전에 검사한다.
+
+```text
+E > 0
+G = E / (2 * (1 + nu)) > 0
+A > 0, Iy > 0, Iz > 0, J > 0
+L > 1e-12 * max(1, norm(X1), norm(X2))
+norm(a_perp) > 1e-12 * max(1, norm(a))
+```
+
+`a_perp = a - dot(a,t)*t`다. 길이 조건 실패는 `invalid-beam-length`, zero guide vector나
+projection 조건 실패는 `invalid-beam-guide-vector`, nonpositive property는
+`invalid-beam-property`, `I12!=0`은 `unsupported-coupled-section` model diagnostic이다.
+Fallback axis, absolute-value 보정 또는 B31 재해석은 허용하지 않는다.
+
+## History Data Mapping
+
+V0는 하나의 history object, canonical `Step-1`만 만든다. `*STATIC`의 네 legacy field는
+각각 `initial_increment`, `time_period`, `minimum_increment`, `maximum_increment`로
+보존한다. 모두 finite positive여야 하고 `minimum_increment <= maximum_increment`여야
+한다. 이 값들은 입력 호환성과 provenance를 위한 값이며 V0가 increment loop나 여러
+frame을 생성하게 하지 않는다. 결과는 항상 `(Step-1, frame 0)`이다.
+
+`*BOUNDARY`의 target은 node source label 또는 node set이다. Assembly set은 그
+`INSTANCE`를 포함해 source node identity로 확장한다. `first_dof <= last_dof`이고 두 값은
+1..6이어야 한다. 생략된 value는 exact zero다. Model-level boundary와 step-level boundary는
+sole step에 활성화되며 같은 expanded node/DOF에 서로 다른 value가 생기면 input error다.
+
+`*CLOAD` target resolution은 boundary와 같고 각 row는 해당 target의 모든 node에 global
+component load를 적용한다. 같은 node/DOF로 resolve되는 여러 load row는 input order로
+결정적으로 합산한다.
+
+| DOF | nodal kinematic component | boundary unit dimension | CLOAD component | load unit dimension |
+| ---: | --- | --- | --- | --- |
+| 1 | `UX` | length | `FX` | force |
+| 2 | `UY` | length | `FY` | force |
+| 3 | `UZ` | length | `FZ` | force |
+| 4 | `URX` | radian | `MX` | force x length |
+| 5 | `URY` | radian | `MY` | force x length |
+| 6 | `URZ` | radian | `MZ` | force x length |
+
+Abaqus output request는 history activation이나 output selection으로 매핑하지 않는다.
+Allowlisted request의 존재 여부와 무관하게 mandatory HDF5 dataset은 모두 생성된다.
+
+## Internal Model Contract
+
+- Domain은 nodes, B33 elements, sets, material, section, boundary, load와 sole static step의
+  완전한 semantic definition을 소유하고 mapping 이후 effectively immutable하다.
+- AnalysisModel은 sole step에 활성인 Domain IDs/references만 제공하며 Domain object를
+  복사하지 않는다.
+- Node/element는 equation ID를 소유하지 않는다. DOF numbering과 constrained/free mapping은
+  이 I/O 계약 밖의 DofManager 책임이다.
+- Boundary와 load는 expansion 전 target identity와 expansion 후 stable node identity를 모두
+  추적할 수 있어야 한다.
+- Result identity는 source identity와 stable internal identity를 모두 보유해야 하며
+  parser의 raw keyword string을 solver physics object로 사용하지 않는다.
+- Endpoint equilibrium action, endpoint section resultant, Gauss generalized result,
+  assembled residual reaction은 서로 다른 quantity/location identity다.
+
+## Output HDF5 Schema
+
+Authoritative output은 하나의 HDF5 file `results.h5`, schema version `0`이다. 아래의
+`<step-name>`은 V0에서 literal `Step-1`이다. 모든 string은 UTF-8, 모든 물리 실수는
+IEEE-754 float64, stable internal ID는 uint64다.
+
+### Metadata and model identity
+
+`/metadata`는 group이며 다음 scalar attributes를 반드시 가진다.
+
+| attribute | required value or meaning |
+| --- | --- |
+| `schema_version` | `0` |
+| `feature_id` | `linear-static-3d-euler-beam` |
+| `solver_version` | 실행 solver version string |
+| `source_input_identity` | normalized input path와 content identity를 추적 가능한 string |
+| `unit_system_label` | ordinary run은 `user-consistent-unspecified` |
+| `coordinate_convention` | `global-cartesian; beam-local=(t,n1,t-cross-n1)` |
+| `element_formulation` | `B33-3D-Euler-Bernoulli` |
+| `step_name` | `Step-1` |
+| `frame_index` | integer `0` |
+
+승인 legacy comparison은 `.inp`에서 SI를 추론하지 않는다. Reference Model Contract와
+verification report가 model `cantilever-beam-b33`에 외부 `SI` provenance를 적용한다.
+
+| dataset path | shape and dtype | row identity / fields | required attributes and ordering |
+| --- | --- | --- | --- |
+| `/model/nodes` | `[node_count]` compound | `internal_node_id:uint64`, `instance_name:utf8`, `source_label:utf8`, `coordinates:float64[3]` | internal node ID ascending; `coordinate_system=global-cartesian`, `units_label=length` |
+| `/model/elements` | `[element_count]` compound | `internal_element_id:uint64`, `instance_name:utf8`, `source_label:utf8`, `node_internal_ids:uint64[2]`, `local_axes:float64[3,3]` | internal element ID ascending; axes row order `[x,y,z]`, `formulation=B33-3D-Euler-Bernoulli` |
+
+### Step/frame result datasets
+
+| quantity | exact dataset path | shape | row identity and component order | units/coordinates/location |
+| --- | --- | --- | --- | --- |
+| displacement | `/steps/<step-name>/frames/0/nodal/displacement` | `[node_count,6]` float64 | `/model/nodes` row; `[UX,UY,UZ,URX,URY,URZ]` | `[length,length,length,radian,radian,radian]`; global; nodal |
+| reaction | `/steps/<step-name>/frames/0/nodal/reaction` | `[node_count,6]` float64 | `/model/nodes` row; `[RF1,RF2,RF3,RM1,RM2,RM3]` | `[force,force,force,force*length,force*length,force*length]`; global; nodal |
+| equilibrium end action | `/steps/<step-name>/frames/0/element/end_force_local` | `[element_count,2,6]` float64 | element row, endpoint `[-1,+1]`; `[FX,FY,FZ,MX,MY,MZ]` | `[force x3, force*length x3]`; beam local; endpoint outward action |
+| endpoint section resultant | `/steps/<step-name>/frames/0/element/section_resultant` | `[element_count,2,4]` float64 | element row, endpoint `[-1,+1]`; `[N,T,My,Mz]` | `[force,force*length,force*length,force*length]`; beam local; positive-local-x section cut |
+| generalized strain | `/steps/<step-name>/frames/0/element/generalized_strain` | `[element_count,2,4]` float64 | element row, Gauss point `[-1/sqrt(3),+1/sqrt(3)]`; `[epsilon0,kappa_x,kappa_y,kappa_z]` | `[1,1/length,1/length,1/length]`; beam local; integration point |
+| generalized resultant | `/steps/<step-name>/frames/0/element/generalized_resultant` | `[element_count,2,4]` float64 | element row, same Gauss points; `[N,T,My,Mz]` | `[force,force*length,force*length,force*length]`; beam local; integration point |
+| axial stress | `/steps/<step-name>/frames/0/element/stress_s11` | `[stress_row_count]` compound | `internal_element_id`, `gauss_point_index`, `section_point_index`, `x1`, `x2`, `source`, `S11` | element/Gauss/section order; `units_label=force/length^2`, beam local section point |
+| diagnostics | `/diagnostics` | `[diagnostic_count]` compound | `severity`, `code`, `file`, `line`, `keyword`, `entity_identity`, `message` | deterministic diagnostic order; empty dataset is required when count is zero |
+
+각 numeric result dataset은 `component_names`, `component_unit_dimensions`,
+`coordinate_system`, `location`, `step_name=Step-1`, `frame_index=0` attributes를 가진다.
+Endpoint axis order는 `xi=-1` then `xi=+1`, Gauss axis order는 negative then positive다.
+Stress row는 internal element ID, Gauss index 1..2, input section-point index 순으로 정렬한다.
+입력 section point가 없으면 `(x1,x2)=(0,0)`, index `0`, `source=fesa-default`인 centroid
+row 하나를 각 Gauss point에 쓴다. 입력 point는 index 1부터 원래 data order를 따른다.
+
+Reaction은 모든 node와 여섯 component에 존재하며 free DOF의 residual도 포함한다.
+Transverse/torsional shear stress dataset이나 averaged nodal stress는 만들지 않는다.
+`S11`은 mandatory HDF5 output이지만 Abaqus reference comparison은 명시적 N/A다.
+
+### Atomic finalization
+
+Writer는 requested final path와 같은 directory에 temporary HDF5를 만들고 모든 mandatory
+group/dataset/attribute 작성, flush, close, schema self-check가 성공한 뒤에만 final path를
+원자적으로 교체한다. 실패하면 temporary artifact는 비권위적이며 기존 final file이
+있다면 그대로 보존한다. 실패한 새 run은 불완전한 `results.h5`를 남기지 않고 exit code
+`6`과 HDF5 diagnostic을 반환한다.
+
+## FESA HDF5 to Reference CSV Comparison Schema
+
+Authoritative 비교는 위 HDF5 rows와 read-only Abaqus CSV rows 사이에서만 수행한다.
+HDF5에서 추출한 deterministic CSV view는 debugging/review 보조물이며 solver output이나
+reference artifact가 아니다.
+
+### Approved legacy artifact precheck
+
+Comparison 전에 다음 exact files가 존재하고 변경되지 않았음을 확인한다.
+
+- `reference/cantilever beam/cantilever beam.inp`
+- `reference/cantilever beam/cantilever beam displacements.csv`
+- `reference/cantilever beam/cantilever beam reactions.csv`
+- `reference/cantilever beam/cantilever beam elemental forces.csv`
+
+Input은 `TYPE=B33`이어야 하고 trim한 CSV header는 아래 mapping 표와 정확히 일치해야
+한다. 각 projected row key는 unique하고 모든 numeric value는 finite여야 한다. 파일
+missing/type mismatch는 `needs-reference-artifacts`, header/value/identity mismatch는
+`schema-mismatch`이며 comparison은 시작하지 않는다. `metadata.json` 부재는 프로젝트
+전역 정책에 따라 허용되고, `README.md`는 이 legacy bundle에서 N/A다. 파일을 rename,
+rewrite, zero-clamp 또는 보정하지 않는다.
+
+### Header and component normalization
+
+| legacy file/header | canonical quantity/component | FESA HDF5 source |
+| --- | --- | --- |
+| `U-U1`, `U-U2`, `U-U3` | displacement `UX`, `UY`, `UZ` | `nodal/displacement` columns 0..2 |
+| `UR-UR1`, `UR-UR2`, `UR-UR3` | displacement `URX`, `URY`, `URZ` | `nodal/displacement` columns 3..5 |
+| `RF-RF1`, `RF-RF2`, `RF-RF3` | reaction `RF1`, `RF2`, `RF3` | `nodal/reaction` columns 0..2 |
+| `RM-RM1`, `RM-RM2`, `RM-RM3` | reaction `RM1`, `RM2`, `RM3` | `nodal/reaction` columns 3..5 |
+| `SF-SF1` | section resultant `N` | `element/section_resultant` component `N` |
+| `SM-SM1` | section resultant `My` | `element/section_resultant` component `My` |
+| `SM-SM2` | section resultant `Mz` | `element/section_resultant` component `Mz` |
+| `SM-SM3` | section resultant `T` | `element/section_resultant` component `T` |
+
+General Abaqus beam component meaning and FESA local mapping은 다음과 같다.
+
+| Abaqus component | equilibrium end-action component | section-resultant component |
+| --- | --- | --- |
+| `SF1` | `FX` | `N` |
+| `SF3` | `FY` | N/A in `[N,T,My,Mz]` |
+| `SF2` | `FZ` | N/A in `[N,T,My,Mz]` |
+| `SM3` | `MX` | `T` |
+| `SM1` | `MY` | `My` |
+| `SM2` | `MZ` | `Mz` |
+
+이 general mapping은 component axis의 의미다. Outward equilibrium end action과
+positive-local-x-face section resultant의 sign identity를 합치지 않는다. 승인 legacy
+CSV는 `SF1/SM1/SM2/SM3`만 제공하고 section-cut result와 비교하므로 `SF2`/`SF3` row를
+0으로 만들거나 reference row로 합성하지 않는다. HDF5의 transverse end action은
+unit/analytical test와 physics sanity 대상이다.
+
+### Frame, instance, and node-station normalization
+
+- Legacy `Frame` value `Increment 1: Step Time = 1.000`은 canonical `(Step-1, frame 0)`으로
+  변환한다. 승인 bundle의 다른 increment/time string은 `schema-mismatch`다.
+- `Part Instance Name`은 HDF5 `/model/nodes` 또는 `/model/elements`의 exact preserved
+  `instance_name`과 case-insensitive lookup 후 raw identity 일치 여부를 확인한다.
+- `Node Label`은 instance 안의 preserved source node label로 resolve한다. Displacement와
+  reaction key는 `(model_id,Step-1,0,instance_name,source_node_label,quantity,component)`다.
+- Elemental-force CSV는 element label이 없으므로 HDF5 endpoint section resultants를
+  source node station으로 project한다. Boundary station은 유일한 incident endpoint를 쓴다.
+- Interior station collapse는 정확히 두 incident B33 endpoints, 동일 section/local-axis
+  orientation, 일관된 chain connectivity, 해당 node의 concentrated force/moment가 없는
+  경우에만 허용한다. 두 positive-face section-cut 값이 아래 승인 component tolerance
+  안에서 먼저 일치해야 한다.
+- Interior 값이 일치하면 stable internal element ID가 작은 endpoint를 deterministic
+  representative로 선택한다. 두 값을 평균하지 않는다. 불일치는 `tolerance-failure`다.
+- Reversed connectivity, local-axis discontinuity, section jump, branch 또는 loaded interior
+  station은 element label 없는 legacy schema로 collapse할 수 없다. 이 approved bundle
+  밖에서는 element-aware reference row가 필요하며 legacy projection은 `schema-mismatch`로
+  중단한다.
+
+Projected canonical comparison row는 다음 fields를 가진다.
+
+```text
+model_id, step_name, frame_index, instance_name, source_node_label,
+quantity, component, value, unit_dimension, coordinate_system, hdf5_dataset_path
+```
+
+Stable ordering은 quantity inventory order, instance declaration order, stable source node
+order, component order다. Approved model ID는 `cantilever-beam-b33`; nodal quantities는
+global Cartesian, section resultants는 beam local이다.
+
+### Row-set precheck and tolerance
+
+먼저 양쪽을 legacy contract가 실제 제공하는 quantity/component projection으로 제한한다.
+그 projection 안에서는 missing, extra, duplicate, nonfinite, schema-mismatched 또는
+identity-mismatched row가 하나라도 있으면 tolerance 계산 전에 실패한다. HDF5에만
+mandatory인 `SF2/SF3` 대응 end action, generalized results와 `S11`은 계약상 비교 대상이
+아니므로 extra reference row가 아니다.
+
+Matched rows는 같은 `model_id`, step/frame, quantity, component로 group한다.
+
+```text
+reference_scale = max(abs(reference_value_i))
+row_tolerance = absolute_floor + 1e-6 * reference_scale
+row_pass = abs(fesa_value_i - reference_value_i) <= row_tolerance
+```
+
+즉 exact policy는 `absolute_floor + 1e-6 * reference_scale`이다. `reference_scale`은
+read-only Abaqus values만 사용하고 FESA 값으로 조정하지 않는다. Scale이 zero면 relative
+term은 zero다. Reference value나 작은 residue를 zero-clamp하지 않고 모든 row를 판정한다.
+
+| approved SI component class | absolute floor |
+| --- | ---: |
+| displacement and rotation | `1e-9` |
+| force and moment | `1e-3` |
+
+Interior endpoint consistency도 해당 CSV quantity/component의 same Abaqus-only scale과
+floor를 사용한다. Verification report는 모든 row pass/fail과 quantity별 max absolute
+error, component-scale normalized error, RMS error, norm error, worst row/component를
+기록한다. 이 reference tolerance는 analytical/formulation tolerance를 대체하지 않는다.
+
+## CLI and Diagnostics Contract
+
+```powershell
+fesa.exe <model.inp> --output <results.h5>
+```
+
+`--output`을 생략하면 현재 작업 directory의 `results.h5`가 final path다. Input path는
+정확히 하나이며 unknown option, missing argument, repeated `--output`은 usage error다.
+
+| exit code | meaning |
+| ---: | --- |
+| `0` | success; authoritative HDF5 finalization complete |
+| `2` | CLI usage error |
+| `3` | input syntax or semantic mapping error, including unsupported keyword/formulation/wrapper |
+| `4` | model validation error, including geometry, section or property invalidity |
+| `5` | factorization or substitution error |
+| `6` | HDF5 write, validation or atomic finalization error |
+
+각 stderr diagnostic record는 exact field order `severity`, `code`, `file`, `line`,
+`keyword`, `entity_identity`, `message`를 사용한다. Source-backed diagnostics는 normalized
+file path와 1-based line을 가지며, source가 없는 solver/output error는 빈 source field를
+명시한다. 출력 순서는 source file declaration order, line, entity stable internal ID,
+diagnostic code의 tuple로 결정하고 같은 tuple에서는 discovery order를 보존한다. Warning은
+성공 run에서도 `/diagnostics`에 기록되며 error가 있으면 해당 exit class를 반환한다.
+
+## Validation Rules
+
+| validation area | required pass condition | failure class |
+| --- | --- | --- |
+| keyword inventory | supported 또는 exact warning no-op allowlist에 속함 | input, exit 3 |
+| nesting/cardinality | closed part/assembly/instance/step; one assembly and one static step | input, exit 3 |
+| source identity | duplicate 없음; all references resolve; multi-instance identity unique | input, exit 3 |
+| B33 semantics | only `TYPE=B33`; two distinct connected nodes | input/model, exit 3 or 4 |
+| section/material | exact data arity/mapping, `I12=0`, all required positive properties | model, exit 4 |
+| geometry/local axes | approved length/projection thresholds and right-handed axes | model, exit 4 |
+| history | DOF 1..6, resolved targets, finite values, sole canonical frame | input, exit 3 |
+| HDF5 | all exact paths, shapes, attributes, identities and finite result values | output, exit 6 |
+| legacy artifacts | exact four files, B33, exact headers, unique finite rows | reference precheck |
+| comparison | exact projected row-set, endpoint eligibility/consistency, approved tolerance | reference verification |
+
+No parser/HDF5 implementation, reference artifact mutation, Abaqus execution, physics pass 또는
+release approval을 이 status가 의미하지 않는다.
+
+## Open Issues and Downstream Handoff
+
+### Resolved numerical-review handoff
+
+`NR-O03-STATION-NORMALIZATION`은 approved legacy bundle에 대해 unloaded, consistently
+oriented two-endpoint interior station만 collapse하고, tolerance check 후 smaller stable
+element ID를 선택하는 규칙으로 구체화했다. Reversed/branched/loaded/jumped station은
+element-aware reference가 없는 한 비교하지 않는다.
+
+### Reference Model Agent
+
+- Exact legacy inventory, generator `Abaqus/CAE Learning Edition 2024`, source commit
+  `2b34d0b`, external SI provenance와 stress comparison N/A를 계약에 고정한다.
+- 추가 reference model은 canonical filenames와 metadata를 사용하며 이 legacy file을
+  변경하지 않는다.
+
+### Implementation Planning Agent
+
+- Keyword별 positive/negative grammar, source location, duplicates/dangling references,
+  B31/transform/nested/multiple-step/NLGEOM diagnostics를 TDD cases로 만든다.
+- Exact HDF5 path/shape/component/identity, mandatory-output independence와 atomic failure를
+  검증한다.
+- C++ API는 이 semantic contract에서 파생하되 여기에 소급해 API 설계를 추가하지 않는다.
+
+### Reference Verification Agent
+
+- Artifact precheck 뒤 HDF5-to-legacy projection, node-station eligibility, row-set equality,
+  component-scale comparison 순서를 유지한다.
+- Missing/extra/nonfinite row를 무시하거나 `SF2/SF3`/stress reference row를 합성하지 않는다.
+

docs/io-definitions/linear-static-mitc4-shell-io.md

@@ -0,0 +1,663 @@
+# Linear Static MITC4 Shell I/O Definition
+
+## Metadata
+
+- feature_id: `linear-static-mitc4-shell`
+- source_requirement: `docs/requirements/linear-static-mitc4-shell.md`
+- source_research: `docs/research/linear-static-mitc4-shell-research.md`
+- source_formulation: `docs/formulations/mitc4-shell-formulation.md`
+- source_numerical_review: `docs/numerical-reviews/linear-static-mitc4-shell-review.md`
+- source_commits: requirements/research/formulation policy revision `73df844`
+- status: `approved-for-implementation-planning`
+- owner_agent: `io-definition-agent`
+- date: `2026-08-13`
+- authoritative_output: `results.h5`
+- hdf5_schema_version: `0`
+- reference_cases: sole acceptance case is read-only full-integration S4 at `reference/shell/`; S4R is covered by non-reference source-mapping/kernel/metadata tests
+- implementation_planning_authorized: `true`
+
+This document defines the approved semantic input and output contract for the
+linear-static MITC4 shell feature. It does not define parser, model, HDF5-writer, or
+comparison-tool C++ APIs and does not claim full Abaqus compatibility or Abaqus
+`S4`/`S4R` formulation equivalence.
+
+The user approved the following I/O-specific decisions on `2026-08-12`:
+
+1. `S4` and `S4R` source types map to one internal full-integration `FESA-MITC4`
+   formulation, while only S4 is an Abaqus acceptance reference.
+2. The optional positive integer on a `*SHELL SECTION` thickness row is accepted
+   without a warning and has no semantic effect on FESA quadrature. FESA always uses
+   the formulation's `2 x 2 x 2` rule.
+3. The existing `reference/shell/` S4 input/displacement files are the sole declared
+   acceptance pair and remain under their current names without mutation. Existing
+   `reference/shellR/` files are untouched optional evidence and are not consumed by
+   acceptance comparison. No canonical or legacy-alias classification is required.
+4. HDF5 schema version `0` is extended additively with MITC4-specific datasets while
+   retaining the existing common metadata, nodal-result, diagnostic, CLI, and
+   failure-atomicity conventions.
+
+The approved requirements fix the drilling rule and the MITC4 fixed absolute
+displacement tolerance `1.0e-5`.
+Drilling calibration/output, `NR-O03`, `NR-O04`, bundle-administration metadata, and
+an expanded reference portfolio are outside this contract.
+
+## 1. Abaqus Input Scope
+
+- input_format: Abaqus input file (`.inp`)
+- supported_analysis: exactly one small-displacement, small-rotation linear-static
+  step containing four-node `S4` and/or `S4R` shell elements
+- ordinary_unit_system: user-consistent; FESA does not infer SI or another unit
+  system from an `.inp` file
+- internal_element_formulation: `FESA-MITC4`
+- compatibility_disclaimer: only the keyword locations, parameters, and data grammar
+  in this document are supported
+
+`supported` means only the documented subset is semantically interpreted. `warning
+no-op` means the syntax is consumed and a structured warning is recorded, but no
+Domain, AnalysisModel, numerical, or mandatory-output meaning changes. The optional
+`*SHELL SECTION` integration-point field is a separately approved silent provenance
+field, not a warning no-op keyword.
+
+| keyword | status and allowed location | required parameters and data grammar | semantic mapping | unsupported behavior |
+| --- | --- | --- | --- | --- |
+| `*HEADING` | supported; optional top-level first keyword | no parameters; zero or more text rows until next keyword | original heading retained as source metadata | nested location or parameters are input errors |
+| `*PART` / `*END PART` | supported; top-level model block | `NAME=<part-name>` required; no `*END PART` data | scope for part-local nodes, elements, sets, and shell sections | unclosed/nested part or duplicate name is an input error |
+| `*NODE` | supported; part scope | no parameters; each row `node_label,x,y,z` | positive source node label and finite global Cartesian coordinates | wrong arity, duplicate label, or nonfinite value is an input error |
+| `*ELEMENT` | supported; part scope | `TYPE=S4` or `TYPE=S4R`; each row `element_label,node_1,node_2,node_3,node_4` | ordered four-node shell connectivity; source type retained separately; internal type is `FESA-MITC4` | another type is `unsupported-element-formulation`; wrong arity, repeated connected node, or dangling node is an error |
+| `*NSET` | supported; part or assembly scope | `NSET=<name>`; optional `GENERATE`; assembly scope requires `INSTANCE=<name>`; explicit labels or `first,last,increment` | deterministic node-set membership | mixed-instance set, invalid generate range, duplicate name, or dangling member is an error |
+| `*ELSET` | supported; part or assembly scope | `ELSET=<name>`; optional `GENERATE`; assembly scope requires `INSTANCE=<name>`; same row rules as `*NSET` | deterministic element-set membership | mixed-instance set, invalid range, duplicate name, or dangling member is an error |
+| `*MATERIAL` | supported; top-level model data | `NAME=<material-name>` required; no data | owns exactly one approved isotropic `*ELASTIC` definition | duplicate name, missing/duplicate elasticity, or another material model is an error |
+| `*ELASTIC` | supported; current material scope | no parameters; exactly one row `E,nu` | homogeneous isotropic elasticity; `G=E/(2(1+nu))` | extra row/field, dependency/temperature data, nonfinite value, `E<=0`, or `nu<=-1`/`nu>=0.5` is an error |
+| `*SHELL SECTION` | supported; part scope | `ELSET=<name>` and `MATERIAL=<name>` required; exactly one row `thickness[,integration_points]` | one centered homogeneous layer with constant thickness | composite/layer data, offset, orientation, distributed/nodal thickness, missing reference, or conflicting assignment is an error |
+| `*ASSEMBLY` / `*END ASSEMBLY` | supported; exactly one top-level assembly | `NAME=<assembly-name>` required; no end data | scope for identity instances and assembly sets | nested/duplicate assembly is `unsupported-nested-assembly` |
+| `*INSTANCE` / `*END INSTANCE` | supported; assembly scope | `NAME=<instance-name>`, `PART=<part-name>` required; no intervening data | named identity copy; multiple instances of a part are allowed | translation/rotation data is `unsupported-instance-transform`; duplicate or dangling instance is an error |
+| `*BOUNDARY` | supported; top-level model data or sole step | no parameters; each row `target,first_dof,last_dof[,value]`; omitted value is exact zero | prescribed global shell DOFs 1 through 6 | invalid arity/range, unresolved target, or conflicting expanded value is an error |
+| `*CLOAD` | supported; sole step | no parameters; each row `target,dof,magnitude` | concentrated global nodal force/moment on DOFs 1 through 6 | invalid arity/DOF, nonfinite magnitude, unresolved target, or drilling-direction aggregate moment is an error |
+| `*STEP` / `*END STEP` | supported; exactly one top-level history block | optional `NAME`; optional `NLGEOM=NO`; no end data | one canonical result identity `(Step-1,frame 0)` | second step is `unsupported-multiple-step`; `NLGEOM=YES` is `unsupported-nonlinear-geometry` |
+| `*STATIC` | supported; exactly once in sole step | no parameters; exactly one row `initial_increment,time_period,minimum_increment,maximum_increment` | source values retained; exactly one linear solve and frame 0 | another procedure or missing/extra/nonfinite/nonpositive field is an error |
+| `*PREPRINT` | warning no-op; top-level | all parameters retained then ignored; no data | accepts generator control | no semantic object is created |
+| `*RESTART` | warning no-op; sole step | all parameters retained then ignored; no data | accepts a legacy restart request | no restart state is created |
+| `*OUTPUT, FIELD` | warning no-op; sole step | parameters and subordinate variable data retained then ignored | accepts field-output request root | cannot select, suppress, or expand mandatory FESA output |
+| `*OUTPUT, HISTORY` | warning no-op; sole step | parameters and subordinate variable data retained then ignored | accepts history-output request root | no history dataset is created |
+| `*NODE OUTPUT` | warning no-op; active output request | all parameters and following variable rows ignored | accepts legacy nodal request | cannot change the HDF5 schema |
+| `*ELEMENT OUTPUT` | warning no-op; active output request | all parameters and following variable rows ignored | accepts legacy element request | cannot change the HDF5 schema |
+| `*CONTACT OUTPUT` | warning no-op; active output request | all parameters and following variable rows ignored | accepts legacy contact-output syntax only | no contact model or output is created |
+
+`*DLOAD`, pressure, gravity, body force, edge traction, follower load, explicit
+normal/director input, `*ORIENTATION`, composite/layer controls, `*INCLUDE`, and
+model-affecting keywords not listed above are `unsupported-keyword` errors. A mixed
+B33/shell model and a shell-beam joint are `unsupported-mixed-element-model`; the
+presence of an existing B33 implementation does not expand this feature contract.
+
+Multiple `*ELEMENT` blocks containing `S4`, `S4R`, or both are allowed. Every element
+retains its own source element type, and source type never changes FESA quadrature,
+tying, drilling, recovery, or numerical path.
+
+### 1.1 Shell-section data rule
+
+The exact accepted data row is
+
+```text
+thickness[,integration_points]
+```
+
+- `thickness` is a finite `double` strictly greater than zero.
+- If present, `integration_points` is a positive base-10 integer.
+- The optional field is syntactically accepted without a warning and has no Domain,
+  quadrature, recovery, or output effect.
+- The raw input remains recoverable through the source file/content identity, but
+  no `source_integration_points` physical property is created.
+- FESA stiffness remains four midsurface Gauss locations times two thickness Gauss
+  locations, including when the source value is `5` in the declared S4 case.
+
+Silently accepting this field is an explicit feature contract, not a general rule
+that Abaqus section parameters may be ignored.
+
+### 1.2 Nesting grammar
+
+```text
+input-file
+  := heading? part+ assembly material+ model-boundary* step EOF
+
+part
+  := *PART
+       node-block+ element-block+ (nset | elset)* shell-section+
+     *END PART
+
+assembly
+  := *ASSEMBLY
+       instance+ assembly-set*
+     *END ASSEMBLY
+
+instance
+  := *INSTANCE *END INSTANCE
+
+step
+  := *STEP *STATIC step-boundary* cload* allowed-no-op* *END STEP
+```
+
+All parts close before assembly. Assembly contains only identity instances and
+assembly-level sets. Instance-local node/element redefinition, nested assembly,
+instance transforms, and dependent/independent mesh semantics are excluded.
+
+## 2. Syntax Policy
+
+- The first non-whitespace character of a keyword line is `*`; `**` begins a comment.
+- Comments have no semantic effect but retain normalized file and 1-based line
+  provenance for neighboring parsed records.
+- Keyword names, parameter names, enumerated values, and named-reference lookup are
+  ASCII case-insensitive. Raw source spelling remains available for identity and
+  diagnostics.
+- Keyword and data fields are comma-separated with surrounding whitespace removed.
+  A required empty field, an unexpected trailing field, or a malformed numeric token
+  is an input error.
+- Keyword continuation, physical-line continuation, quoted/multiline names, and
+  include files are unsupported. Each logical keyword or data row is complete on one
+  physical line.
+- Node/element labels and explicit set members are positive base-10 integers.
+  Internal numeric IDs do not replace preserved source label text.
+- All real-valued input is finite. `NaN` and positive/negative infinity are rejected.
+- Every parsed keyword, parameter, data row, and semantic entity remains traceable to
+  normalized file path, 1-based line, raw keyword, and source identity.
+- Output-request variable data is a warning no-op only while subordinate to an
+  allowlisted output keyword. An unexpected standalone data line is an input error.
+
+### 2.1 Duplicate and dangling-reference policy
+
+- Part, assembly, instance, material, set, and section identities are unique in
+  their documented case-insensitive scope.
+- Node and element source labels are unique within a part.
+- Multiple identity instances of the same part are distinct through instance name.
+- Connectivity, set membership, instance `PART`, section `ELSET`/`MATERIAL`, assembly
+  set `INSTANCE`, boundary target, and load target all resolve before Domain commit.
+- Duplicate definitions use `duplicate-entity`; unresolved references use
+  `unresolved-reference`. A partial Domain is never passed to analysis.
+
+## 3. Model Data Mapping
+
+### 3.1 Stable source identity and ordering
+
+After identity-instance expansion, each node and element has
+
+```text
+SourceEntityId { instance_name, source_label }
+```
+
+Raw spelling and the case-insensitive lookup key are separate. Stable internal IDs
+follow input part declaration order, instance declaration order, and part-local
+entity declaration order. Hash iteration and thread scheduling cannot affect IDs,
+director accumulation, result rows, or diagnostics.
+
+Assembly sets name one identity instance and resolve their numeric members to that
+instance's part-local source identities. A set cannot mix members from multiple
+instances in the approved grammar.
+
+### 3.2 Nodes, elements, sets, material, and section
+
+- A node has global Cartesian coordinates, stable internal ID, source identity,
+  geometry-derived initial director, and deterministic tangent frame.
+- A shell element has ordered connectivity `[node_1,node_2,node_3,node_4]`, stable
+  internal ID, source identity, preserved source type `S4` or `S4R`, internal type
+  `FESA-MITC4`, and exactly one resolved section/material.
+- Connectivity order fixes natural corners `1=(-1,-1)`, `2=(+1,-1)`,
+  `3=(+1,+1)`, `4=(-1,+1)` and positive thickness through
+  `A_xi x A_eta`. Connectivity is not silently reversed.
+- Explicit set order follows data rows. Generated sets use inclusive
+  `first,last,increment` order. Set members remain round-trippable to source identity.
+- Material preserves `E` and `nu`; `G=E/(2(1+nu))` is derived.
+- Section preserves positive constant thickness and resolved material. It represents
+  one centered homogeneous isotropic layer.
+- Multiple materials, sections, element sets, `S4` blocks, and `S4R` blocks are
+  allowed when each element resolves to exactly one valid assignment.
+
+### 3.3 Director and geometry preprocessing
+
+Initial directors are semantic model data derived after instance expansion, not
+parser-provided rotations.
+
+1. Process accepted shell elements in stable source-element order.
+2. Compute each source-order-positive center normal candidate and its `2 x 2`
+   surface-area weight.
+3. At each node, sort incident elements by stable source identity and reject any
+   nonpositive pairwise normal dot product before averaging.
+4. Form and normalize the deterministic area-weighted director.
+5. Select the least-aligned global basis axis with fixed `x,y,z` tie order and form
+   right-handed nodal frame `[a,b,d]`.
+
+The complete center, volume-Gauss, tying, and committed-recovery inventory requires
+finite nonzero surface area, finite covariant/reciprocal bases, and finite positive
+`J`. This document supplies no point omission, normal flip, or default axis.
+
+Geometry and director failures are model-validation errors. Duplicate connectivity,
+self-intersection, degenerate/reversed geometry, invalid Jacobians, opposed incident
+normals, and invalid basic mappings fail closed. No calibrated smooth-angle,
+distortion, aspect, or warpage threshold is applied.
+
+## 4. History Data Mapping
+
+### 4.1 Step and procedure
+
+Exactly one history object is created. The source step name remains provenance, but
+the result identity is literal `Step-1`, frame index `0`. The four `*STATIC` values
+are finite positive source data and `minimum_increment <= maximum_increment`; they do
+not create increments, iteration history, or additional frames.
+
+`NLGEOM=NO` or omission is accepted. `NLGEOM=YES`, another procedure, or another step
+is unsupported. The future nonlinear formulation does not expand this history
+contract.
+
+### 4.2 Boundary conditions
+
+Boundary target is a direct source node label or node set and expands to stable
+source node identities. `first_dof <= last_dof`, with both in `1..6`. Omitted value
+is exact zero; a finite nonzero value is supported. Model-level and step-level
+boundaries activate in the sole step. Different prescribed values on one expanded
+node/DOF are an error.
+
+| DOF | kinematic component | unit dimension |
+| ---: | --- | --- |
+| 1 | `U1` | length |
+| 2 | `U2` | length |
+| 3 | `U3` | length |
+| 4 | `UR1` | radian/dimensionless angle |
+| 5 | `UR2` | radian/dimensionless angle |
+| 6 | `UR3` | radian/dimensionless angle |
+
+### 4.3 Concentrated loads and drilling projection
+
+`*CLOAD` target expansion matches boundary expansion. Rows resolving to the same
+node/DOF are accumulated in stable source order before physical admissibility is
+tested.
+
+| DOF | load component | unit dimension |
+| ---: | --- | --- |
+| 1 | `F1` | force |
+| 2 | `F2` | force |
+| 3 | `F3` | force |
+| 4 | `M1` | force*length |
+| 5 | `M2` | force*length |
+| 6 | `M3` | force*length |
+
+For aggregate nodal moment `M_I` and approved unit director `d_I`, exact-zero moment
+is accepted as a separate case. Otherwise compute, without denominator clamping,
+
+```text
+rho_M = abs(dot(d_I,M_I)) / norm(M_I)
+```
+
+and require `rho_M <= 1e-12`. Failure is `unsupported-drilling-load`. No part of a
+rejected physical moment is transferred to numerical drilling stabilization.
+
+### 4.4 Output requests
+
+Allowlisted Abaqus output requests do not activate history output and cannot change
+the mandatory HDF5 inventory. FESA writes all datasets in Section 6 on a successful
+run even when the input contains no output request. Requested Abaqus variables that
+have no FESA dataset do not create empty synthetic physical results.
+
+## 5. Internal Model Contract
+
+- Domain owns the complete immutable-after-mapping definition of nodes, shell
+  elements, sets, materials, sections, boundary/load data, sole static step, stable
+  source identities, initial directors, and source formulation labels.
+- `S4`/`S4R` remains source metadata. Numerical selection uses one explicit internal
+  identity, `FESA-MITC4`.
+- AnalysisModel is a non-owning view of active Domain objects and does not copy them.
+- Nodes/elements do not own equation IDs. Six-DOF numbering, constrained/free maps,
+  scatter maps, and sparse pattern are DofManager responsibilities.
+- Boundary and load records retain both the source target and their deterministic
+  expanded source-node identities.
+- Section/material assignment is resolved before element processing. An element with
+  zero or multiple assignments is invalid.
+- AnalysisState contains only the current linear-static displacement, external and
+  internal force, full residual/reaction, shell recovery, equilibrium, and energy
+  rows. No nonlinear director history, iteration state, velocity, or acceleration is
+  allocated.
+- Midsurface generalized rows, section-position stress rows, nodal rows, and global
+  equilibrium rows have distinct quantity/location identity. Values from different
+  locations are never averaged to satisfy a schema. Drilling-specific result rows do
+  not exist.
+
+## 6. Output HDF5 Schema
+
+The sole authoritative output is `results.h5`, schema version `0`. MITC4 extends
+that schema additively; it does not migrate or reinterpret B33 datasets. Every
+string is UTF-8, every physical real is IEEE-754 float64, stable internal IDs are
+uint64, and constraint masks are uint8.
+
+The literal result path identity is `(Step-1,frame 0)`. No history or nonlinear
+frame group is created.
+
+### 6.1 Metadata
+
+`/metadata` is a group with these required scalar attributes:
+
+| attribute | required value or meaning |
+| --- | --- |
+| `schema_version` | integer `0` |
+| `feature_id` | `linear-static-mitc4-shell` |
+| `solver_version` | executing solver version |
+| `source_input_identity` | normalized input path plus auditable content identity |
+| `unit_system_label` | `user-consistent-unspecified`; FESA does not infer a named unit system from `.inp` or reference artifacts |
+| `coordinate_convention` | `global-cartesian; shell-local=(e1,e2,e3); positive-thickness=+zeta` |
+| `internal_formulation` | `FESA-MITC4` |
+| `integration_rule` | `2x2x2-gauss; mitc4-edge-midpoint-shear` |
+| `step_name` | `Step-1` |
+| `frame_index` | integer `0` |
+
+No drilling coefficient/ratio/energy, `theta_smooth`, or distortion/warp calibration
+attribute is required. The fixed drilling formula is part of the formulation identity,
+not a per-run result policy.
+
+### 6.2 Model identity datasets
+
+| exact dataset path | shape/dtype | row identity and fields | attributes/order |
+| --- | --- | --- | --- |
+| `/model/nodes` | `[node_count]` compound | `internal_node_id:uint64`, `instance_name:utf8`, `source_label:utf8`, `coordinates:float64[3]` | internal node ID ascending; global Cartesian; coordinate unit `length` |
+| `/model/elements` | `[element_count]` compound | `internal_element_id:uint64`, `instance_name:utf8`, `source_label:utf8`, `source_element_type:utf8`, `internal_formulation:utf8`, `node_internal_ids:uint64[4]`, `shell_section_internal_id:uint64`, `material_internal_id:uint64` | internal element ID ascending; connectivity in exact source order; source type `S4|S4R`; formulation `FESA-MITC4` |
+| `/model/shell/nodal_director` | `[node_count,3]` float64 | `/model/nodes` row | dimensionless global components; unit norm within `1e-12` frame check |
+| `/model/shell/nodal_frame` | `[node_count,3,3]` float64 | `/model/nodes` row, axis row `[a,b,d]`, global component column | dimensionless; right-handed and orthonormal |
+| `/model/shell/materials` | `[material_count]` compound | `internal_material_id`, raw `name`, `E`, `nu` | stable declaration order; units `[force/length^2,1]` |
+| `/model/shell/sections` | `[section_count]` compound | `internal_section_id`, source keyword file/line identity, source ELSET, `material_internal_id`, `thickness` | stable declaration order; centered single layer; thickness unit `length` |
+| `/model/nodal_constraint_mask` | `[node_count,6]` uint8 | node row and global DOF order | `0=free`, `1=constrained`; existing HDF5 component names `[UX,UY,UZ,URX,URY,URZ]` |
+| `/model/prescribed_displacement` | `[node_count,6]` float64 | same row/component order | constrained entry is prescribed value; free entry is exact zero with mask as authority |
+| `/model/shell/midsurface_locations` | `[4,2]` float64 | `location_index` implicit row 1..4; columns `[xi,eta]` | exact order in Section 6.3; dimensionless |
+| `/model/shell/section_positions` | `[3]` float64 | rows `BOTTOM,MIDDLE,TOP`; value is `zeta` | exact values `[-1,0,+1]`; physical `z=t*zeta/2` |
+
+The optional source shell-section integration-point field is not written as a
+physical model property. Exact source bytes remain auditable through
+`source_input_identity`.
+
+### 6.3 Fixed shell location ordering
+
+Let `g=1/sqrt(3)`. Every shell result with a four-location axis uses:
+
+| location index | name | `(xi,eta)` |
+| ---: | --- | --- |
+| 1 | `GP1` | `(-g,-g)` |
+| 2 | `GP2` | `(+g,-g)` |
+| 3 | `GP3` | `(+g,+g)` |
+| 4 | `GP4` | `(-g,+g)` |
+
+Every three-section-position axis uses `BOTTOM(zeta=-1)`, `MIDDLE(zeta=0)`, then
+`TOP(zeta=+1)`. Location indices are not Abaqus integration-point numbers and must
+not be relabeled as such in a reference comparison.
+
+### 6.4 Step/frame result datasets
+
+All datasets are mandatory after a successful run, independent of Abaqus output
+requests.
+
+| quantity | exact dataset path | shape | row identity and component order | units/coordinates/location |
+| --- | --- | --- | --- | --- |
+| displacement | `/steps/Step-1/frames/0/nodal/displacement` | `[node_count,6]` float64 | `/model/nodes` row; existing HDF5 component names `[UX,UY,UZ,URX,URY,URZ]` | `[length x3,radian x3]`; global; nodal |
+| reaction/full residual | `/steps/Step-1/frames/0/nodal/reaction` | `[node_count,6]` float64 | `/model/nodes` row; `[RF1,RF2,RF3,RM1,RM2,RM3]` | `[force x3,force*length x3]`; global; nodal; constrained entry is physical reaction, free entry is residual evidence |
+| local frame | `/steps/Step-1/frames/0/element/shell/local_frame` | `[element_count,4,3,3]` float64 | element row, location row, axis row `[e1,e2,e3]`, global component column | dimensionless; location-specific shell local frame |
+| generalized strain | `/steps/Step-1/frames/0/element/shell/generalized_strain` | `[element_count,4,8]` float64 | element row, location row; `[E11,E22,G12,K11,K22,K12,G13,G23]` | `[1,1,1,1/length,1/length,1/length,1,1]`; shell local; midsurface location |
+| section resultant | `/steps/Step-1/frames/0/element/shell/section_resultant` | `[element_count,4,8]` float64 | element row, location row; `[N11,N22,N12,M11,M22,M12,Q13,Q23]` | `[force/length x3,force x3,force/length x2]`; shell local; midsurface location |
+| in-plane stress | `/steps/Step-1/frames/0/element/shell/stress` | `[element_count,4,3,3]` float64 | element row, location row, section-position row, component `[S11,S22,S12]` | `force/length^2`; shell local; direct bottom/middle/top evaluation |
+| energy | `/steps/Step-1/frames/0/global/energy` | `[1]` float64 | `[PHYSICAL_STRAIN_ENERGY]` | `force*length`; deterministic element reduction; excludes numerical drilling stabilization |
+| force/moment balance | `/steps/Step-1/frames/0/global/equilibrium` | `[6]` float64 | `[FORCE_1,FORCE_2,FORCE_3,MOMENT_1,MOMENT_2,MOMENT_3]` | `[force x3,force*length x3]`; global; moment reference point is global origin `[0,0,0]` |
+| verification metrics | `/steps/Step-1/frames/0/global/verification_metrics` | `[3]` float64 | `[FREE_RESIDUAL_NORMALIZED,FORCE_BALANCE_NORMALIZED,MOMENT_BALANCE_NORMALIZED]` | dimensionless; metric-definition IDs and thresholds required as attributes |
+| diagnostics | `/diagnostics` | `[diagnostic_count]` compound | `severity`, `code`, `file`, `line`, `keyword`, `entity_identity`, `message` | deterministic order; required empty dataset when count is zero |
+
+`S33=0` is a plane-stress assumption and is not emitted. `S13`, `S23`, physical
+drilling stress/resultant, and nodally extrapolated/averaged shell stress are not
+created. Transverse shear is externally represented through `Q13/Q23`.
+
+Each numeric result dataset has required attributes `component_names`,
+`component_unit_dimensions`, `coordinate_system`, `location`, `step_name=Step-1`,
+and `frame_index=0`. Shell element results additionally identify their source
+element type, internal formulation, midsurface-location dataset, section-position
+dataset when applicable, and local-frame dataset.
+
+Verification-metric definitions and thresholds follow the approved formulation and
+requirements; they are not reference-bundle metadata.
+
+### 6.5 Reaction, residual, equilibrium, and energy meaning
+
+`nodal/reaction` stores the assembled full residual `K*d-F`; a duplicate nodal
+residual dataset is not written. `/model/nodal_constraint_mask` controls meaning:
+
+- constrained entry: physical reaction;
+- free entry: equation-equilibrium residual evidence.
+
+Global force/moment balance uses applied `CLOAD` plus constrained reaction about
+the global origin. Free residual entries remain separate evidence and are not added
+as physical reactions. The energy dataset contains only physical shell strain energy;
+no drilling energy or drilling-to-physical ratio is written.
+
+### 6.6 Atomic finalization
+
+The writer creates a temporary candidate in the final output directory, writes every
+mandatory group/dataset/attribute, validates finite values, shape, identity, and
+ordering, flushes, closes, reopens read-only, and self-checks the schema. Only then
+may it atomically replace/create the requested final path. A failure preserves any
+previous valid final output when possible, removes or quarantines the non-authority
+candidate, emits an output diagnostic, and returns exit code `6`.
+
+## 7. FESA HDF5 to Reference CSV Comparison Schema
+
+Authoritative comparison reads `results.h5` and read-only Abaqus CSV artifacts.
+A deterministic FESA CSV projection is a debugging/review view only; it is neither
+solver output nor a reference artifact.
+
+### 7.1 Full-integration reference boundary
+
+- FESA maps S4 and S4R source types to the same full `2 x 2 x 2` FESA-MITC4 path.
+- Reference comparison consumes only the declared S4 input/displacement pair.
+- Equality of FESA internal numerical rows after changing only source type is a
+  separate implementation test; it does not consume or compare Abaqus S4R rows.
+
+### 7.2 Declared S4 case
+
+The blocking S4 case uses:
+
+| role | exact path | SHA-256 | observed inventory |
+| --- | --- | --- | --- |
+| input | `reference/shell/shell.inp` | `4005851E1AB22FD3A16AC17A8D5DA3E051233F69F37419079F3553AD134ECFCF` | `TYPE=S4`; declared comparison input |
+| displacement | `reference/shell/shell displacements.csv` | `C81D94E0B4A849F87AA0F79C83A79B94D5661AC79E44ED826919AB432C87746B` | 49 finite data rows; U and UR columns |
+
+The files must not be renamed, rewritten, zero-clamped, normalized, or repaired.
+The reaction and stress CSV files in the same directory are optional review evidence
+and are not comparison inputs.
+
+### 7.3 S4R non-reference coverage
+
+No file under `reference/shellR/` is required or consumed by this acceptance
+comparison. S4R source support is verified by parser mapping, S4/S4R common-kernel
+and deterministic-assembly equivalence, plus preserved HDF5 source-type metadata.
+Any existing S4R artifacts remain immutable optional inspection evidence. No README,
+`metadata.json`, canonical name, legacy alias, provenance record, or duplicated model
+description is required.
+
+### 7.4 Displacement header mapping
+
+After trimming header whitespace, the declared S4 displacement CSV uses:
+
+| CSV column | comparison field/component | FESA HDF5 source |
+| --- | --- | --- |
+| `Part Instance Name` | `instance_name` | `/model/nodes.instance_name` |
+| `Node Label` | `source_node_label` | `/model/nodes.source_label` |
+| `U-U1` | displacement `U1` | `nodal/displacement` column 0, HDF5 component `UX` |
+| `U-U2` | displacement `U2` | `nodal/displacement` column 1, HDF5 component `UY` |
+| `U-U3` | displacement `U3` | `nodal/displacement` column 2, HDF5 component `UZ` |
+| `UR-UR1` | displacement `UR1` | `nodal/displacement` column 3, HDF5 component `URX` |
+| `UR-UR2` | displacement `UR2` | `nodal/displacement` column 4, HDF5 component `URY` |
+| `UR-UR3` | displacement `UR3` | `nodal/displacement` column 5, HDF5 component `URZ` |
+
+Reaction and stress CSVs do not enter MITC4 pass/fail. No row is synthesized from
+those optional files.
+
+### 7.5 Normalized comparison row
+
+CSV and HDF5 displacement rows normalize in memory to:
+
+```text
+case_id, instance_name, source_node_label, component, value, hdf5_dataset_path
+```
+
+The unique key is `(case_id,instance_name,source_node_label,component)`. Stable
+ordering is case, instance declaration order, stable source node order, then component order
+`[U1,U2,U3,UR1,UR2,UR3]`.
+
+### 7.6 Row-set precheck and comparison policy
+
+Before tolerance evaluation:
+
+1. Verify the declared input and displacement CSV path exists without mutating it.
+2. Verify the trimmed displacement headers in Section 7.4.
+3. Verify finite values, unique row keys, and exact source node/instance identities.
+4. Project HDF5 and reference to the same six-component displacement inventory.
+5. Fail on any missing, extra, duplicate, nonfinite, header-mismatched, or
+   identity-mismatched projected row.
+
+Only `U1/U2/U3` affect pass/fail. `UR1/UR2/UR3` are always compared and reported but
+can emit only an approved deterministic nonblocking warning.
+
+For every matched displacement row:
+
+```text
+row_tolerance = 1.0e-5
+row_pass = abs(fesa_value-reference_value) <= row_tolerance
+```
+
+The `1.0e-5` value is in the user-consistent length unit for U and dimensionless for
+UR. No reference or result value is zero-clamped and neither component scale nor a
+row-specific denominator changes the fixed value. A reference scale may remain in the
+report as diagnostic information only. U exceedance fails; UR exceedance emits a
+deterministic warning only. The separate B33 mixed tolerance is unchanged.
+
+The report records every U/UR row, blocking/nonblocking decision, absolute error,
+fixed-tolerance-normalized error, RMS error, displacement/rotation vector-norm
+error, worst source row/component, and every UR warning.
+
+## 8. CLI and Diagnostics Contract
+
+```powershell
+fesa.exe <model.inp> --output <results.h5>
+```
+
+Omitting `--output` uses `results.h5` in the current directory. Unknown option,
+missing input, missing output argument, or repeated `--output` is usage failure.
+
+| exit code | meaning |
+| ---: | --- |
+| `0` | successful analysis and authoritative HDF5 finalization |
+| `2` | CLI usage error |
+| `3` | input syntax or semantic mapping error, including unsupported keyword, formulation, wrapper, step, or distributed load |
+| `4` | model validation error, including section/material property, geometry, director, Jacobian, or drilling-direction aggregate moment |
+| `5` | factorization or substitution error |
+| `6` | HDF5 write, schema validation, or atomic finalization error |
+
+Each stderr and HDF5 diagnostic has exact field order `severity`, `code`, `file`,
+`line`, `keyword`, `entity_identity`, `message`. Source-backed records carry
+normalized file and 1-based line; source-less solver/output records use explicit
+empty source fields. Order is source declaration order, file line, stable entity ID,
+diagnostic code, then discovery order for an otherwise equal key.
+
+The approved shell-specific diagnostic inventory includes:
+
+| code | class/exit | meaning |
+| --- | --- | --- |
+| `unsupported-element-formulation` | input/3 | element type is not S4/S4R in this feature |
+| `unsupported-mixed-element-model` | input/3 | shell and non-shell element/joint semantics are mixed |
+| `invalid-shell-connectivity` | input/3 | connectivity arity is not four, a node repeats, or a connected source node is unresolved |
+| `unresolved-shell-section` | input/3 | section/material/ELSET reference is unresolved |
+| `invalid-shell-section-assignment` | input/3 | an element resolves to zero or multiple shell sections |
+| `unsupported-shell-section-option` | input/3 | composite, offset, orientation, variable thickness, or other excluded meaning appears |
+| `invalid-shell-thickness` | model/4 | thickness is nonfinite or nonpositive |
+| `invalid-shell-material` | model/4 | isotropic material violates finite `E,nu` bounds |
+| `invalid-shell-geometry` | model/4 | duplicate, self-intersecting, zero-area, reversed, or nonfinite surface geometry |
+| `opposed-incident-normal` | model/4 | an incident normal pair has nonpositive dot product before averaging |
+| `invalid-shell-director` | model/4 | candidate, average, interpolation, or tangent-frame construction is invalid |
+| `invalid-shell-jacobian` | model/4 | a required point has nonfinite/nonpositive `J` or nonfinite basis data |
+| `unsupported-drilling-load` | model/4 | nonzero aggregate moment violates `rho_M<=1e-12` |
+| `unsupported-distributed-load` | input/3 | DLOAD, pressure, gravity, body/edge/follower load is requested |
+
+The accepted optional `*SHELL SECTION` integration-point field emits no diagnostic.
+Allowlisted `*PREPRINT`, `*RESTART`, and output-request no-ops retain their existing
+warning behavior.
+
+## 9. Validation Rules
+
+| validation area | required pass condition | failure class |
+| --- | --- | --- |
+| keyword inventory | supported or exact allowlisted no-op | input, exit 3 |
+| nesting/cardinality | closed part/assembly/instance/step; one assembly and one static step | input, exit 3 |
+| source identity | duplicates absent; all references resolved; multi-instance identity unique | input, exit 3 |
+| element syntax/semantics | only four-node S4/S4R, distinct resolved connectivity, internal FESA-MITC4, no mixed element model | input, exit 3 |
+| resolved element geometry | source order, finite nonzero area, topology and positive-Jacobian predicates pass | model, exit 4 |
+| material/section syntax | exact row grammar, resolvable references, exactly one centered homogeneous assignment per element | input, exit 3 |
+| material/section values | finite approved `E,nu,t` bounds | model, exit 4 |
+| director/geometry | deterministic pairwise orientation, average and frame construction pass | model, exit 4 |
+| boundary/load syntax | global DOF 1..6, resolved finite values, no conflicting prescribed values | input, exit 3 |
+| aggregate nodal moment | exact-zero case or nonzero `rho_M<=1e-12` | model, exit 4 |
+| history | sole static Step-1/frame 0, NLGEOM disabled | input, exit 3 |
+| HDF5 model | exact paths, dtypes, shapes, IDs, source types, directors, sections, and finite values | output, exit 6 |
+| HDF5 results | every mandatory row/location/component exists in stable order and is finite | output, exit 6 |
+| S4 case | exact declared input/displacement paths and unique finite U/UR rows | reference precheck |
+| S4R source support | parser/common-kernel/deterministic-assembly/HDF5 metadata tests; no Abaqus artifact consumption | implementation verification |
+| comparison | exact normalized row-set; U blocking; UR warning-only; approved tolerance | reference verification |
+
+No successful parser/HDF5 implementation, numerical solution, reference comparison,
+physics review, or release status follows from approval of this document alone.
+
+## 10. Requirement Traceability
+
+| requirement group | I/O contract coverage | remaining owner |
+| --- | --- | --- |
+| `001-004`, `021-023`, `030`, `037` | exact step, S4/S4R mapping, source/internal identity, wrapper and no-op policies | Implementation Planning tests |
+| `005-010` | six global DOFs, isotropic ELASTIC, single-row SHELL SECTION, exact assignment | Implementation Planning tests |
+| `011-016` | auto-director semantic mapping, basic geometry predicates and fail-closed diagnostics | Implementation Planning tests |
+| `017-020` | BOUNDARY/CLOAD grammar, deterministic aggregation, `rho_M<=1e-12`, distributed-load rejection | Implementation Planning tests |
+| `024-029` | Domain/AnalysisModel/DofManager/AnalysisState semantic ownership and residual meaning | Implementation Planning |
+| `031-038` | source-independent MITC4 identity, fixed drilling stabilization and full-integration policy; no drilling output | Implementation Planning tests |
+| `039-048` | additive HDF5 v0 paths, mandatory quantities, location identity, atomic output | Reference Model and Implementation Planning |
+| `049-057` | diagnostic/schema hooks and required verification-metric/physical-energy evidence | Numerical Review and planning |
+| `058-064` | normalized U/UR rows, fixed absolute `1.0e-5`, blocking/warning behavior, report inventory | Reference Verification |
+| `065-072` | exact current S4 paths, S4R reference non-consumption, immutability and displacement-only gate | Reference Model |
+
+## 11. Open Issues and Downstream Handoff
+
+### 11.1 Numerical Review boundary
+
+No I/O-owned calibration value remains open. Numerical Review shall verify the exact
+fixed drilling rule, basic geometry predicates, required HDF5 inventory, and fixed
+absolute MITC4 tolerance mapping. Drilling calibration/energy output, `NR-O03`, `NR-O04`, bundle
+administration and reference-portfolio expansion are removed scope.
+
+### 11.2 Reference Model Agent
+
+- Write `docs/reference-models/linear-static-mitc4-shell-reference-models.md` using
+  this exact keyword/HDF5/reference-row contract.
+- Record only the two exact existing input/displacement pairs, comparison components,
+  HDF5 projection, source-row identity, fixed absolute MITC4 tolerance and immutability rule.
+- Treat reaction/stress artifacts as nonblocking review evidence and do not create
+  location-equivalence claims absent from this contract.
+
+### 11.3 Numerical Review Agent
+
+- Confirm cross-document numerical consistency and rerun the gate before authorizing
+  Implementation Planning.
+
+### 11.4 Implementation Planning Agent
+
+- Planning is authorized by the numerical review; implementation and Harness execution
+  remain separately unauthorized until explicitly requested.
+- After approval, convert every supported/unsupported keyword row, source identity,
+  geometry/director error, drilling-load projection, exact HDF5 path/shape/order,
+  atomic failure, source-row normalization, and U-versus-UR decision into
+  `RED -> GREEN -> VERIFY` tests.
+- Use the project Harness skill to draft multiple self-contained Steps and obtain user
+  approval before creating phase-planning files. Do not run the executor without a
+  separate explicit request.
+- Keep distributed loads, mixed beam-shell models, Abaqus reduced integration,
+  nonlinear state/tangent, and reference artifact mutation outside the plan.
+
+### 11.5 Reference Verification Agent
+
+- Enforce artifact/schema precheck before numeric tolerance.
+- Match HDF5 and Abaqus rows only by the normalized identity in Section 7.5.
+- Never ignore missing/extra/nonfinite rows, synthesize S33/S13/S23, average location
+  mismatches, or let UR warnings change U pass/fail.

docs/numerical-reviews/README.md

@@ -32,12 +32,12 @@ Numerical Review Agent는 정식화의 수학적 일관성, 수치 안정성 위
 ## Metadata
 - feature_id: <feature-id>
 - source_formulation: docs/formulations/<feature-id>-formulation.md
-- status: pass-for-implementation-planning | needs-formulation-revision | needs-research | needs-reference-model | blocked
+- status: pass-for-implementation-planning | needs-formulation-revision | needs-research | blocked
 - owner_agent: numerical-review-agent
 - date: <YYYY-MM-DD>
 
 ## Review Verdict
-- verdict: pass-for-implementation-planning | needs-formulation-revision | needs-research | needs-reference-model | blocked
+- verdict: pass-for-implementation-planning | needs-formulation-revision | needs-research | blocked
 - reason: <판정 이유>
 
 ## Critical Findings
@@ -82,7 +82,7 @@ Numerical Review Agent는 정식화의 수학적 일관성, 수치 안정성 위
 - <연구 보강 지시>
 
 ### Reference Model Agent
-- <reference model 또는 artifact 요구사항>
+- <optional downstream test note; not a formulation blocker>
 
 ## Downstream Handoff
 
@@ -99,4 +99,6 @@ Numerical Review Agent는 정식화의 수학적 일관성, 수치 안정성 위
 - `pass-for-implementation-planning`은 구현 계획으로 넘겨도 된다는 뜻이며 기능 완료나 release 승인이 아니다.
 - 정식화 문서를 직접 수정하지 않고 필요한 수정을 명확히 지시해야 한다.
 - 모든 검토는 dimension, sign, DOF ordering, coordinate transform, Jacobian, integration weight, element equation, output recovery를 포함해야 한다.
-- numerical risk는 rigid body modes, patch test, symmetry, positive definiteness, hourglass, locking, singular Jacobian, conditioning을 포함해야 한다.
+- numerical risk는 approved feature scope가 요구하는 항목만 포함한다. 이후 Reference Model
+  문서, canonical naming, README, metadata, provenance, expanded portfolio 또는 아직 없는
+  comparison result는 formulation verdict의 blocker가 아니다.

docs/numerical-reviews/linear-static-3d-euler-beam-review.md

@@ -0,0 +1,228 @@
+# Linear Static 3D Euler Beam Numerical Review
+
+## Metadata
+
+- feature_id: `linear-static-3d-euler-beam`
+- source_formulation: `docs/formulations/3d-isoparametric-euler-beam-formulation.md`
+- source_requirements: `docs/requirements/linear-static-3d-euler-beam.md`
+- source_research: `docs/research/linear-static-3d-euler-beam-research.md`
+- approved_design: `docs/superpowers/specs/2026-08-08-linear-static-3d-euler-beam-design.md`
+- status: `pass-for-implementation-planning`
+- owner_agent: `numerical-review-agent`
+- date: `2026-08-09`
+- scope: formulation correctness and implementation-planning readiness only
+
+## Review Verdict
+
+- verdict: `pass-for-implementation-planning`
+- reason: The DOF/sign convention, natural boundary actions, 4x12 B matrix, 12x12 stiffness, 2-point Gauss rule, transformation, constant line-load vector, constrained partition, and residual reaction are mutually consistent. No confirmed mathematical defect was found.
+- qualification: This verdict permits implementation planning only; it is not reference-comparison, physics-sanity, release, or full Abaqus-compatibility approval.
+
+## Critical Findings
+
+### Confirmed defects
+
+- None.
+
+### Independent DOF, curvature, and end-action derivation
+
+The fixed local nodal order is
+
+$$
+[u_1,v_1,w_1,\theta_{x1},\theta_{y1},\theta_{z1},
+ u_2,v_2,w_2,\theta_{x2},\theta_{y2},\theta_{z2}].
+$$
+
+For a small right-handed section rotation,
+$\boldsymbol\theta\times[0,y,z]^T
+=[z\theta_y-y\theta_z,-z\theta_x,y\theta_x]^T$.
+The zero-shear constraints are therefore
+$\theta_z=v'$ and $\theta_y=-w'$. Hence
+
+$$
+\varepsilon_{xx}=u'-zw''-yv'
+=\varepsilon_0+z\kappa_y-y\kappa_z,
+\quad \kappa_y=-w'',\quad \kappa_z=v''.
+$$
+
+Using the reviewed section-force definitions independently gives
+
+$$
+M_y=EI_y\kappa_y=-EI_yw'',\qquad
+M_z=EI_z\kappa_z=EI_zv''.
+$$
+
+Twice integrating the bending virtual work, with outward sign $n=-1$ at
+$x=0$ and $n=+1$ at $x=L$, yields
+
+$$
+F_y=-nM_z',\quad M_z^{end}=nM_z,\qquad
+F_z=nM_y',\quad M_y^{end}=nM_y.
+$$
+
+The axial and torsional pairs are $F_x=nN$ and $M_x=nT$. Direct expansion of
+$K_ld_l$ reproduces these relations at both endpoints when the V0 distributed
+load is zero. Thus the equilibrium end action is an outward action, while
+$DBd$ is the positive-local-x section resultant before the outward-normal
+sign is applied. These outputs must remain distinct.
+
+### B matrix, stiffness, quadrature, and modes
+
+- Differentiating the Hermite fields reproduces the documented 4x12 B matrix. The $\kappa_y=-w''$ row has $[-H_1'',H_2'',-H_3'',H_4'']$ in the $[w_1,\theta_{y1},w_2,\theta_{y2}]$ columns; the $\kappa_z=v''$ row has $[H_1'',H_2'',H_3'',H_4'']$ in the $[v_1,\theta_{z1},v_2,\theta_{z2}]$ columns.
+- Axial/torsional B rows are constant and bending rows are linear in $\xi$, so $B^TDBJ_x$ is degree at most two. The 2-point Gauss rule, exact through degree three, exactly produces the closed-form 12x12 stiffness.
+- The axial and torsion blocks each have rank one, and each exact bending block has rank two. With positive $EA,GJ,EI_y,EI_z$, the free-element stiffness is symmetric positive semidefinite with rank 6.
+- The six rigid modes are the three equal nodal translations, equal $\theta_x$, $\theta_{y1}=\theta_{y2}$ with $w_2-w_1=-L\theta_y$, and $\theta_{z1}=\theta_{z2}$ with $v_2-v_1=L\theta_z$. Each gives $Bd=0$.
+- Since $d^TKd=\int(Bd)^TD(Bd)dx$, energy is strictly positive outside the six-dimensional rigid kernel, but the unconstrained element itself is not positive definite.
+- A 1-point bending rule reduces the total element rank to 4 and introduces two spurious zero-energy modes. Production must use the approved 2-point rule or the reviewed closed form.
+
+### Transformation and energy invariance
+
+Projection/normalization of `n1` gives orthogonal unit $e_x,e_y$, and
+$e_z=e_x\times e_y$ makes $R=[e_x^T;e_y^T;e_z^T]$ orthogonal and
+right-handed: $RR^T=I$, $\det R=+1$. With
+$T=\operatorname{diag}(R,R,R,R)$ in node translation/rotation block order,
+
+$$
+d_l=Td_g,\quad K_g=T^TK_lT,\quad f_g=T^Tf_l,
+\quad d_g^TK_gd_g=d_l^TK_ld_l.
+$$
+
+This also confirms virtual-work invariance. Reversing the transform direction
+would violate the documented component contract.
+
+### Constant local line-load vector
+
+Exact integration of $N_q^T[p_x,p_y,p_z,m_x,0,0]^T$ gives equal half-span
+nodal forces/torques and
+
+$$
+M_{y1}=-p_zL^2/12,\quad M_{y2}=+p_zL^2/12,\qquad
+M_{z1}=+p_yL^2/12,\quad M_{z2}=-p_yL^2/12.
+$$
+
+The signs follow from the $-H_2,-H_4$ interpolation for $w$ and
+$H_2,H_4$ for $v$. The 2-point rule integrates the cubic load integrand
+exactly. This remains a formulation-only kernel: `*DLOAD` input, a Domain
+distributed-load object, and CLI distributed loading are out of scope.
+
+### Independent numerical cross-check
+
+An independent double-precision evaluation at $L=3.7$ with unequal positive
+$EA,GJ,EI_y,EI_z$ produced:
+
+| check | observed result |
+| --- | ---: |
+| 2-point Gauss/closed-form normalized error | $3.20\times10^{-16}$ |
+| symmetry normalized error | $2.00\times10^{-17}$ |
+| six rigid-mode residual norms | 0 to $2.81\times10^{-15}$ |
+| numerical rank at relative $10^{-10}$ | rank 6 |
+| constant line-load normalized error | $3.08\times10^{-16}$ |
+| 1-point stiffness | rank 4 |
+| rotated local/global energy difference | 0 |
+| $\det R$ | $0.9999999999999999$ |
+
+These calculations corroborate the derivation but do not replace production
+tests.
+
+## Numerical Risk Assessment
+
+Confirmed defects, risks, and open issues are separated.
+
+| id | risk or limit | assessment and required control |
+| --- | --- | --- |
+| NR-R01 | zero/near-zero length | Singular Jacobian and divergent $L^{-3}$ terms; `NR-T05` tests the approved scale-aware boundary before evaluation. |
+| NR-R02 | zero/tangent-parallel `n1` | Undefined axes and inertia directions; `NR-T05` tests the projection boundary and forbids a silent fallback. |
+| NR-R03 | under-integration | 1-point integration adds two mechanisms; `NR-T03` must show 2-point rank 6 and negative-control rank 4. |
+| NR-R04 | mixed translation/rotation scaling | Raw rank is length-unit dependent; `NR-T04` uses length scaling and a well-scaled fixture. |
+| NR-R05 | incomplete constraints | `Kff` is singular while any rigid mode survives; `NR-T09` covers free, partial, and stable systems. |
+| NR-R06 | extreme stiffness ratios/units | A mathematically SPD system may be ill-conditioned; `NR-T10` checks residual/analytical error. Automatic scaling or a new threshold is not approved. |
+| NR-R07 | transform direction | Rotated bending signs/components can be wrong; `NR-T05` checks orthogonality, handedness, work, and energy. |
+| NR-R08 | end-action/section-cut confusion | Opposite signs can contaminate comparison; `NR-T07` checks both endpoints and distinct result types. |
+| NR-R09 | sparse duplicate reduction | Thread-dependent summation can break reproducibility; `NR-T11` checks canonical CSR and normalized values. |
+| NR-R10 | short/deep beam | Euler–Bernoulli may be too stiff; explicit limitation only. No unapproved slenderness diagnostic and no B31 reinterpretation. |
+| NR-R11 | warping, eccentricity, or `I12!=0` | The diagonal constitutive model is insufficient; explicit rejection/exclusion, never silent approximation. |
+| NR-R12 | result averaging | Averaging can hide discontinuities; baseline nodal averaging is excluded and `NR-T07` preserves endpoint identity. |
+
+- shear_locking: N/A because no independent shear strain exists; deep-beam applicability remains limited.
+- volumetric_locking: N/A.
+- hourglass: N/A for the approved 2-point rule; the distinct 1-point rank deficiency is NR-R03.
+- distortion: no curved/distorted mapping exists in this straight affine element; length and axis singularities are NR-R01/NR-R02.
+- nonlinear convergence: N/A; linear residual and conditioning are NR-T09/NR-T10.
+- mesh convergence: tip-force/tip-moment polynomial fields are one-element exact; the formulation-only constant transverse load has a quartic exact displacement and requires refinement evidence.
+
+## Consistency Checks
+
+| check | result | evidence |
+| --- | --- | --- |
+| units | pass | Stiffness blocks and nodal work pairs are dimensionally consistent. |
+| dimensions | pass | B is 4x12, D is 4x4, and $B^TDBJ_x$ is 12x12. |
+| signs | pass | Cross-product, curvature, natural-boundary, end-action, and line-load derivations agree. |
+| dof_ordering | pass | Node blocks preserve `[u,v,w,theta_x,theta_y,theta_z]`. |
+| coordinate_transforms | pass | R/T are right-handed orthogonal maps with local = transform times global. |
+| jacobian | pass with validation | $J_x=L/2>0$ for accepted elements. |
+| constitutive | pass | Positive diagonal $EA,GJ,EI_y,EI_z$ gives nonnegative energy; `I12!=0` is rejected. |
+| integration | pass | The 2-point locations, unit weights, and $J_x$ integrate stiffness and constant-load kernels exactly. |
+| symmetry | pass | Variational and numerical checks agree. |
+| rank 6 and rigid modes | pass | Independent ranks $1+1+2+2=6$ and six rigid vectors span the kernel. |
+| positive deformation energy | pass | Strictly positive outside the rigid kernel. |
+| constrained partition | pass | $K_{ff}d_f=F_f-K_{fc}d_c$ includes nonzero $d_c$. |
+| residual reaction | pass | $R_c=(Kd-F)_c=K_{cf}d_f+K_{cc}d_c-F_c$. |
+| output locations | pass with downstream contract | Gauss values, section resultants, end actions, and residual reactions remain distinct. |
+
+## Verification Readiness
+
+| test id | concrete criterion |
+| --- | --- |
+| `NR-T01-DOF-SIGN` | Compare `B*d` with independently differentiated Hermite fields at multiple $\xi$; normalized error $\le10^{-12}$ and explicit $\theta_y=-w'$, $M_y=-EI_yw''$. |
+| `NR-T02-PATCH` | Check endpoint value/slope, constant axial strain/twist, both constant-curvature patches, and six rigid modes; rigid residual $\le10^{-10}$. |
+| `NR-T03-GAUSS-CLOSED` | All 12x12 entries and symmetry normalized $\le10^{-12}$; negative 1-point control must be rank 4. |
+| `NR-T04-RANK-ENERGY` | Use $Q=\operatorname{diag}(1,1,1,L,L,L,1,1,1,L,L,L)$ and $\widehat K=Q^{-T}KQ^{-1}$. For a documented well-scaled fixture require six singular values $\le10^{-10}\sigma_{max}$, six $>10^{-10}\sigma_{max}$, and positive energy for six deformation vectors. |
+| `NR-T05-TRANSFORM` | For a non-axis-aligned member require normalized orthogonality, handedness, virtual-work, transformed-stiffness, and energy errors $\le10^{-12}$; test geometry thresholds. |
+| `NR-T06-LINE-LOAD` | Compare all 12 signed closed-form components at normalized $\le10^{-12}$; separately verify `*DLOAD` remains unsupported. |
+| `NR-T07-END-SIGNS` | Pure axial/torsion/two-plane bending states must match outward natural actions and positive-face resultants at both endpoints, normalized $\le10^{-12}$; no averaging. |
+| `NR-T08-ANALYTICAL` | Axial, torsion, local-y, and local-z cantilevers at relative $\le10^{-9}$; constant transverse load requires load-vector equality and mesh convergence. |
+| `NR-T09-PARTITION-SPD` | Nonzero $d_c,F_c$: displacement and free/reaction residual normalized $\le10^{-10}$. Stable `Kff` factorizes; surviving rigid modes fail structurally with no result. |
+| `NR-T10-CONDITIONING` | Sweep documented valid scales; accepted well-conditioned cases require residual $\le10^{-10}$ and analytical error $\le10^{-9}$; numerically unresolved cases fail explicitly. |
+| `NR-T11-DETERMINISTIC-ASSEMBLY` | Across repeated thread counts require identical CSR structure/reduction order and values normalized $\le10^{-12}$. |
+
+### Open issues
+
+1. `NR-O01-PARDISO-CONTRACT`: official oneMKL evidence is still required for SPD matrix type, phases, zero-based CSR, repeated RHS, conditioning/error reporting, and failure codes before that adapter plan is approved. This is non-blocking for element mathematics and connects to NR-T09/NR-T10.
+2. `NR-O02-DETERMINISTIC-REDUCTION`: stable COO sort and duplicate-summation rules are project policy and must be made explicit before NR-T11.
+3. `NR-O03-STATION-NORMALIZATION`: reversed connectivity/local-axis orientation and legitimate jumps at loaded interior nodes need an explicit downstream row-normalization/eligibility rule. The legacy baseline may use its documented stable orientation and unloaded interior stations, but mismatch must never be averaged. NR-T07 covers element signs.
+
+No open issue requires formulation revision. NR-O01/NR-O02 are implementation-planning
+handoffs; NR-O03 belongs to I/O and reference-model contracts.
+
+## Required Revisions
+
+### Formulation Agent
+
+- None. No confirmed mathematical defect or missing derivation blocks implementation planning.
+
+### Research Agent
+
+- Resolve NR-O01 from official Intel documentation before finalizing the PARDISO adapter plan.
+
+### Reference Model Agent
+
+- Make NR-O03 orientation and unloaded-interior assumptions explicit without modifying the approved legacy artifacts.
+
+## Downstream Handoff
+
+### Implementation Planning Agent
+
+- Convert NR-T01 through NR-T11 into TDD `RED -> GREEN -> VERIFY` work without changing approved tolerances.
+- Preserve stiffness/partition/factorization before load/effective-RHS/substitution.
+- Treat SPD as a post-constraint property and retain singularity/conditioning diagnostics.
+- Resolve NR-O01 and NR-O02 before the corresponding implementation steps.
+
+### I/O Definition Agent
+
+- Preserve outward endpoint action, positive-face section resultant, Gauss result, and assembled residual reaction as distinct identities.
+- Define NR-O03 without broadening the approved Abaqus subset.
+
+### Reference Model Agent
+
+- Cover axial, torsion, both bending planes, rotated-space transformation, endpoint signs, and nonzero prescribed displacement.
+- Keep `reference/cantilever beam/` read-only, stress comparison N/A, and `*DLOAD` outside CLI support.

docs/numerical-reviews/linear-static-mitc4-shell-review.md

@@ -0,0 +1,366 @@
+# Linear Static MITC4 Shell Numerical Review
+
+## 1. Metadata
+
+- feature_id: `linear-static-mitc4-shell`
+- source_formulation: `docs/formulations/mitc4-shell-formulation.md`
+- source_requirements: `docs/requirements/linear-static-mitc4-shell.md`
+- source_research: `docs/research/linear-static-mitc4-shell-research.md`
+- source_io_definition: `docs/io-definitions/linear-static-mitc4-shell-io.md`
+- source_reference_inventory: `docs/reference-models/linear-static-mitc4-shell-reference-models.md`
+- repository_policy: `AGENTS.md`, `docs/SOLVER_AGENT_DESIGN.md`,
+  `docs/numerical-reviews/README.md`
+- reviewed_head: `cf769aa` (`mathematical implementation baseline`)
+- prior_pass_commit: `60b42f4` (`context-only; verdict not inherited`)
+- status: `pass-for-implementation-planning`
+- owner_agent: `numerical-review-agent`
+- date: `2026-08-13`
+- implementation_planning_authorized: `true`
+- implementation_complete: `false`
+- build_test_complete: `false`
+- reference_comparison_complete: `false`
+- physics_evaluation_complete: `false`
+- release_ready: `false`
+
+이번 재검토는 현재 HEAD의 요구조건, 연구, 정식화, I/O 및 reference-case 계약을
+처음부터 상호 대조했다. 기존 review의 판정과 artifact 관찰 결과는 결론의 전제로
+사용하지 않았고, 이전 finding은 현 문서의 수식으로 다시 검산한 뒤 disposition만
+기록했다. 원 MITC4 local paper는 tying 위치와 covariant shear 보간을 확인하는 데
+read-only로 사용했다.
+
+이 단계에서는 Abaqus, Harness, C++ build/test, FESA 실행 및 reference comparison을
+수행하지 않았다. Reference artifact를 생성, 수정, 복원 또는 정규화하지 않았다.
+
+## 2. Review Verdict
+
+- verdict: `pass-for-implementation-planning`
+- critical_blockers: `none`
+- confirmed_defects: `none in the approved current linear-static scope`
+- open_blocking_questions: `none`
+- reason: 현재 정식화는 24 global DOF와 20 physical DOF의 관계, MITC4 shear
+  tying, plane-stress section law, 공통 `2 x 2 x 2` quadrature, residual/stiffness,
+  고정 drilling 안정화, 물리 recovery 및 검증 불변식을 구현계획으로 옮길 수 있을
+  만큼 명시한다. 요구조건, I/O 및 reference 계약과 모순되는 차원, 부호, 위치 또는
+  pass/fail 의미도 발견되지 않았다.
+- downstream_boundary: 이 판정은 Implementation Planning 진입만 허용한다. 구현,
+  MSVC build/CTest, reference comparison, physics sanity 또는 release를 승인하지 않는다.
+
+정식화 Section 15의 geometrically nonlinear residual/tangent는 future-only다. 완전한
+`Phi: R24 -> R20`, map Hessian, objective drilling potential 및 finite-rotation load work가
+미정인 사실은 미래 nonlinear 구현을 막지만 현재 linear-static 판정은 막지 않는다.
+
+## 3. Critical Findings
+
+### 3.1 Confirmed defects
+
+현재 승인된 선형 정적 범위에서 구현계획 전에 Formulation 또는 Research로 돌려보낼
+confirmed mathematical defect는 없다.
+
+`K20`의 exact-arithmetic 대칭/positive-semidefinite 구조와 20-to-24 congruence는
+일관된다. 다만 실제 구현의 rank, rigid action, patch field와 reference error는 문서
+검토만으로 통과했다고 볼 수 없으며 Section 6의 downstream test evidence가 필요하다.
+
+### 3.2 Previous finding disposition
+
+| previous item | rerun disposition | current independent basis |
+| --- | --- | --- |
+| `NR-C01` Jacobian/geometry inventory | `resolved` | Formulation 9.2-9.3은 center, eight stiffness points, four tying points 및 committed recovery points를 공통 fail-closed inventory로 두고 finite bases, nonzero surface measure와 `J>0`를 요구한다. 승인 범위는 calibrated distortion/warp cutoff를 요구하지 않는다. |
+| `NR-C02` drilling normalization | `resolved` | Formulation 12.2는 `R+`를 오직 8 physical tangent-rotation diagonals의 finite positive 값으로 제한하므로 모든 후보의 단위가 `force*length`로 같다. |
+| `NR-C03` mixed-DOF spectrum scaling | `resolved` | Formulation 12.5의 `(L_e I3,I2)` 및 `(L_e I3,I3)` congruence는 rank/condition evidence에서 translation/rotation 단위 혼합을 제거한다. Raw mixed-unit spectrum은 금지된다. |
+| `NR-C04` 20/24 weak-form mismatch | `resolved` | Formulation 5.2-5.3과 7.1-7.2는 physical, drilling, external work를 모두 `V24`에서 `T_p^T`와 `T_d^T`로 결합한다. |
+| `NR-C05` nonlinear 20-to-24 closure | `resolved for current scope` | Section 15는 physical chart tangent와 conditional global pullback을 분리하고 map-curvature 항을 보존하며, 미정인 global map/objective drill을 future-only blocker로 명시한다. |
+| `NR-D01` drilling-direction moment | `retained and consistent` | Exact-zero moment는 별도 처리하고 nonzero moment에 `rho_M=abs(d dot M)/norm(M)<=1e-12`를 적용한다. Numerical drilling은 거부된 moment를 운반하지 않는다. |
+| `NR-D02` normalized algebraic checks | `retained and consistent` | `1e-12` symmetry/frame/energy와 `1e-10` rigid/residual/equilibrium 기준은 scaled matrices와 unclamped denominators에 적용된다. |
+| `NR-O01` coefficient sweep/plateau | `closed by product decision` | `k_d=1e-3 min(R+)`가 고정 계약이다. Sweep, plateau 및 coefficient optimality는 구현 gate가 아니다. |
+| `NR-O02` drilling-energy ratio | `removed from scope` | Drilling energy는 내부 quadratic identity일 뿐 physical energy나 mandatory output이 아니며 ratio/warning threshold도 요구하지 않는다. |
+| `NR-O03` smooth-director calibration | `removed from scope` | Pairwise positive incident-normal orientation, finite/nonzero averaging 및 duplicate-node fold modeling이 승인된 exact predicate다. 별도 angle calibration은 gate가 아니다. |
+| `NR-O04` distortion/warp calibration | `removed from scope` | Basic topology, finite/nonzero surface measure 및 required-point `J>0`가 승인된 predicate다. Quality sweep이나 cutoff는 gate가 아니다. |
+| `NR-O05` U/UR tolerance | `resolved` | 모든 관련 문서가 sole S4 reference에 고정 절대오차 `1.0e-5`, U blocking, UR warning-only를 동일하게 정의한다. Reference scale은 판정에 사용하지 않으며 S4R은 reference gate가 아닌 common-path evidence다. |
+
+이전의 `needs-reference-model` 판정에 포함됐던 canonical naming, README,
+`metadata.json`, provenance, expanded portfolio 및 아직 없는 comparison result는 현재
+프로젝트 정책상 formulation verdict의 blocker가 아니다. 현 Reference Model 문서는
+정확한 기존 input/displacement path와 row/tolerance 계약을 제공한다.
+
+### 3.3 Open questions
+
+- current_linear_scope: `none blocking`
+- future_geometric_nonlinearity: finite global rotation coordinate, `Phi`와 그 1/2차
+  미분, chart recentering, objective drilling, nodal-moment work 및 nonlinear output/state
+  계약이 미정이다. 이는 별도 future formulation/review가 소유한다.
+- optional_characterization: near-singular positive-J geometry의 conditioning과 original
+  MITC4의 distorted-curved membrane locking을 더 넓게 정량화할 수 있으나 현재 승인된
+  planning/completion gate는 아니다.
+- downstream_results: implementation rank/patch evidence, S4 reference comparison과
+  S4R common-path test 결과는 해당 후속 Agent가 판정한다. 부재 자체는
+  pre-implementation review의 결함이 아니다.
+
+## 4. Numerical Risk Assessment
+
+| risk label | assessment | required in-scope control |
+| --- | --- | --- |
+| `rigid_body_modes` | Physical `K20`은 six rigid modes와 expected rank 14를 가져야 한다. 24-DOF embedding은 네 drill null coordinates를 더하고 fixed drill block 뒤 expected rank 18/nullity 6이다. | 세 translation과 세 rotation을 명시적으로 구성한다. Rotation mode는 `u_I=omega x X_I`, `theta_I=omega-(omega dot d_I)d_I`, `gamma_I=0`를 사용한다. |
+| `patch_test` | Bilinear membrane/bending field와 MITC tied shear는 required patch states를 표현할 계약을 갖는다. | `E11/E22/G12`, `K11/K22/K12`, `G13/G23`를 독립 시험하고 signs/component order/resultants/stress를 함께 확인한다. |
+| `symmetry` | `B^T C B`, `T_p^T K20 T_p`, `T_d^T(k_d I)T_d`는 exact arithmetic에서 symmetric이다. | Scaled Frobenius check `<=1e-12`; deterministic assembly가 대칭을 깨지 않는지 확인한다. |
+| `positive_definiteness` | Free element는 six-mode semidefinite이고, 충분히 구속된 nonsingular `Kff`는 positive definite가 기대된다. Geometry 또는 supports가 부적절하면 singularity가 정당하다. | Scaled spectrum/rank, non-rigid positive physical energy, constrained solve 및 singular negative cases를 분리한다. |
+| `hourglass` | `1 x 1` reduced integration을 쓰지 않으므로 Abaqus-style hourglass path는 `N/A`다. | Full `2 x 2` midsurface rank test는 유지한다. S4R source label로 reduced rule을 선택하지 않는다. |
+| `shear_locking` | Edge-midpoint MITC projection이 transverse-shear locking을 다루지만 모든 mesh/thickness에서 완전 제거를 주장할 수 없다. | Required shear/bending patch와 declared S4 reference를 통과한다. Broader thin/thick convergence는 nonblocking characterization이다. |
+| `membrane_locking` | Original MITC4는 membrane strain을 수정하지 않아 distorted curved meshes에서 알려진 locking 위험이 남는다. | Known limitation을 유지하고 MITC4+ 성능을 주장하지 않는다. Expanded curved/distorted portfolio는 optional이다. |
+| `volumetric_locking` | 승인된 homogeneous plane-stress shell에는 `N/A`다. | `C5`를 3D nearly-incompressible law로 확장하지 않는다. |
+| `distortion` | 양의 `J`를 유지하는 심한 distortion/warpage는 정확도와 rank/conditioning을 악화할 수 있다. | 모든 required location의 exact predicates와 rank/finite-result checks를 시행한다. 승인되지 않은 quality cutoff를 추가하지 않는다. |
+| `singular_jacobian` | Nonfinite/nonpositive `J`, zero surface measure, invalid reciprocal basis는 mapping을 무효화한다. | Center, stiffness, tying 및 recovery inventory 전체를 omission/clamp 없이 fail closed한다. |
+| `conditioning` | Thin shells, near-degenerate positive-J geometry 및 작은 fixed drill scale에서 `Kff` conditioning이 나빠질 수 있다. | Spectrum/condition evidence는 오직 length-scaled matrix를 사용한다. Threshold calibration은 gate가 아니지만 factorization failure는 결정적으로 진단한다. |
+| `convergence` | Current solve는 direct linear solve라 Newton convergence는 `N/A`; spatial convergence와 locking trend는 모델 의존이다. | Free residual/global equilibrium `<=1e-10`과 declared S4 reference case를 확인한다. Broader mesh sequences는 optional이다. |
+| `drilling_contamination` | Numerical drill이 physical strain/recovery에 들어가면 비물리 결과가 생긴다. | `T_p`/`T_d`를 분리하고 pure drill에서 physical strain/resultant/stress/energy가 zero임을 시험한다. Full residual은 의도대로 stabilized system 전체를 포함한다. |
+| `future_nonlinear_misuse` | Section 15만으로 global nonlinear element를 만들면 nonobjective drill 또는 inconsistent tangent가 된다. | Current plan에서 완전히 제외하고 별도 승인 전 실행하지 않는다. |
+
+## 5. Consistency Checks
+
+### 5.1 Units, dimensions, DOF order, and constrained/free system — `pass`
+
+- Per-node global order is exactly `[UX,UY,UZ,URX,URY,URZ]`; element order is 24
+  global coordinates and 20 physical coordinates
+  `[uX,uY,uZ,alpha,beta]` per node plus four separately selected `gamma` coordinates.
+- `T_p` is `20 x 24`, `T_d` is `4 x 24`, `K20` is `20 x 20`, and both global
+  stiffness contributions are `24 x 24`.
+- Translation-translation, translation-rotation, and rotation-rotation stiffness
+  blocks have units `force/length`, `force`, and `force*length`; `R+` therefore
+  excludes every translational diagonal.
+- The constrained/free equation is `Kff*df=Ff-Kfc*dc`. Stiffness partition and
+  factorization precede load assembly, and an all-constrained valid `0 x 0 Kff` is
+  not reclassified as singular.
+- `r=K*d-F` fixes the internal-minus-external sign. Constrained entries are the
+  required reaction rows and free entries remain residual evidence.
+
+### 5.2 Local/global transforms, congruence, and energy — `pass`
+
+- `(a_I,b_I,d_I)` and `(e1,e2,e3)` are deterministic right-handed orthonormal frames.
+  The least-aligned-axis nodal rule avoids a fixed-axis parallel singularity.
+- `[alpha,beta,gamma]^T=R_I^T theta_I^g` gives
+  `delta d=beta*a-alpha*b=theta x d` with the required sign.
+- `q20=T_p qg` and `gamma=T_d qg` preserve virtual work. Congruence gives
+  `Kphys24=T_p^T K20 T_p` and `Kdrill24=T_d^T(k_d I4)T_d`; the corresponding local and
+  global quadratic energies are identical.
+- A physical rigid rotation uses only the tangent projection of `omega`, so `gamma=0`
+  and drilling does not destroy the six physical rigid modes.
+
+### 5.3 Kinematic operators and MITC tying — `pass`
+
+- Bilinear `N_I` satisfies partition, Kronecker and derivative-sum identities.
+- Membrane and bending content comes from the direct covariant small-strain operator.
+  Only `epsilon_xi-zeta` and `epsilon_eta-zeta` are replaced.
+- `epsilon_xi-zeta` is tied at `(0,-1,0)` and `(0,+1,0)` and interpolated in `eta`;
+  `epsilon_eta-zeta` is tied at `(-1,0,0)` and `(+1,0,0)` and interpolated in `xi`.
+  Each interpolation reproduces its own edge value and is constant along the edge
+  direction, matching the original MITC4 construction.
+- The assumed covariant tensor is reconstructed through reciprocal bases, projected
+  into the stored local Cartesian frame, and converted once to engineering shear
+  `gamma_ij=2 epsilon_ij`. The same projected `B_bar` drives strain, internal force,
+  stiffness and recovery.
+
+### 5.4 Constitutive and section matrices — `pass`
+
+- `Cps=E/(1-nu^2)[[1,nu,0],[nu,1,0],[0,0,(1-nu)/2]]` uses engineering `G12`; its
+  shear coefficient is exactly `G=E/[2(1+nu)]`.
+- `C5=diag(Cps,(5/6)G I2)` is symmetric positive definite for `E>0` and
+  `-1<nu<0.5`. `sigma33=0` and absent thickness stretch remain assumptions.
+- `A=t Cps`, `B=0`, `D=t^3 Cps/12`, and `As=(5/6)Gt I2` have consistent dimensions.
+  Membrane/shear strains are dimensionless, curvature is `1/length`, `N/Q` is
+  `force/length`, `M` is `force`, stress is `force/length^2`, and energy is
+  `force*length`.
+
+### 5.5 Jacobian, derivative transform, and integration — `pass`
+
+- The three-dimensional degenerated mapping uses
+  `X=sum(N X_I)+(t*zeta/2)sum(N d_I)` with a unit nodal director and separate
+  thickness, preventing nodal thickness double counting.
+- `J=det[G_xi,G_eta,G_zeta]` and finite covariant/reciprocal bases are checked at all
+  eight stiffness points, all four midsurface tying points, center, and every
+  committed bottom/middle/top recovery evaluation. Failed points are not skipped,
+  averaged, clamped or repaired.
+- Direct natural derivatives are converted covariantly and then to the local
+  Cartesian tensor through contravariant bases; no flat-element derivative shortcut
+  is substituted for curved/warped accepted geometry.
+- Both S4 and S4R use the common in-plane `2 x 2` points
+  `+-1/sqrt(3)` with unit weights and two identical thickness points, for eight
+  volume evaluations. Tied shear is evaluated at `zeta=0` and reused at both
+  thickness points while the remaining mapping and direct components use the actual
+  thickness point.
+
+### 5.6 Internal force, residual, stiffness, and future tangent — `pass`
+
+- Current `K20=integral(B_bar^T C5 B_bar dV)` and `f_int20=K20 q20` are mutually
+  consistent and symmetric positive semidefinite in exact arithmetic.
+- The complete current weak form is in `V24` and adds the numerical drilling
+  gradient before subtracting the global nodal `CLOAD` vector.
+- No geometric stiffness or nonlinear state enters the current product path.
+  Future Section 15 correctly separates `Kmat` and the stress-dependent `Kgeo` and,
+  conditionally on a future `Phi`, includes both `A^T K20 A` and the
+  residual-weighted map-Hessian term.
+
+### 5.7 Fixed drilling contract — `pass`
+
+- `R+` contains only finite strictly positive diagonals of the eight physical
+  tangent-rotation coordinates. `k_ref=min(R+)`, `k_d=1e-3 k_ref`, and
+  `Kd_local=k_d I4` are dimensionally consistent and deterministic; empty `R+`
+  fails validation.
+- `T_d^T(k_d I4)T_d` is symmetric and positive on the four pure drilling
+  coordinates. It must remove those four nonphysical null modes without changing
+  the physical rank/null modes.
+- Drilling is excluded from generalized strain/resultant/stress and reported
+  physical strain energy. A director-parallel applied nodal moment is rejected as
+  `unsupported-drilling-load`; no numerical drill load channel exists.
+
+### 5.8 Recovery, signs, locations, units, and external comparison — `pass`
+
+- Nodal `[U1,U2,U3,UR1,UR2,UR3]` and full-residual
+  `[RF1,RF2,RF3,RM1,RM2,RM3]` are global and source-node ordered.
+- Four midsurface Gauss rows recover
+  `[E11,E22,G12,K11,K22,K12,G13,G23]` and
+  `[N11,N22,N12,M11,M22,M12,Q13,Q23]` in the stored local frame. The definition
+  `e_m(z)=epsilon0+z*kappa` fixes curvature, moment, and bottom/top stress signs.
+- `[S11,S22,S12]` is evaluated directly at `zeta=-1,0,+1`; `S33=0` is documented but
+  not emitted, and `S13/S23` point stress is not synthesized. Different natural or
+  section locations are never averaged.
+- Reference comparison first rejects missing, extra, duplicate, nonfinite or
+  identity-mismatched rows. Every U/UR row then uses fixed absolute tolerance
+  `1.0e-5`; no reference-scale decision term, zero clamp or row denominator is
+  introduced. U1/U2/U3 is blocking and UR1/UR2/UR3 is warning-only.
+- Source S4 and S4R select the same FESA MITC4 kernel/quadrature/recovery path while
+  preserving source type. This is an input mapping, not an Abaqus formulation,
+  integration, stabilization or recovery equivalence claim.
+
+## 6. Verification Readiness
+
+### 6.1 Downstream unit and invariant tests
+
+Implementation Planning shall convert the following to `RED -> GREEN -> VERIFY`:
+
+1. Shape identities; nodal/integration frame orthonormality, handedness and axis
+   tie-break determinism.
+2. `T_p`/`T_d` dimensions, orthogonal channel selection, virtual-work equality and
+   nonzero transformation-energy equality.
+3. Hand-calculated direct membrane/bending columns, all four covariant tying values,
+   interpolation weights and engineering-shear factors.
+4. `Cps/C5/A/D/As` coefficients, symmetry, positive definiteness, dimensions and
+   force/length unit-rescaling invariance.
+5. Common `2 x 2 x 2` point/weight order and an independent analytical or
+   higher-order flat-element stiffness/recovery cross-check.
+6. Required-location geometry validation: valid planar/rotated/warped cases and
+   duplicate, bow-tie/self-intersecting, zero-area, reversed, nonfinite,
+   nonpositive-J and opposed-normal negative cases.
+7. Scaled symmetry `<=1e-12`, physical rigid action `<=1e-10`, expected physical
+   rank 14, stabilized rank 18/nullity six, and positive non-rigid physical energy.
+8. Exact `R+` membership, exclusion of translations, fixed coefficient, empty-`R+`
+   failure, pure drill action and zero physical recovery/energy.
+9. Stable COO/reduction, source/result/diagnostic order and thread-count
+   repeatability.
+10. `Kff/Kfc` effective RHS, nonzero prescribed values, full-residual reaction,
+    singular-support negative case, and valid all-constrained `0 x 0 Kff` case.
+11. Exact-zero and accepted/rejected `rho_M` moment projections, including proof
+    that rejected drilling moments never reach stabilization.
+12. Mandatory HDF5 locations/components/units, physical-only energy, nonfinite
+    recovery failure and atomic finalization.
+
+### 6.2 Required patch and sign tests
+
+- independent constant `E11`, `E22`, and `G12` membrane fields with `N` and
+  middle-stress signs;
+- pure `K11` and `K22` bending with `M` order and bottom/top stress reversal;
+- pure `K12` twist with `M12` sign;
+- constant `G13` and `G23` transverse shear with `Q13/Q23` order;
+- six physical rigid states and four pure drilling states;
+- source-type-only S4/S4R variants producing identical FESA numeric rows and
+  different preserved source metadata.
+
+### 6.3 Reference and physics handoff readiness
+
+The sole declared read-only acceptance pair is:
+
+- `reference/shell/shell.inp` with
+  `reference/shell/shell displacements.csv` for full-integration S4.
+
+S4R remains required input coverage through source mapping, common-kernel,
+deterministic-assembly and HDF5 metadata tests, but no S4R Abaqus artifact is
+consumed by reference acceptance.
+
+The Reference Model and I/O documents define deterministic HDF5-to-CSV identity,
+precheck and tolerance sufficiently for later comparison. This review did not assert
+that `results.h5` exists or that any row passes. Reference Verification owns numeric
+U/UR outcome; Physics Evaluation owns force/moment balance, displacement direction,
+symmetry, result signs, recovered-resultant consistency and physical plausibility.
+
+### 6.4 Missing evidence classification
+
+- blocking_for_current_formulation: `none`
+- required_after_implementation: invariant, patch, MSVC build/CTest, declared
+  reference comparison and physics evidence above
+- nonblocking_optional: drilling coefficient sweep/energy ratio, `NR-O03`, `NR-O04`,
+  canonical naming, README/metadata/provenance, expanded benchmark portfolio and
+  broader mesh convergence studies
+- future_only: nonlinear directional-derivative/objectivity/Newton evidence after
+  its missing formulation decisions are separately approved
+
+## 7. Required Revisions
+
+### Formulation Agent
+
+- None for the approved current linear-static implementation scope.
+- Do not promote Section 15 to executable status until a separate formulation closes
+  the nonlinear global coordinate map, objective drilling and load-work contracts.
+
+### Research Agent
+
+- None before current Implementation Planning.
+- Optional locking/convergence characterization must remain clearly outside the
+  approved implementation gate and must not imply MITC4+ or Abaqus equivalence.
+
+### I/O Definition Agent
+
+- None for the current numerical verdict. Preserve exact physical/full-residual
+  distinction, source identity, locations, units and U-versus-UR decision rule.
+
+### Reference Model Agent
+
+- None for the current numerical verdict. Preserve the two declared S4 files and every
+  optional existing reference artifact read-only, exclude S4R artifacts from acceptance
+  comparison, and do not add administrative or portfolio gates.
+
+## 8. Downstream Handoff
+
+### Implementation Planning Agent
+
+Implementation Planning is authorized and shall:
+
+- trace the required tests in Section 6 to the approved requirement IDs before
+  production work;
+- keep `24 global -> 20 physical + 4 drilling` transforms, covariant MITC tying,
+  common `2 x 2 x 2` integration, fixed drilling and physical recovery as explicit
+  independent test seams;
+- preserve stiffness assembly/partition/factorization-before-load, stable reduction,
+  full-residual reaction and failure-atomic HDF5 lifecycle;
+- keep future nonlinear execution, coefficient calibration, drilling output,
+  `NR-O03/NR-O04`, reference-artifact mutation and Abaqus-equivalence claims outside
+  the plan.
+
+This handoff authorizes planning only. It does not authorize Harness execution,
+production implementation, reference artifact changes, or completion claims.
+
+### Reference Verification Agent
+
+- Compare authoritative FESA HDF5 rows directly with the matching declared Abaqus
+  displacement CSV after exact row-set precheck.
+- Let only U1/U2/U3 affect pass/fail; report every UR1/UR2/UR3 warning without
+  changing the verdict.
+
+### Physics Evaluation Agent
+
+- After reference verification, independently evaluate force and global moment
+  balance, free residual, reaction sign, displacement direction, symmetry, positive
+  physical energy and consistency of local resultants/stresses.
+
+### Coordinator and Release Agents
+
+- Record the Numerical Review gate as passed for planning at HEAD `a058ef7`.
+- Do not infer implementation or release completion. Build/test, reference,
+  physics-sanity and release-readiness gates remain pending.

docs/physics-evaluations/README.md

@@ -40,7 +40,7 @@ EVIDENCE CHECK -> PHYSICS CHECKS -> CLASSIFY -> REPORT
 
 - Reference Verification report status가 `pass-for-physics-evaluation`인지 여부
 - checked solver HDF5 file: `<solver output directory>/results.h5`
-- checked Abaqus reference CSV files under `reference/<model-id>/`
+- checked feature-declared Abaqus reference CSV files
 - optional FESA deterministic CSV view derived from `results.h5` for review only
 - compared quantities
 - model purpose
@@ -97,10 +97,7 @@ EVIDENCE CHECK -> PHYSICS CHECKS -> CLASSIFY -> REPORT
 | reference_verification | docs/reference-verifications/<feature-id>-reference-verification.md | pass-for-physics-evaluation | <summary> |
 | solver_hdf5 | <solver output directory>/results.h5 | present | missing | <summary> |
 | solver_csv_views | <solver output directory>/csv/ | present | missing | <summary or N/A> |
-| reference_displacements_csv | reference/<model-id>/<model-id>_displacements.csv | present | missing | <summary> |
-| reference_reactions_csv | reference/<model-id>/<model-id>_reactions.csv | present | missing | <summary> |
-| reference_internalforces_csv | reference/<model-id>/<model-id>_internalforces.csv | present | missing | <summary> |
-| reference_stresses_csv | reference/<model-id>/<model-id>_stresses.csv | present | missing | <summary> |
+| declared_reference_csv | <exact feature-declared path> | present | missing | <blocking/warning quantity summary> |
 | model_purpose | docs/reference-models/<feature-id>-reference-models.md | documented | missing | <summary> |
 | physical_expectations | <source docs> | documented | missing | <summary> |
 
@@ -154,7 +151,7 @@ EVIDENCE CHECK -> PHYSICS CHECKS -> CLASSIFY -> REPORT
 
 - `pass-for-release-agent`: documented physics checks가 통과했고 Release Agent가 release readiness를 평가할 수 있다.
 - `needs-correction`: implementation-owned physical failure가 있어 Correction Agent가 필요하다.
-- `needs-reference-model`: reference model coverage가 부족하거나 추가 physical expectation이 필요하다.
+- `needs-reference-model`: feature-required case 또는 명시적으로 요구된 physical expectation이 누락됐다.
 - `needs-formulation-review`: formulation 또는 numerical review 재검토가 필요하다.
 - `needs-io-decision`: output location, component naming, sign convention, unit, coordinate mapping이 evaluation을 막는다.
 - `needs-upstream-decision`: physical expectation, sign convention, model purpose, acceptance criterion이 누락 또는 충돌한다.
@@ -163,7 +160,9 @@ EVIDENCE CHECK -> PHYSICS CHECKS -> CLASSIFY -> REPORT
 ## 품질 기준
 
 - Reference Verification report가 `pass-for-physics-evaluation`이 아니면 physics pass를 판정하지 않는다.
-- documented expectation이 없는 항목은 pass/fail로 판정하지 않고 `skipped`, `needs-upstream-decision`, 또는 `needs-reference-model`로 둔다.
+- documented expectation이 없는 항목은 `skipped`로 두며 expanded portfolio나 calibration을
+  새 gate로 만들지 않는다. Feature-required expectation 자체가 누락된 경우에만
+  `needs-upstream-decision` 또는 `needs-reference-model`을 사용한다.
 - 평형 검토는 적용 하중, 반력, element/internal force sign convention이 문서화된 경우에만 수행한다.
 - stress/strain 검토는 output location, component naming, coordinate system, units가 정의된 경우에만 수행한다.
 - FESA `results.h5`, Abaqus reference CSV files, optional FESA debug CSV view는 읽기 전용 evidence로만 사용한다.

docs/physics-evaluations/linear-static-3d-euler-beam-physics-evaluation.md

@@ -0,0 +1,268 @@
+# Linear Static 3D Euler Beam Physics Evaluation Report
+
+## Metadata
+
+- feature_id: `linear-static-3d-euler-beam`
+- model_id: `cantilever-beam-b33`
+- evaluated_head: `d76d052456ec134a98bcd5aa3b3c18a6b0ad6ba4`
+- source_reference_verification_report: `docs/reference-verifications/linear-static-3d-euler-beam-reference-verification.md`
+- source_reference_model: `docs/reference-models/linear-static-3d-euler-beam-reference-models.md`
+- source_requirement: `docs/requirements/linear-static-3d-euler-beam.md`
+- source_formulation: `docs/formulations/3d-isoparametric-euler-beam-formulation.md`
+- source_numerical_review: `docs/numerical-reviews/linear-static-3d-euler-beam-review.md`
+- source_io_definition: `docs/io-definitions/linear-static-3d-euler-beam-io.md`
+- status: `pass-for-release-agent`
+- owner_agent: `physics-evaluation-agent`
+- date: `2026-08-09`
+
+This verdict means that the documented physical checks pass and the Release Agent may audit
+release readiness. It does not approve release readiness and does not re-evaluate the Step 26
+reference tolerance decision.
+
+## Input Evidence
+
+The reference-verification prerequisite has status `pass-for-physics-evaluation`. Its checked
+artifact identity was reproduced before the physics checks and again after the targeted CTest.
+
+| evidence | exact path or identity | status | notes |
+| --- | --- | --- | --- |
+| reference verification | `docs/reference-verifications/linear-static-3d-euler-beam-reference-verification.md` | pass-for-physics-evaluation | Required gate satisfied. |
+| solver HDF5 | `.harness/build/reference/cantilever-beam-b33/results.h5` | present and readable | 25,336 bytes; post-acceptance-run SHA-256 `13ECCF68262C14BBDE0F63667C0F10896ACD40EFEC56E8C9121C298333FD9B6D`. |
+| comparison evidence | `.harness/build/reference/cantilever-beam-b33/comparison.json` | present and passing | 128,118 bytes; SHA-256 `258347AEA791D981AEA9B2BCAD85DE5344D4859ECA3692DC5E7AA01A848F8E0D`; `passed=true`, 176 rows, 16 metrics. |
+| reference input | `reference/cantilever beam/cantilever beam.inp` | exact read-only artifact | SHA-256 `E406EA9560321B791DB829E03BD24593B9875E0195D35B86BD931EDA122EF3`; `TYPE=B33`. |
+| reference displacement | `reference/cantilever beam/cantilever beam displacements.csv` | exact read-only artifact | SHA-256 `7B3312FBC8848E81D9A0FD4FF2B56BC1954636A2C14B5C1CBB269CB9477D3C31`. |
+| reference reaction | `reference/cantilever beam/cantilever beam reactions.csv` | exact read-only artifact | SHA-256 `BF30CDB0CD50106885DE14D63492737736C587426EBD787DE4F7EE6AA86DAA23`. |
+| reference elemental force | `reference/cantilever beam/cantilever beam elemental forces.csv` | exact read-only artifact | SHA-256 `E5E77FEC0FA9482AE018DBF296E74D396335C7C711BD2E9AA2315247A34290BA`. |
+| solver CSV views | N/A | not used | No derived FESA CSV was generated or used. |
+| stress reference CSV | N/A by approved contract | not applicable | `S11` is evaluated from HDF5 schema, formulation, and analytical/unit evidence only. |
+| targeted physics tests | `.harness/build`, MSVC x64 Debug | pass | Exact Step 27 CTest passed 17/17: EulerBeam3D 10, ResultRecovery 6, B33ReferenceComparison 1. |
+
+Read-only HDF5 inspection confirmed schema `0`, solver `0.1.0`, feature identity, `Step-1` frame
+`0`, formulation `B33-3D-Euler-Bernoulli`, source content identity
+`fnv1a64:04543464cc970405`, and coordinate convention
+`global-cartesian; beam-local=(t,n1,t-cross-n1)`. The file contains 11 nodes at
+`(x,y,z)=(0..10,0,0)` m and 10 consecutive one-metre elements. Every element has identity local
+axes, so local `(x,y,z)` equals global `(X,Y,Z)` for this model.
+
+The documented physical model is a 10 m cantilever with node 1 fixed in all six DOFs and a
+free-end global/local `FZ=-1.0e6 N` at node 11. The section and material are SI:
+`E=2.1e11 Pa`, `Iy=I11=0.0833333 m^4`, and the only expected deformation mode is local-`z`
+translation with bending about local `y`.
+
+## Physics Checks
+
+All normalized physics criteria below come from the approved `1e-10` residual/equilibrium,
+`1e-12` matrix/transform/end-sign, or `1e-9` analytical contracts. They are independent checks of
+physical meaning, not a second application of the Abaqus row tolerance.
+
+### 1. global equilibrium
+
+In global Cartesian coordinates, force equilibrium is
+
+`r_F = sum(F_applied) + sum(R)`,
+
+with criterion
+
+`||r_F|| / max(||sum(F_applied)||, ||sum(R)||) <= 1e-10`.
+
+The comparison physics evidence records `sum(F_applied)=[0,0,-1000000] N` and
+`sum(R)=[0,0,999999.9999998808] N`. Therefore
+`r_F=[0,0,-1.1920928955078125e-7] N`, its norm is
+`1.1920928955078125e-7 N`, and the normalized value is
+`1.1920928955078125e-13`. Verdict: **pass**.
+
+Moment equilibrium about the global origin is
+
+`r_M = sum(M_applied) + sum(X cross F_applied) + sum(M_reaction) + sum(X cross R_force)`.
+
+The free-end force gives `[0,1.0e7,0] N*m`; the complete HDF5 reaction field gives
+`[0,-9999999.999997258,0] N*m`. Thus `r_M=[0,2.7418136596679688e-6,0] N*m`,
+with normalized norm `2.7418136596679688e-13` against `1.0e7 N*m`. Verdict: **pass**.
+
+### 2. reaction consistency and true free residual
+
+The constrained reaction contract is `R_c=(K*d-F)_c`. At fixed node 1 the observed global row is
+`[RF1,RF2,RF3,RM1,RM2,RM3] = [0,0,1000000.0000008196,0,-10000000.000005051,0]`
+in `[N,N,N,N*m,N*m,N*m]`. It opposes the applied `-Z` force and balances its positive origin
+moment. Differences from the physical closed-form reactions are `8.195638656616211e-7 N` and
+`5.0514936447143555e-6 N*m`, normalized to `8.195638656616211e-13` and
+`5.0514936447143555e-13`. Verdict: **pass**.
+
+The reaction dataset intentionally preserves free residuals. The implementation uses
+
+`rho_f = ||(K*d-F)_f||_2 / max(||K*d||_f, ||F||_f)`
+
+with no artificial unit floor. The serialized true free residual norm is
+`9.356339321107032e-7 N-equivalent`; the physical free scale is `1.0e6 N`, so
+`rho_f=9.356339321107032e-13 <= 1e-10`. The largest observed free force-residual component is
+`5.9604644775390625e-7 N`, and the largest free moment-residual component is
+`2.0861625671386719e-7 N*m`. Verdict: **pass**.
+
+### 3. displacement direction and rotation sign
+
+For free-end local `Pz=-1.0e6 N`, the documented Euler-Bernoulli solution is
+
+`w(L)=Pz*L^3/(3*E*Iy)`,  `theta_y(L)=-Pz*L^2/(2*E*Iy)`.
+
+The expected values are `-0.0190476266666697 m` and `+0.00285714400000046 rad`.
+HDF5 gives tip `UZ=-0.019047626666677083 m` and `URY=+0.0028571440000013902 rad`, with relative
+errors `3.87e-13` and `3.27e-13`, below the analytical `1e-9` criterion. All non-root `UZ` values
+are negative and monotonically increase in magnitude toward the loaded tip; all non-root `URY`
+values are positive, as required by `theta_y=-dw/dx`. Verdict: **pass**.
+
+### 4. expected zero and uncoupled symmetry
+
+The fixed-root displacement row is exactly zero in all six components. Across all nodes,
+`UX`, `UY`, `URX`, and `URZ` are exactly zero. The only nonzero kinematic components are `UZ` and
+`URY`, and the only physical constrained reactions are `RF3` and `RM2`. In the element recovery,
+`epsilon0`, `kappa_x`, and `kappa_z`, and the corresponding `N`, `T`, and `Mz`, are exactly zero.
+This is the documented uncoupled local-`z` bending symmetry, with no axial, torsional, or
+cross-plane leakage. Verdict: **pass**.
+
+### 5. element force, adjacent endpoints, and boundary balance
+
+The HDF5 `end_force_local` rows are outward endpoint actions in
+`[FX,FY,FZ,MX,MY,MZ]`; `section_resultant` rows are positive-local-`x` section cuts in
+`[N,T,My,Mz]`. With no distributed load,
+
+`F_X=n*N`, `M_X=n*T`, `M_Y=n*My`, `M_Z=n*Mz`,
+`F_Y=-n*dMz/dx`, and `F_Z=n*dMy/dx`, where `n=-1` at `xi=-1` and `n=+1` at `xi=+1`.
+
+Observed section `My` is positive and decreases linearly from
+`10000000.000005048 N*m` at the root to `2.4286118949223834e-7 N*m` at the free end. The maximum
+positive-face `My` mismatch between adjacent unloaded endpoints is
+`2.73110345005989e-7 N*m`, normalized to `2.73110345005989e-14` against the model moment scale.
+The comparison ledger independently records `endpoint_consistency_passed=true` without averaging.
+
+Adjacent outward actions cancel. The maximum interior `FZ_right+FZ_left` magnitude is
+`5.364418029785156e-7 N` (`5.364418029785156e-13` normalized); the maximum interior
+`MY_right+MY_left` magnitude is `2.682209014892578e-7 N*m`
+(`2.682209014892578e-14` normalized). Both satisfy the documented end-sign/residual criteria.
+
+At the root, the first element action is exactly the constrained reaction evidence:
+`FZ=+1000000.0000008196 N`, `MY=-10000000.000005051 N*m`. At the free boundary, the last element
+has `FZ=-999999.9999998808 N` and `MY=-5.9604644775390625e-8 N*m`, balancing the applied end force
+and the zero applied end moment to normalized residual scale. Verdict: **pass**.
+
+### 6. local/global mapping and section-force signs
+
+Every stored local-axis matrix is the identity. Therefore the global `-Z` load is local
+`Pz=-1.0e6 N`, `UZ=w<0`, `URY=theta_y>0`, and the positive-face section resultant is
+`My=-Pz*(L-x)>0`. The observed outward signs are `FZ>0, MY<0` at left endpoints and
+`FZ<0, MY>0` at right endpoints, except for the physically zero free-end moment residue. These
+values satisfy the documented `theta_y=-w'`, `My=-E*Iy*w''`, outward-normal, and
+positive-face-section-cut conventions. Verdict: **pass**.
+
+### 7. stress location, unit, and sign sanity
+
+The stress contract is
+
+`S11(xi,y,z)=E*(epsilon0 + z*kappa_y - y*kappa_z)`,
+
+where `x1=y`, `x2=z`, the coordinate system is beam local, the unit is `force/length^2`, and the
+location is a section point at each of two Gauss points. The reference input has no section
+points, so HDF5 correctly contains 20 ordered `fesa-default` centroid rows
+`(x1,x2)=(0,0)`, one at each Gauss point of ten elements. This model has pure bending with
+`epsilon0=0`; consequently all 20 observed centroid `S11` values are exactly `0 Pa`.
+
+Nonzero location/sign evidence comes only from the approved analytical/unit portfolio, not from
+an Abaqus stress comparison. `EulerBeam3D.RecoversSectionPointAndDefaultCentroidS11` passed with
+`epsilon0=0.01`, `kappa_y=0.02 1/m`, `kappa_z=-0.03 1/m`, `E=2.1e11 Pa`: the formula gives
+`1.575e9 Pa` at `(y,z)=(0.25,-0.5)`, `8.4e8 Pa` at `(-0.4,0.3)`, and `2.1e9 Pa` at the default
+centroid. The test enforces the formula at both Gauss points with normalized `1e-12` evidence.
+Abaqus beam stress comparison remains explicitly N/A. Verdict: **pass**.
+
+### 8. nonfinite, rigid-body, abnormal-magnitude, and energy symptoms
+
+All mandatory numeric HDF5 rows inspected here are finite; `comparison.json` also records no
+nonfinite row among the 176 compared rows and the 20 stress rows are finite. The fixed root is
+exactly zero, factorization/solution completed, the normalized free residual is `9.36e-13`, and
+the displacement field is smooth, so there is no rigid-body-mode symptom.
+
+For this one-load linear case, the recoverable strain energy is
+`U=0.5*F^T*d=9523.81333333854 N*m`, which is finite and positive. The ratios
+`|UZ_tip|/L=0.00190476266666771` and `|URY_tip|=0.00285714400000139 rad` agree with the analytical
+solution and show no abnormal magnitude relative to the documented small-displacement/rotation
+model. The targeted rank/energy test also passed the six-rigid-mode, rank-six, and positive
+deformation-energy checks. Verdict: **pass**.
+
+### 9. model coverage
+
+The approved B33 bundle is one identity-axis local-`z` bending cantilever. It directly covers the
+end-to-end parser/solver/HDF5 path, global equilibrium, reaction sign, `UZ/URY`, `My/FZ`, endpoint
+continuity, and the centroid stress fallback. It does not by itself cover axial, torsion, local-`y`
+bending, rotated space, nonzero fiber stress, prescribed displacement, or the formulation-only
+line-load kernel. The targeted analytical/unit portfolio supplies the documented complementary
+coverage:
+
+| coverage | targeted passing evidence | criterion |
+| --- | --- | --- |
+| axial, torsion, both bending planes | `EulerBeam3D.AnalyticalAxialTorsionAndTwoPlaneBendingRecover` and `ResultRecovery.MatchesAxialTorsionAndTwoPlaneEndSigns` | analytical relative `1e-9`; signed recovery contract |
+| rotated local/global mapping | `EulerBeam3D.RotatedTransformPreservesWorkAndEnergy` | transform/work/energy normalized `1e-12` |
+| constant local line-load kernel | `EulerBeam3D.ConstantLineLoadMatchesAllSignedComponents` | all 12 signed components normalized `1e-12`; `*DLOAD` remains outside CLI scope |
+| rigid modes, rank, and energy | `EulerBeam3D.HasSixRigidModesRankSixAndPositiveDeformationEnergy` | rigid residual `1e-10`, rank six, positive deformation energy |
+| prescribed displacement and residual | `ResultRecovery.ComputesResidualReactionForNonzeroPrescription`, `ResultRecovery.EnforcesNormalizedFreeResidual` | partition/reaction and normalized residual `1e-10` |
+| result identity and continuity | `ResultRecovery.KeepsEndActionSectionAndGaussResultsDistinct`, `ResultRecovery.RequiresInteriorEndpointConsistencyWithoutAveraging` | distinct locations and no-average consistency |
+| S11 location/sign/default | `EulerBeam3D.RecoversSectionPointAndDefaultCentroidS11`, `ResultRecovery.OrdersStressPointsAndDefaultCentroid` | formula/schema normalized `1e-12` |
+
+The exact acceptance command passed all 17 selected tests. The single reference model plus this
+analytical portfolio covers every documented physical expectation without attributing unsupported
+coverage to the legacy CSV bundle. Verdict: **pass**.
+
+## Failure Classification
+
+- classification: `N/A`
+- primary_failure: `N/A`
+- evidence: all documented physics checks passed; no equilibrium, reaction, displacement,
+  symmetry, element-force, stress-location, rigid-body, nonfinite, coverage, contract, or
+  environment failure was found
+- correction_handoff: `N/A`
+
+## Evaluation Verdict
+
+- verdict: `pass-for-release-agent`
+- reason: the exact reference gate and artifact identity are valid; force and origin-moment
+  equilibrium, constrained reaction consistency, true free residual, deformation signs, expected
+  zeros, element force balance, local/global and section-force signs, S11 schema/analytical sanity,
+  finite/energy/mode checks, and complementary model coverage all satisfy their documented criteria
+- release_approval: `not granted by this report`
+
+## Handoff Recommendation
+
+| target_agent | reason | required_input |
+| --- | --- | --- |
+| Release Agent | All documented physical checks passed. | This report, the Step 26 reference-verification report, exact build-local HDF5/comparison identities, targeted CTest evidence, and the limitations below. |
+
+## No-Change Assertion
+
+- source_files_modified: `false`
+- test_files_modified: `false`
+- cmake_files_modified: `false`
+- requirements_modified: `false`
+- formulations_modified: `false`
+- numerical_review_modified: `false`
+- io_contract_modified: `false`
+- reference_model_contract_modified: `false`
+- reference_verification_report_modified: `false`
+- reference_artifacts_modified: `false`
+- tolerance_policies_modified: `false`
+- Abaqus_or_other_reference_solver_executed: `false`
+- owned_report_created: `true`
+- phase_index_step27_modified: `true`
+- notes: HDF5, comparison JSON, and legacy reference artifacts were inspected read-only; the only
+  generated files were the ignored build-local evidence regenerated by the exact approved CTest.
+
+## Open Issues
+
+- Non-blocking coverage limitation: the approved Abaqus bundle is one identity-axis local-`z`
+  bending cantilever. Axial, torsion, local-`y`, rotated, prescribed-displacement, line-load, and
+  nonzero stress checks rely on the approved analytical/unit portfolio; no broader Abaqus reference
+  coverage is claimed.
+- Non-blocking stress limitation: the B33 bundle has no section points, so its physical `S11`
+  evidence is the correct zero centroid result. Nonzero fiber location/sign evidence is analytical;
+  Abaqus beam stress comparison remains N/A.
+- Non-blocking output limitation: HDF5 has no strain-energy dataset by contract. The positive energy
+  value in this report is calculated from `0.5*F^T*d` and is supported by the rank/energy unit test.
+- Known formulation limitations remain: Euler-Bernoulli deep-beam applicability, transverse and
+  torsional shear stress, warping, `I12!=0`, B31/Timoshenko behavior, and CLI `*DLOAD` are outside V0.
+- No open issue blocks Release Agent review.

docs/physics-evaluations/linear-static-mitc4-shell-physics-evaluation.md

@@ -0,0 +1,331 @@
+# Linear Static MITC4 Shell Physics Evaluation Report
+
+## Metadata
+
+- feature_id: `linear-static-mitc4-shell`
+- model_id: `shell-s4`
+- evaluated_head: `820ba30c717b3d0e113775608e20dfd5fbc05d53`
+- source_build_test_report:
+  `docs/build-test-reports/linear-static-mitc4-shell-build-test.md`
+- source_reference_verification_report:
+  `docs/reference-verifications/linear-static-mitc4-shell-reference-verification.md`
+- source_reference_model:
+  `docs/reference-models/linear-static-mitc4-shell-reference-models.md`
+- source_requirement: `docs/requirements/linear-static-mitc4-shell.md`
+- source_formulation: `docs/formulations/mitc4-shell-formulation.md`
+- source_numerical_review:
+  `docs/numerical-reviews/linear-static-mitc4-shell-review.md`
+- source_io_definition: `docs/io-definitions/linear-static-mitc4-shell-io.md`
+- status: `pass-for-release-agent`
+- owner_agent: `physics-evaluation-agent`
+- date: `2026-08-13`
+
+This verdict means that the documented physical checks pass and the Release Agent
+may audit release readiness. It does not approve release readiness, re-approve the
+reference comparison, or change its tolerance decision.
+
+## Input Evidence
+
+The prerequisite reference-verification report has status
+`pass-for-physics-evaluation`. The existing S4 reference-test route was rebuilt and
+executed to regenerate fresh FESA evidence. Abaqus and other reference solvers were
+not executed.
+
+| evidence | exact path or identity | status | notes |
+| --- | --- | --- | --- |
+| build/test report | `docs/build-test-reports/linear-static-mitc4-shell-build-test.md` | `pass-for-reference-verification` | Clean MSVC x64 Debug build, focused `87/87`, lifecycle `10/10`, reference `8/8`, and full `144/144` CTest passed. |
+| reference verification | `docs/reference-verifications/linear-static-mitc4-shell-reference-verification.md` | `pass-for-physics-evaluation` | Required prerequisite satisfied; 147/147 blocking U rows passed and no UR warning was emitted. |
+| solver HDF5 | `.harness/build/reference/mitc4-shell-s4-comparison/results.h5` | present and readable | Freshly generated, 95,024 bytes; observed raw SHA-256 `E102D80E82BA133EBDF1C5532F3A0A4FE9984AB6CC36D00264399F7308D9230F` (inventory only). |
+| comparison ledger | `.harness/build/reference/mitc4-shell-s4-comparison/comparison.json` | present and passing | 94,349 bytes; SHA-256 `8E8DEA51B6F7C663BACC41FDA6103A4596DB26E02F1EAD6069D458F51E0102E6`; `passed=true`. |
+| declared S4 input | `reference/shell/shell.inp` | present, unchanged, read-only | SHA-256 `4005851E1AB22FD3A16AC17A8D5DA3E051233F69F37419079F3553AD134ECFCF`. |
+| declared displacement CSV | `reference/shell/shell displacements.csv` | present, unchanged, read-only | SHA-256 `C81D94E0B4A849F87AA0F79C83A79B94D5661AC79E44ED826919AB432C87746B`. |
+| optional Abaqus reaction/stress CSVs | `reference/shell/shell reactions.csv`, `reference/shell/shell stresses.csv` | not used as equality gates | Their presence did not expand the approved U-only blocking boundary. |
+| solver CSV views | N/A | not generated | HDF5 was inspected directly. |
+| fresh S4 route | `.harness/build`, MSVC x64 Debug | pass | `Mitc4S4Reference.*` passed `2/2`. |
+
+The HDF5 contains 49 nodes, 36 source-`S4` elements, internal formulation
+`FESA-MITC4`, and the required full `2 x 2 x 2` result inventory. All inspected
+numeric model and result values were finite. The diagnostics dataset contains four
+approved warning rows for ignored `PREPRINT`, `RESTART`, and `OUTPUT` keywords and
+no error diagnostic.
+
+Raw HDF5 bytes are not a physics decision identity and may change across valid
+regenerations. The projected values and deterministic comparison ledger are the
+relevant evidence.
+
+### Documented model expectation
+
+The reference input is a flat `10 x 10`, thickness `0.5`, homogeneous isotropic
+square plate with `E=2.1e11` and `nu=0.3`. Its 24 perimeter nodes are fully clamped
+in all six global DOFs, and center node 2 at the global origin carries one
+`F3=-100000` concentrated force. The geometry, boundary, material, and load are
+symmetric about both global `x=0` and `y=0` planes.
+
+The documented physical expectations are therefore:
+
+- total constrained reaction force opposes the applied `-Z` force;
+- total force and moment about the global origin balance within the approved
+  normalized `1e-10` limit;
+- perimeter displacements are zero and the interior deflects in `-Z`, with the
+  largest magnitude at the center;
+- the displacement and rotation field obeys the polar/axial-vector reflection
+  parity about both symmetry planes;
+- a linear, flat transverse plate response has no membrane strain/resultant or
+  middle-surface in-plane stress, while bottom and top in-plane stresses reverse;
+- stored physical strain energy is finite, strictly positive, and consistent with
+  the recovered generalized fields and `0.5 F^T d`;
+- free residual, finite results, rank/rigid-mode evidence, and the approved
+  one-case coverage show no rigid-body or unsupported-mode symptom.
+
+## Physics Checks
+
+| check | documented expectation | observed evidence | verdict | classification |
+| --- | --- | --- | --- | --- |
+| global equilibrium | Applied plus constrained reaction force/moment about origin; normalized metrics `<=1e-10` | force residual `[0,0,-1.12049747258425e-9]`; moment residual `[6.45741238258779e-10,-2.63753463514149e-10,0]`; normalized force/moment `1.12049747258425e-14` / `2.35981341581908e-15` | pass | N/A |
+| reaction consistency | Perimeter-only reactions from full residual oppose `F3=-100000`; constrained motion is zero | summed constrained force `[0,0,99999.9999999989]`; constrained displacement exactly zero | pass | N/A |
+| displacement direction | Interior bends in `-Z`; center is maximum; no in-plane or drilling leakage | center `U3=-2.35504417650849e-5`; all 25 free-node U3 values nonpositive; `U1/U2/UR3` exactly zero | pass | N/A |
+| symmetry | Correct polar/axial reflection parity about `x=0` and `y=0` | max absolute reflection mismatch `4.27126230127111e-20` / `2.29087480670778e-20` | pass | N/A |
+| element force balance | No documented direct element-end-action output exists for shell GP resultants | Global assembled residual/equilibrium passed; direct element-end-action balance is skipped rather than inferred from mismatched locations | skipped | N/A |
+| recovered resultant consistency | `N=A*epsilon0`, `M=D*kappa`, `Q=As*gamma0` at each of 144 GP rows | absolute L2 residual `9.9301874551584e-12`; normalized L2 `5.56240926027087e-17` | pass | N/A |
+| stress/location/sign sanity | Local `[S11,S22,S12]` at bottom/middle/top; middle zero and faces reverse for this linear flat bending field | absolute L2 constitutive residual `1.29488994752188e-9`; normalized `3.05323934859307e-16`; middle stress exactly zero; face reversal exact | pass | N/A |
+| rigid body/nonfinite | Complete constraints, finite solution, acceptable residual, no abnormal uncontrolled mode | zero nonfinite values; `FREE_RESIDUAL_NORMALIZED=1.07747756058988e-14`; rank/rigid-mode tests passed upstream | pass | N/A |
+| physical energy | Positive and consistent physical-only energy; no drilling-energy gate | `1.17752208825422`; independently recovered value identical to relative `1.88569375589575e-16`; `0.5F^Td=1.17752208825424` | pass | N/A |
+| model coverage | Approved sole S4 case plus declared invariant/patch/common-path portfolio | S4 case covers end-to-end symmetric plate response; focused build/test portfolio passed; expanded models are explicitly nonblocking | pass | N/A |
+
+### 1. Global force and moment equilibrium
+
+The reaction dataset is the assembled full residual `K*d-F`. Applying the
+constraint mask gives
+
+```text
+sum constrained RF = [0, 0, 99999.9999999989]
+sum applied F       = [0, 0, -100000]
+force residual      = [0, 0, -1.12049747258425e-9]
+```
+
+The load acts at the global origin and therefore contributes no origin moment.
+The constrained force and moment rows give
+
+```text
+moment residual = [ 6.45741238258779e-10,
+                   -2.63753463514149e-10,
+                    0 ]
+```
+
+These independently reconstructed values match the stored HDF5 equilibrium vector
+exactly. The serialized normalized metrics are:
+
+| metric | value | threshold | result |
+| --- | ---: | ---: | --- |
+| `FREE_RESIDUAL_NORMALIZED` | `1.07747756058988e-14` | `1.0e-10` | pass |
+| `FORCE_BALANCE_NORMALIZED` | `1.12049747258425e-14` | `1.0e-10` | pass |
+| `MOMENT_BALANCE_NORMALIZED` | `2.35981341581908e-15` | `1.0e-10` | pass |
+
+### 2. Reaction consistency and constrained/free meaning
+
+The 24 perimeter nodes provide 144 constrained DOFs; the remaining 150 DOFs are
+free. The HDF5 constraint mask agrees with the input set exactly, all prescribed
+values are zero, and the maximum constrained displacement is exactly zero.
+
+The total positive `RF3=99999.9999999989` opposes the center `F3=-100000`. The
+nearly zero total `RF1/RF2` and origin `RM1/RM2/RM3` are required by the centered
+load and double symmetry. The largest raw free residual component is
+`7.62156560085714e-10`; because translational and rotational entries have different
+dimensions, the decision uses the documented normalized metric rather than this
+raw maximum. The normalized free residual passes by more than three orders of
+magnitude.
+
+### 3. Displacement direction and deformation mode
+
+Center node 2 has
+
+```text
+[U1,U2,U3,UR1,UR2,UR3]
+= [0, 0, -2.35504417650849e-5, 0, 0, 0]
+```
+
+Every free-node `U3` is nonpositive, the center is the maximum-magnitude
+translation, and every clamped boundary displacement is zero. Across the complete
+model, maximum absolute `U1`, `U2`, and `UR3` are exactly zero. Maximum absolute
+`UR1` and `UR2` are `7.55060026636931e-6` and
+`7.55060026636933e-6`, respectively. This is the expected symmetric plate-bending
+mode under a negative transverse center load, with no in-plane or drilling
+deformation leakage.
+
+### 4. Reflection symmetry and expected zeros
+
+For reflection through `x=0`, polar displacement components transform as
+`[-U1,+U2,+U3]`, while the axial rotation vector transforms as
+`[+UR1,-UR2,-UR3]`. Reflection through `y=0` similarly uses
+`[+U1,-U2,+U3,-UR1,+UR2,-UR3]`.
+
+All 294 scalar nodal component comparisons per reflection were paired by source
+coordinates. The maximum absolute mismatch was `4.27126230127111e-20` for the
+`x` reflection and `2.29087480670778e-20` for the `y` reflection. The equality
+evidence is numerical roundoff, not a new acceptance tolerance.
+
+### 5. Shell generalized resultants and physical work signs
+
+At every one of 36 elements times four midsurface Gauss locations, an independent
+constitutive reconstruction applied the documented centered-section identities:
+
+```text
+N = A * epsilon0
+M = D * kappa
+Q = As * gamma0
+```
+
+The complete 1,152-component resultant comparison has absolute L2 residual
+`9.9301874551584e-12` and normalized L2 residual
+`5.56240926027087e-17`. All membrane strains and `N` resultants are exactly zero,
+as required for this linear flat plate bending response.
+
+The generalized work density `generalized_strain dot section_resultant` is strictly
+positive at all 144 locations: minimum `4.46321446508071e-4`, maximum
+`1.27059464107458e-1`, negative count `0`. This supports the physical sign and
+component-order interpretation.
+
+The shell contract does not expose element-end nodal actions and explicitly forbids
+averaging mismatched result locations. Consequently a separate GP-to-element-end
+force-balance assertion is not documented and is marked `skipped`; the assembled
+global residual and equilibrium checks provide the required force-balance evidence.
+
+### 6. Stress component, location, and sign sanity
+
+HDF5 stores local in-plane `[S11,S22,S12]` directly at each GP and ordered section
+positions `BOTTOM(-1), MIDDLE(0), TOP(+1)`. Independent reconstruction used
+`Cps*(epsilon0+z*kappa)` at all 432 section locations. The absolute L2 residual is
+`1.29488994752188e-9`, or normalized `3.05323934859307e-16`, against a maximum
+absolute stored stress of `313250.779137971`.
+
+All middle-surface in-plane stresses are exactly zero. For every component and GP,
+bottom and top stresses are equal in magnitude and opposite in sign. This is the
+documented curvature/stress-location convention for a centered homogeneous section.
+No `S33`, `S13`, `S23`, nodal stress, or Abaqus stress equality was inferred.
+
+### 7. Physical energy, residual, and rigid-body symptoms
+
+The stored `PHYSICAL_STRAIN_ENERGY` is finite and positive:
+
+```text
+HDF5 physical energy              = 1.17752208825422
+independent GP generalized energy = 1.17752208825422
+0.5 * F^T * d                     = 1.17752208825424
+```
+
+The HDF5-versus-recovered normalized difference is
+`1.88569375589575e-16`; the final fresh HDF5-versus-external-work normalized
+difference is `9.14561471609432e-15`. The HDF5 value excludes numerical drilling stabilization,
+as required. No drilling-energy ratio, calibration, or warning criterion was
+introduced.
+
+The solution is finite, the full perimeter support is enforced, the expected
+deformation mode is smooth and symmetric, all three normalized verification
+metrics pass `1e-10`, and the build/test evidence passes six-rigid-mode,
+stabilized-rank, non-rigid positive-energy, and pure-drill separation tests. No
+rigid-body, singular, nonfinite, or abnormal-mode symptom is present.
+
+### 8. Approved model coverage
+
+The sole approved reference model provides end-to-end evidence for the
+full-integration `S4 -> FESA-MITC4` path, a nonzero transverse bending response,
+fully constrained reaction recovery, global force/moment balance, two-axis
+symmetry, physical energy, and shell result recovery.
+
+The prerequisite focused `87/87` build/test portfolio supplies the documented
+complementary element evidence: membrane, bending, transverse-shear and twist patch
+fields; six physical rigid modes; expected physical/stabilized rank; frame and
+energy invariance; fixed numerical drilling and physical-recovery separation; and
+S4/S4R common-kernel/source-metadata behavior. The reference verification supplies
+the approved external displacement comparison.
+
+This is the complete approved coverage for the feature. Pinched-cylinder,
+hemisphere, Scordelis-Lo, locking/convergence sequences, drilling calibration,
+expanded distorted/curved portfolios, and `NR-O01` through `NR-O04` are explicitly
+nonblocking or out of scope and were not invented as new physics gates.
+
+## Execution Evidence
+
+| order | exact command or read-only operation | exit code | result |
+| ---: | --- | ---: | --- |
+| 1 | `cmake --build .harness/build --config Debug --target fesa_reference_tests` | `0` | Existing S4 reference route rebuilt. |
+| 2 | `ctest --test-dir .harness/build -C Debug -R '^Mitc4S4Reference\.' --output-on-failure` | `0` | Fresh S4 tests `2/2` passed; FESA HDF5 and ledger regenerated. |
+| 3 | `h5dump.exe -n .harness/build/reference/mitc4-shell-s4-comparison/results.h5` with HDF5/oneAPI runtime on `PATH` | `0` | Required HDF5 inventory inspected read-only. |
+| 4 | `h5dump.exe -y -w 0 -m '%.17g' -d <dataset> .harness/build/reference/mitc4-shell-s4-comparison/results.h5` for model nodes/elements/mask/prescribed values, nodal U/R, shell frames/strain/resultant/stress, energy/equilibrium/metrics/diagnostics | `0` | High-precision read-only numerical audit supplied all reported values. |
+| 5 | PowerShell independent input/mask, reaction/equilibrium, reflection, constitutive recovery, stress-location, energy, finite, and diagnostics audit over the `h5dump` values | `0` | All documented physics assertions passed. |
+| 6 | `cmake --build .harness/build --config Debug --target fesa_unit_tests fesa_reference_tests`, then `ctest --test-dir .harness/build -C Debug -R 'Mitc4Shell(Kernel|Patch|Drilling|PhysicalRecovery)|ResultRecovery\..*Shell|Mitc4S4Reference' --output-on-failure` | `0` | Final focused verification passed `17/17`; the regenerated ledger retained `passed=true`, 294 rows, and zero warnings. |
+
+Three intermediate audit-helper incidents were diagnostic-only and did not alter
+the product or verdict: a compound-record regular expression initially omitted the
+last node, a PowerShell array-expression initially bound subtraction to an array,
+and a final optional `h5ls` operand-order probe exited `1`. The root causes were
+confirmed as audit-command/parser usage, while successful high-precision HDF5
+inspection established 49/49 nodes and the complete evidence above. They are not
+solver, HDF5-schema, reference, or physics failures.
+
+## Failure Classification
+
+- classification: `N/A`
+- primary_failure: `N/A`
+- evidence: all documented force/moment equilibrium, reaction, displacement,
+  symmetry, recovery, stress-location, physical-energy, residual, finite-result,
+  rigid-mode and approved coverage checks passed
+- correction_handoff: `N/A`
+- non_gating_incident: resolved read-only audit helper parsing/usage errors only
+
+## Evaluation Verdict
+
+- verdict: `pass-for-release-agent`
+- reason: the prerequisite reference status is valid and fresh FESA S4 evidence
+  satisfies every documented physical expectation under its approved threshold;
+  no implementation, formulation, I/O, model-coverage, nonfinite, rigid-body, or
+  environment failure remains
+- release_approval: `not granted by this report`
+- reference_reapproval: `not performed by this report`
+
+## Handoff Recommendation
+
+| target_agent | reason | required_input |
+| --- | --- | --- |
+| Release Agent | All documented MITC4 physics checks passed. | This report, the build/test and reference-verification reports, the fresh build-local HDF5/comparison evidence, and the nonblocking limitations below. |
+
+## No-Change Assertion
+
+- source_files_modified: `false`
+- test_files_modified: `false`
+- cmake_files_modified: `false`
+- requirements_modified: `false`
+- formulation_modified: `false`
+- numerical_review_modified: `false`
+- io_contract_modified: `false`
+- reference_model_contract_modified: `false`
+- build_test_report_modified: `false`
+- reference_verification_report_modified: `false`
+- phase_files_modified: `false`
+- tolerance_policies_modified: `false`
+- reference_artifacts_modified: `false`
+- Abaqus_or_other_reference_solver_executed: `false`
+- owned_report_created: `true`
+- generated_build_local_evidence: `true`, ignored under `.harness/build/`
+- pre_existing_untracked_build_test_report_preserved: `true`
+- pre_existing_untracked_reference_verification_report_preserved: `true`
+
+## Open Issues
+
+- Nonblocking coverage limitation: the approved external reference inventory is one
+  flat, symmetric, fully clamped S4 plate. The approved analytical/unit portfolio
+  supplies membrane, shear, twist, rigid-mode, rank, drilling-separation and S4R
+  common-path evidence. No broader Abaqus or benchmark portfolio is claimed.
+- Known original-MITC4 limitations remain: transverse-shear locking is mitigated by
+  the tying field, but distorted-curved membrane locking and broader thin/thick mesh
+  convergence are not characterized by this release gate.
+- Source `S4R` maps to the same full-integration FESA kernel and is not compared to
+  the optional Abaqus S4R artifacts. This is an approved boundary, not missing
+  physics evidence.
+- The fixed numerical drilling stiffness is not a physical stress/resultant/energy
+  channel. No drilling calibration, coefficient sweep, energy-ratio gate, or
+  director-parallel moment support is claimed.
+- Geometrically nonlinear execution remains outside the current feature even though
+  future-only residual/tangent equations are documented. No nonlinear release claim
+  is made.
+- No open issue blocks Release Agent review.

docs/reference-models/README.md

@@ -1,213 +1,91 @@
-# Reference Model 문서 작성 가이드
+# Reference Case 문서 작성 가이드
 
-이 디렉터리는 Reference Model Agent가 작성하거나 제안한 기능별 reference model 설계 문서를 보관하는 위치다.
+이 디렉터리는 Reference Model Agent가 작성하는 기능별 lightweight reference-case
+inventory를 보관한다. Abaqus는 외부 수치 reference이며 FESA의 formulation 또는 내부
+동작 계약이 아니다.
 
-Reference Model Agent는 FESA 기능 검증에 필요한 Abaqus `.inp` 기반 테스트 모델 포트폴리오와 `reference/<model-id>/` artifact bundle 계약을 정의한다. Agent는 Abaqus, Nastran 또는 레퍼런스 솔버를 직접 실행하지 않고, Abaqus reference CSV 파일을 생성하거나 수정하지 않으며, solver 결과 비교나 release readiness 승인도 하지 않는다.
+기본 파일명은 `docs/reference-models/<feature-id>-reference-models.md`다. Agent는 Abaqus
+또는 다른 reference solver를 실행하지 않고 `reference/` 파일을 생성, 수정, rename,
+repair 또는 normalize하지 않는다.
 
-기본 파일명은 `docs/reference-models/<feature-id>-reference-models.md` 형식을 사용한다. 각 문서는 요구조건, 연구 브리프, 정식화, 수치 리뷰, I/O 정의를 입력으로 받아 구현 전에 준비해야 할 테스트 모델과 reference artifact 요구사항을 정의해야 한다.
+## 필수 내용
 
-## Reference Model Agent 역할
+기능이 실제로 비교하는 case마다 다음만 기록한다.
 
-수행한다:
-- 기능별 reference model portfolio를 smoke, analytical, patch test, benchmark, regression, negative/invalid-input model로 구분한다.
-- `model.inp`가 I/O Definition Agent의 supported Abaqus keyword subset 안에 있는지 확인한다.
-- `reference/<model-id>/` artifact bundle 구조와 필수 파일을 정의한다.
-- `metadata.json` provenance, 단위, 좌표계, Abaqus version/source, output request, tolerance 정책을 정의한다.
-- Abaqus reference CSV 파일 요구사항을 정의한다.
-- requirement와 model, compared quantity, FESA HDF5 dataset, reference CSV, tolerance, artifact status를 연결하는 Coverage Matrix를 작성한다.
+- case id와 목적
+- existing `.inp` exact path
+- blocking 또는 warning-only quantity의 existing CSV exact path
+- FESA HDF5 dataset
+- source identity와 component mapping
+- missing/extra/duplicate/nonfinite row precheck
+- approved tolerance
+- artifact presence/readability status
 
-수행하지 않는다:
-- C++ 코드를 구현하지 않는다.
-- parser를 구현하지 않는다.
-- C++ API나 파일 구조를 설계하지 않는다.
-- Abaqus, Nastran 또는 레퍼런스 솔버를 직접 실행하지 않는다.
-- Abaqus reference CSV 파일을 생성하거나 수정하지 않는다.
-- solver 결과를 비교하지 않는다.
-- release readiness를 승인하지 않는다.
-- reference 값, tolerance, Abaqus compatibility를 임의로 만들지 않는다.
+다음은 기본 readiness 조건이 아니다.
+
+- canonical directory/file naming 또는 legacy-alias 승인
+- bundle `README.md` 또는 `metadata.json`
+- Abaqus version/generation provenance
+- duplicated units, coordinates, model, step/frame, material, section, thickness, element type
+- reference CSV schema version
+- 비교하지 않는 quantity CSV
+- 요구조건이 요청하지 않은 benchmark portfolio
+
+단일 static step/final frame 기능은 input/CSV pair로 result state를 식별한다. Material,
+section, loads, constraints와 source element type은 `.inp`에서 읽는다.
 
 ## 문서 템플릿
 
 ```markdown
-# <feature title> Reference Models
+# <Feature Title> Reference Cases
 
 ## Metadata
 - feature_id: <feature-id>
-- source_requirement: docs/requirements/<feature-id>.md
-- source_research: docs/research/<feature-id>-research.md
-- source_formulation: docs/formulations/<feature-id>-formulation.md
-- source_numerical_review: docs/numerical-reviews/<feature-id>-review.md
-- source_io_definition: docs/io-definitions/<feature-id>-io.md
 - status: draft | needs-user-decision | needs-reference-artifacts | ready-for-implementation-planning | blocked
 - owner_agent: reference-model-agent
 - date: <YYYY-MM-DD>
 
-## Reference Strategy
-- verification_scope: <feature verification purpose>
-- code_verification: <unit/math-level checks supported by this portfolio>
-- solution_verification: <mesh, convergence, patch, or analytical checks>
-- benchmark_reference_comparison: <Abaqus/NAFEMS/NASA/paper-derived comparison plan>
-- excluded_validation_scope: <physical experiment validation excluded unless explicitly available>
+## Reference Acceptance Scope
+- blocking_quantities: [<quantity/components>]
+- warning_only_quantities: [<quantity/components>]
+- excluded_quantities: [<quantity/reason>]
 
-## Model Inventory
+## Reference Case Inventory
 
-| model_id | category | purpose | status | required_artifacts |
-| --- | --- | --- | --- | --- |
-| <model-id> | smoke | <basic parser/solve path> | draft | model.inp, metadata.json, required Abaqus reference CSV files |
-| <model-id> | analytical | <closed-form comparison> | draft | model.inp, metadata.json, required Abaqus reference CSV files |
-| <model-id> | patch test | <element consistency check> | draft | model.inp, metadata.json, required Abaqus reference CSV files |
-| <model-id> | benchmark | <trusted benchmark comparison> | draft | model.inp, metadata.json, required Abaqus reference CSV files |
-| <model-id> | regression | <known defect guard> | draft | model.inp, metadata.json, required Abaqus reference CSV files |
-| <model-id> | negative/invalid-input | <unsupported keyword or invalid model diagnostic> | draft | model.inp, metadata.json |
+| case_id | purpose | input | required_csv | quantity | behavior | status |
+| --- | --- | --- | --- | --- | --- | --- |
+| <case> | <purpose> | reference/<dir>/<file>.inp | reference/<dir>/<file>.csv | <components> | blocking | warning-only | present | missing |
 
-## Model Record
+## HDF5-to-CSV Comparison Mapping
 
-### <model-id>
-- category: smoke | analytical | patch test | benchmark | regression | negative/invalid-input
-- purpose: <what this model proves>
-- verified_requirements: [<requirement-id>]
-- analysis_type: <linear static | nonlinear static | modal | other>
-- element_type: <Abaqus element type and FESA feature element>
-- material: <material model and values>
-- boundary_conditions: <BC summary>
-- loads: <load summary>
-- expected_physical_quantities: displacement | reaction | internal force | stress | strain | energy | residual
-- tolerance: <absolute/relative/norm policy or needs-user-decision>
-- source: <user | analytical | Abaqus Verification Guide | Abaqus Benchmarks Guide | NAFEMS | NASA/FEMCI | paper>
-- artifact_status: draft | needs-reference-artifacts | ready-for-implementation-planning | blocked
+| case_id | hdf5_dataset | source_id | csv_id_column | components | row_precheck |
+| --- | --- | --- | --- | --- | --- |
+| <case> | <path> | <node/element source id> | <column> | <components> | exact set; unique; finite |
 
-## Abaqus Input Requirements
-- input_file: reference/<model-id>/model.inp
-- supported_keyword_subset: <keywords from docs/io-definitions/<feature-id>-io.md>
-- model_data: <nodes, elements, sets, material, section, coordinates, units>
-- history_data: <step, procedure, boundary conditions, loads, output requests>
-- output_requests: <requests needed to populate Abaqus reference CSV files>
-- unsupported_keyword_policy: unsupported | ignored-with-warning | requires-user-decision
+## Tolerance and Blocking/Warning Policy
+- reference_scale: <formula>
+- row_tolerance: <formula>
+- zero_policy: no clamp
+- blocking_behavior: <rule>
+- warning_behavior: <rule>
 
-## Artifact Bundle Contract
-
-```text
-reference/
-  <model-id>/
-    model.inp
-    metadata.json
-    <model-id>_displacements.csv
-    <model-id>_reactions.csv
-    <model-id>_internalforces.csv
-    <model-id>_stresses.csv
-    README.md
-```
-
-Required files:
-- `model.inp`: Abaqus input file for the reference model.
-- `metadata.json`: provenance and model contract metadata.
-- `<model-id>_displacements.csv`: required when nodal displacement is a verification quantity.
-- `<model-id>_reactions.csv`: required when constrained DOF reactions or global equilibrium are verification quantities.
-- `<model-id>_internalforces.csv`: required when element internal force is a verification quantity.
-- `<model-id>_stresses.csv`: required when stress is a verification quantity.
-- `README.md`: short description, generation notes, and limitations.
-
-Optional files:
-- `<model-id>_strains.csv`: required when strain is part of the acceptance criteria.
-- `<model-id>_energy_or_residual.csv`: required when energy balance, residual, or convergence data is part of the acceptance criteria.
-- `<model-id>_<quantity>.csv`: feature-specific reference quantity when upstream contracts require it.
-- `notes.md`: manual review notes.
-
-## Metadata JSON Contract
-
-```json
-{
-  "feature_id": "<feature-id>",
-  "model_id": "<model-id>",
-  "artifact_status": "draft | needs-reference-artifacts | ready-for-implementation-planning | blocked",
-  "input_file": "model.inp",
-  "abaqus_version": "<version or needs-user-decision>",
-  "generation_owner": "<person/procedure>",
-  "generation_date": "<YYYY-MM-DD>",
-  "source_documents": ["docs/requirements/<feature-id>.md"],
-  "units": "<unit system>",
-  "coordinate_system": "global Cartesian unless otherwise documented",
-  "analysis_type": "<analysis type>",
-  "element_types": ["<Abaqus element type>"],
-  "material_values": {},
-  "boundary_condition_summary": "<summary>",
-  "load_summary": "<summary>",
-  "output_requests": ["U", "RF", "S", "<feature-specific quantities>"],
-  "reference_csv_schema_version": "<version>",
-  "reference_csv_files": [
-    "<model-id>_displacements.csv",
-    "<model-id>_reactions.csv",
-    "<model-id>_internalforces.csv",
-    "<model-id>_stresses.csv"
-  ],
-  "tolerance_policy": "<absolute/relative/norm policy>",
-  "limitations": ["<known limitation>"]
-}
-```
-
-## Abaqus Reference CSV Requirements
-
-### `<model-id>_displacements.csv`
-- Required when nodal displacement is a verification quantity.
-- Must include step/frame identity, node id, displacement components, coordinate system, and units.
-
-### `<model-id>_reactions.csv`
-- Required when constrained DOF reactions or global equilibrium are verification quantities.
-- Must include step/frame identity, node id, reaction components, coordinate system, and units.
-
-### `<model-id>_internalforces.csv`
-- Required when element internal force is a verification quantity.
-- Must include step/frame identity, element id, output location, component, value, and units.
-
-### `<model-id>_stresses.csv`
-- Required when stress is a verification quantity.
-- Must include step/frame identity, element id, integration point or recovery location, component, value, coordinate system, and units.
-
-### Optional Reference CSV Files
-- `<model-id>_strains.csv`: required when strain is part of the acceptance criteria.
-- `<model-id>_energy_or_residual.csv`: required when energy balance, residual, or convergence data is part of the acceptance criteria.
-- `<model-id>_<quantity>.csv`: required when a feature-specific quantity is part of the acceptance criteria.
-
-## Coverage Matrix
-
-| requirement_id | model_id | compared_quantity | fesa_hdf5_dataset | reference_csv | tolerance | verification_method | status |
-| --- | --- | --- | --- | --- | --- | --- | --- |
-| <req-id> | <model-id> | displacement | /steps/<step>/frames/<frame>/field_outputs/U | reference/<model-id>/<model-id>_displacements.csv | <policy> | hdf5-to-reference-csv | draft |
-| <req-id> | <model-id> | reaction | /steps/<step>/frames/<frame>/field_outputs/RF | reference/<model-id>/<model-id>_reactions.csv | <policy> | hdf5-to-reference-csv | draft |
-| <req-id> | <model-id> | internal force | /steps/<step>/frames/<frame>/field_outputs/element_forces | reference/<model-id>/<model-id>_internalforces.csv | <policy> | hdf5-to-reference-csv | draft |
-| <req-id> | <model-id> | stress | /steps/<step>/frames/<frame>/field_outputs/S | reference/<model-id>/<model-id>_stresses.csv | <policy> | hdf5-to-reference-csv | draft |
-
-## Artifact Acceptance Checklist
-- 모든 `must` requirement가 최소 하나의 `model_id`와 `compared_quantity`에 연결되어 있다.
-- `model.inp`가 기능별 supported Abaqus keyword subset을 벗어나지 않는다.
-- `metadata.json`에 provenance, Abaqus version/source, units, coordinate system, tolerance, reference CSV schema version이 기록되어 있다.
-- 필요한 Abaqus reference CSV 파일이 존재하거나, 기능상 불필요한 quantity는 명확한 reason과 함께 제외되어 있다.
-- output request가 필요한 Abaqus reference CSV 물리량을 생성할 수 있도록 정의되어 있다.
-- required Abaqus reference CSV 또는 metadata provenance가 없으면 status는 `needs-reference-artifacts`다.
-- tolerance, source, units, coordinate system이 불명확하면 status는 `needs-user-decision`이다.
+## Readiness Checklist
+- declared input exists and is readable
+- every required CSV exists and is readable
+- source identity and required components are deterministic
+- row-set/nonfinite prechecks are defined
+- tolerance and blocking/warning behavior are approved
 
 ## Open Issues and Downstream Handoff
-
-### I/O Definition Agent
-- <supported keyword, output request, FESA HDF5 schema clarification, reference CSV row schema clarification>
-
-### Implementation Planning Agent
-- <tests that should fail before implementation, model order, acceptance criteria>
-
-### Reference Verification Agent
-- <FESA HDF5 dataset paths, reference CSV schema, ID matching, units, coordinate conventions, output locations, tolerance mapping>
-
-### Physics Evaluation Agent
-- <equilibrium, symmetry, displacement direction, stress location, rigid body mode, load path sanity checks>
+- <only missing required files, matching, tolerance, or feature-owned decisions>
 ```
 
-## 품질 기준
+## 상태 규칙
 
-- Reference model의 목적과 검증 대상 requirement가 명확해야 한다.
-- `model.inp`는 Abaqus input file이며, 기능별 supported keyword subset을 따라야 한다.
-- model data와 history data를 구분해야 한다.
-- output request와 required Abaqus reference CSV 사이의 연결이 명확해야 한다.
-- `reference/<model-id>/` 구조와 필수 artifact가 명시되어야 한다.
-- `metadata.json`에는 provenance, Abaqus version/source, units, coordinate system, tolerance, reference CSV schema version이 포함되어야 한다.
-- required Abaqus reference CSV가 없으면 완료 상태가 아니라 `needs-reference-artifacts` 상태로 둔다.
-- 모든 `must` requirement는 Coverage Matrix에서 model, compared quantity, FESA HDF5 dataset, reference CSV, tolerance, verification method로 추적되어야 한다.
+- `ready-for-implementation-planning`: required input/CSV files, mapping, and tolerance are complete.
+- `needs-reference-artifacts`: a declared input or required comparison CSV is missing.
+- `needs-user-decision`: required quantity, mapping, or tolerance is undefined.
+- `blocked`: no safe progress is possible without an external decision or state change.
+
+Canonical naming, README, metadata, provenance, and unrequested portfolio coverage do not select
+any failure status.

docs/reference-models/linear-static-3d-euler-beam-reference-models.md

@@ -0,0 +1,422 @@
+# Linear Static 3D Euler Beam Reference Models
+
+## Metadata
+
+- feature_id: `linear-static-3d-euler-beam`
+- source_requirement: `docs/requirements/linear-static-3d-euler-beam.md`
+- source_research: `docs/research/linear-static-3d-euler-beam-research.md`
+- source_formulation: `docs/formulations/3d-isoparametric-euler-beam-formulation.md`
+- source_numerical_review: `docs/numerical-reviews/linear-static-3d-euler-beam-review.md`
+- source_io_definition: `docs/io-definitions/linear-static-3d-euler-beam-io.md`
+- approved_design: `docs/superpowers/specs/2026-08-08-linear-static-3d-euler-beam-design.md`
+- status: `ready-for-implementation-planning`
+- owner_agent: `reference-model-agent`
+- date: `2026-08-09`
+- approved_reference_model: `cantilever-beam-b33`
+- approved_reference_schema: `abaqus-cae-report-csv-v0`
+- reference_baseline: `reference/cantilever beam/` at source commit `2b34d0b`
+
+이 문서는 구현 전에 필요한 code verification, analytical solution verification 및
+approved B33 reference comparison의 모델·artifact 계약을 정의한다. 이 status는 모델과
+테스트를 구현 계획으로 넘길 준비가 되었다는 뜻일 뿐, FESA 결과 비교, physics sanity,
+release readiness 또는 Abaqus full compatibility의 pass를 뜻하지 않는다.
+
+## Reference Strategy
+
+### Code verification
+
+요소 수식과 solver infrastructure를 외부 reference 값 없이 직접 검사한다. Hermite
+보간, `theta_y=-dw/dx`, 4x12 `B`, 12x12 closed-form stiffness, 2-point Gauss, six rigid
+modes/rank 6, positive deformation energy, local/global transform, constant local line-load
+kernel, constrained partition, deterministic assembly 및 HDF5 schema가 대상이다. Numerical
+Review의 `NR-T01`부터 `NR-T11`까지를 구현 전 RED test inventory로 사용한다.
+
+### Analytical solution verification
+
+서로 분리된 axial, torsion, local y bending, local z bending cantilever와 rigidly rotated
+beam을 사용한다. 각 모델은 displacement/rotation, reaction, end action, section
+resultant, residual 및 해당되는 axial `S11`을 upstream closed form과 비교한다. Nonzero
+prescribed displacement는 partition 식을, constant local line load는 formulation-only
+equivalent-vector 식을 검증한다. 이 모델들은 Abaqus CSV를 요구하지 않는 code/solution
+test fixtures이며 reference artifact bundle로 가장하지 않는다.
+
+### B33 reference comparison
+
+논리 모델 `cantilever-beam-b33`의 exact read-only legacy bundle만 사용하여 FESA
+`results.h5`의 displacement, reaction 및 endpoint section resultant를 Abaqus/CAE report
+CSV row와 비교한다. Artifact precheck와 exact row-set matching이 먼저 통과해야 하며,
+수치 비교는 component-scale mixed tolerance를 사용한다. Axial `S11` output은 필수지만
+Abaqus beam stress comparison은 명시적 N/A다.
+
+### Excluded validation scope
+
+실험 자료에 대한 physical validation, Abaqus/Nastran 실행, 새로운 reference 값 생성,
+deep-beam/Timoshenko validation, warping, `I12!=0`, instance transform, nonlinear/dynamic
+behavior는 이 portfolio에 포함하지 않는다.
+
+## Model Inventory
+
+| model_id | category | purpose | target quantities or tests | required artifacts | status |
+| --- | --- | --- | --- | --- | --- |
+| `smoke-b33-cli` | smoke | 단일 B33 deck의 parse-to-HDF5와 mandatory output 확인 | CLI, diagnostics, HDF5 paths/identity/atomicity | implementation test fixture; Abaqus CSV N/A | planned |
+| `cv-b33-shape-stiffness` | code verification | Hermite, `B`, closed-form stiffness, 2-point Gauss와 signed line-load kernel 격리 | `NR-T01`, `NR-T03`, `NR-T06` | in-process test data; reference bundle N/A | planned |
+| `cv-b33-patch-rigid-assembly` | patch test | constant strain/curvature, six rigid modes, rank/energy와 deterministic assembly 확인 | `NR-T02`, `NR-T04`, `NR-T11` | implementation test mesh; Abaqus CSV N/A | planned |
+| `an-b33-axial-cantilever` | analytical | axial response와 centroidal axial stress 확인 | `UX`, `RF1`, `N`, `FX`, `S11`, residual | analytical test fixture; Abaqus CSV N/A | planned |
+| `an-b33-torsion-cantilever` | analytical | Saint-Venant torsion response 확인 | `URX`, `RM1`, `T`, `MX`, residual | analytical test fixture; Abaqus CSV N/A | planned |
+| `an-b33-local-y-bending` | analytical | local `+y` force와 `Iz=I22` bending 확인 | `UY`, `URZ`, `RF2`, `RM3`, `Mz`, `FY`, residual | analytical test fixture; Abaqus CSV N/A | planned |
+| `an-b33-local-z-bending` | analytical | local `+z` force와 `Iy=I11`, `theta_y=-w'` 확인 | `UZ`, `URY`, `RF3`, `RM2`, `My`, `FZ`, `S11`, residual | analytical test fixture; Abaqus CSV N/A | planned |
+| `an-b33-rotated-space` | analytical | non-axis-aligned 3D beam의 transform와 energy invariance 확인 | transformed displacement/reaction/resultant, work, energy, `NR-T05` | analytical test fixture; Abaqus CSV N/A | planned |
+| `an-b33-prescribed-displacement` | analytical | nonzero `dc` effective RHS, full reconstruction와 reaction 확인 | `df`, `dc`, `K*d-F`, `NR-T09` | analytical algebra fixture; Abaqus CSV N/A | planned |
+| `an-b33-line-load-kernel` | analytical | formulation-only constant local line-load equivalent vector 확인 | signed 12-component vector, mesh convergence negative/positive control | element unit fixture; `*DLOAD` reference N/A | planned |
+| `neg-b33-input-contract` | negative/invalid-input | unsupported/malformed input과 model-validation diagnostic 확인 | B31, second step, transform, nested assembly, `I12`, geometry, property, keyword cases | invalid input fixtures; result CSV N/A | planned |
+| `cantilever-beam-b33` | benchmark and regression | approved Abaqus B33 nodal/section rows와 end-to-end 회귀 비교 | displacement, reaction, section resultant; stress N/A | exact legacy four-file bundle | inventory-ready; comparison not run |
+
+`planned` analytical/code rows do not have missing reference artifacts: their acceptance source is
+the reviewed formulation or an exact invariant. Only a model intended for Abaqus reference
+comparison is subject to the CSV bundle requirement.
+
+## Model Records
+
+### Code and patch verification records
+
+| model_id | analysis and element | material/section | boundary/load | expected target and tolerance | source |
+| --- | --- | --- | --- | --- | --- |
+| `smoke-b33-cli` | single linear static, two-node `B33` minimum deck | finite positive isotropic `E,nu,A,Iy,Iz,J`, `I12=0` | stable cantilever constraint and one `*CLOAD` | mandatory HDF5 inventory, identity and finite rows; exact schema | requirements and I/O definition |
+| `cv-b33-shape-stiffness` | free two-node Euler beam element | unequal positive `EA,GJ,EIy,EIz` to expose component swaps | no global BC/load; direct element states and local line load | matrix/Gauss/line-load normalized error `<=1e-12`; signed components exact by contract | formulation sections 8-13; `NR-T01/T03/T06` |
+| `cv-b33-patch-rigid-assembly` | one/multiple identity-oriented B33 elements | positive, well-scaled properties | rigid translation/rotation and constant strain/curvature fields | rigid residual `<=1e-10`, rank 6, positive deformation energy; identical CSR structure and values normalized `<=1e-12` | numerical review `NR-T02/T04/T11` |
+
+### Analytical inventory
+
+All analytical beam records use a straight prismatic B33 member, homogeneous isotropic linear
+elasticity with positive `E,G,A,Iy,Iz,J`, `I12=0`, small displacement/rotation and a fixed root.
+Signs follow the approved local `(x,y,z)=(t,n1,t x n1)` convention.
+
+| model_id | boundary conditions and load | target quantity/test | analytical target | tolerance/status |
+| --- | --- | --- | --- | --- |
+| `an-b33-axial-cantilever` | root DOFs fixed; free-end local axial force `Px` | tip `UX`, root `RF1`, constant `N`, outward `FX`, centroid `S11`, residual | `u(L)=Px*L/(E*A)` with force equilibrium and `S11=N/A` | relative `1e-9`; residual normalized `1e-10`; planned |
+| `an-b33-torsion-cantilever` | root fixed; free-end local torque `Mx` | tip `URX`, root `RM1`, constant `T`, outward `MX`, residual | `theta_x(L)=Mx*L/(G*J)` with torque equilibrium | relative `1e-9`; residual normalized `1e-10`; planned |
+| `an-b33-local-y-bending` | root fixed; free-end force `Py` along local `+y` | tip `UY`, `URZ`, root `RF2/RM3`, endpoint `Mz/FY`, residual | `v(L)=Py*L^3/(3*E*Iz)`, `theta_z(L)=Py*L^2/(2*E*Iz)` | relative `1e-9`; end-sign normalized `1e-12`; planned |
+| `an-b33-local-z-bending` | root fixed; free-end force `Pz` along local `+z` | tip `UZ`, `URY`, root `RF3/RM2`, endpoint `My/FZ`, section-point `S11`, residual | `w(L)=Pz*L^3/(3*E*Iy)`, `theta_y(L)=-Pz*L^2/(2*E*Iy)` | relative `1e-9`; end-sign normalized `1e-12`; planned |
+| `an-b33-rotated-space` | rigidly rotate the axial/torsion/two-bending fixtures to a non-axis-aligned direction | `R*R^T`, `det(R)`, transformed displacement/reaction/resultant, work and energy | inverse-rotated physical results equal axis-aligned cases; `det(R)=+1` | normalized `1e-12`; planned |
+| `an-b33-prescribed-displacement` | stable free/constrained partition with nonzero `dc`, finite `Ff` and `Fc` | effective RHS, `df`, full `d`, constrained reaction and free residual | `rhs=Ff-Kfc*dc`, `Rc=Kcf*df+Kcc*dc-Fc` | normalized `1e-10`; planned |
+| `an-b33-line-load-kernel` | element-level constant local `[px,py,pz,mx]`; no parser/CLI `*DLOAD` | all 12 equivalent nodal components and signed end moments | formulation section 12.2 closed-form vector | normalized `1e-12`; planned |
+
+The rotated record covers transformation rather than Abaqus instance transforms. The line-load
+record covers only the element kernel and must be paired with a negative parser test proving that
+`*DLOAD` remains unsupported.
+
+### Invalid-input record
+
+`neg-b33-input-contract` is a table-driven portfolio. Each case uses the smallest otherwise-valid
+single-step deck and changes only the named condition.
+
+| case | expected result |
+| --- | --- |
+| `TYPE=B31` | `unsupported-element-formulation`; no Euler element |
+| second `*STEP` | `unsupported-multiple-step`; no solve/output |
+| instance translation or rotation data | `unsupported-instance-transform` |
+| nested assembly/dependent mesh semantic | structured unsupported diagnostic |
+| `I12!=0` | `unsupported-coupled-section` model failure |
+| nonpositive `E,G,A,Iy,Iz,J` | `invalid-beam-property` model failure |
+| zero/near-zero length | `invalid-beam-length` at the approved scale-aware boundary |
+| zero/tangent-parallel guide vector | `invalid-beam-guide-vector` at the approved projection boundary |
+| `*DLOAD` or unlisted model-affecting keyword | `unsupported-keyword`; no distributed-load Domain object |
+| malformed row, duplicate entity or dangling reference | input failure with source-backed deterministic diagnostic |
+| missing/extra/duplicate/nonfinite/schema- or identity-mismatched reference row | comparison precheck failure before tolerance evaluation |
+
+### Approved reference record: `cantilever-beam-b33`
+
+- category: benchmark and regression
+- purpose: end-to-end B33 displacement, reaction and section-resultant comparison
+- analysis_type: single linear static
+- element_type: ten straight two-node `TYPE=B33` elements, source labels 1 through 10
+- geometry: global x-axis cantilever, total length 10 m, eleven source nodes
+- material: `E=2.1e11`, `nu=0.3`, SI
+- section: `A=1`, `I11=0.0833333`, `I12=0`, `I22=0.0833333`, `J=0.140833`; `n1=(0,1,0)`
+- boundary_conditions: source node 1, DOFs 1 through 6 fixed
+- load: source node 11, global DOF 3, magnitude `-1e6` N
+- model_id: `cantilever-beam-b33`
+- logical_schema: `abaqus-cae-report-csv-v0`
+- source_commit: `2b34d0b`
+- generator: `Abaqus/CAE Learning Edition 2024`
+- units: SI
+- nodal_coordinate_system: global Cartesian
+- section_force_coordinate_system: beam local
+- step_name: `Step-1`
+- increment: `1`
+- step_time: `1.0`
+- artifact_status: all four exact paths present; structural precheck observed; FESA comparison not run
+- stress: N/A for Abaqus reference comparison; mandatory FESA `S11` remains covered by unit/analytical and HDF5 schema tests
+
+The input and CSV numeric reference values are not recalculated, repaired, rounded, clamped or
+otherwise re-derived by this contract.
+
+## Abaqus Input Requirements
+
+The approved input is exactly
+`reference/cantilever beam/cantilever beam.inp`. Read-only inspection confirms that it contains
+`*ELEMENT, TYPE=B33` and remains within the V0 supported subset plus the documented warning
+no-op output-request allowlist. Its single identity instance is `PART-1_1-1`; its canonical result
+identity is `(Step-1, frame 0)` from increment 1, step time 1.0.
+
+For later reference models:
+
+- `model.inp` shall use only the feature-approved Abaqus keyword subset.
+- Model data shall define nodes, B33 connectivity, sets, material, general section and orientation.
+- History data shall define exactly one `*STEP, *STATIC`, supported boundary conditions and nodal
+  loads.
+- `TYPE=B31`, instance transform, nested assembly, `I12!=0` and `*DLOAD` are not admissible ways
+  to create a positive V0 reference model.
+- Abaqus output requests may be present for human generation of required CSVs, but they are
+  warning no-ops for FESA and never select mandatory HDF5 output.
+
+## Artifact Bundle Contract
+
+### Approved legacy exception
+
+The following exact paths are the entire approved read-only bundle:
+
+```text
+reference/cantilever beam/cantilever beam.inp
+reference/cantilever beam/cantilever beam displacements.csv
+reference/cantilever beam/cantilever beam reactions.csv
+reference/cantilever beam/cantilever beam elemental forces.csv
+```
+
+These files shall not be generated, modified, renamed, corrected or restored by an agent or
+Harness. Their spaces and existing CAE report headers are legacy aliases, not a naming pattern for
+new models.
+
+For this approved legacy bundle:
+
+- `metadata.json`: absent-allowed under the project-wide optional metadata policy
+- `README.md`: N/A
+- stress CSV: N/A because beam stress reference comparison is outside the approved V0 scope
+
+The approved design and this contract record model ID, provenance, generator, source commit,
+units, coordinate systems, step/frame identity, logical CSV schema, exact inventory, tolerance
+policy and the stress N/A reason. The optional metadata file's absence and the approved legacy
+README/stress exclusions therefore do not change the record to `needs-reference-artifacts`.
+
+### Future reference bundles
+
+Every later reference model shall use this structure unless its approved requirement explicitly
+marks a quantity N/A:
+
+```text
+reference/
+  <model-id>/
+    model.inp
+    metadata.json                     # optional
+    <model-id>_displacements.csv
+    <model-id>_reactions.csv
+    <model-id>_internalforces.csv
+    <model-id>_stresses.csv
+    README.md
+```
+
+CSV names are canonical `<model-id>_*.csv` names. `README.md` is mandatory for later bundles;
+`metadata.json` is optional. A quantity CSV may be omitted only when the upstream acceptance
+contract explicitly records N/A and gives its verification replacement. Missing required files
+or required Reference Model Contract provenance keep that model at `needs-reference-artifacts`.
+
+## Reference Metadata Contract
+
+This document is the required source of truth for the following metadata. A later bundle may
+optionally duplicate it in `metadata.json` using at least this schema:
+
+```json
+{
+  "feature_id": "linear-static-3d-euler-beam",
+  "model_id": "<model-id>",
+  "artifact_status": "needs-reference-artifacts | ready-for-verification",
+  "input_file": "model.inp",
+  "abaqus_version": "<exact generator/version>",
+  "generation_owner": "<person or approved procedure>",
+  "generation_date": "<YYYY-MM-DD>",
+  "source_commit": "<commit>",
+  "units": "<consistent unit system>",
+  "coordinate_system": "<nodal and element result systems>",
+  "analysis_type": "single linear static",
+  "element_types": ["B33"],
+  "step_name": "Step-1",
+  "increment": 1,
+  "step_time": 1.0,
+  "output_requests": ["U", "RF", "SF"],
+  "reference_csv_schema_version": "<approved schema>",
+  "reference_csv_files": ["<canonical filenames>"],
+  "tolerance_policy": "<approved quantity/component policy>",
+  "limitations": ["<known limitations and explicit N/A quantities>"]
+}
+```
+
+No agent may invent unknown provenance fields or mark a bundle ready merely because filenames
+exist. An absent `metadata.json` is allowed. If the file exists, inventory it read-only and report
+any disagreement with this contract or stored artifacts as an upstream contract/provenance issue.
+
+## Abaqus Reference CSV Requirements
+
+Header comparison trims whitespace around each comma-separated field but does not rename fields.
+For every file, `Frame` must normalize exactly from
+`Increment 1: Step Time = 1.000` to `(Step-1, frame 0)`, `Part Instance Name` must resolve to the
+preserved instance identity, `Node Label` must be a unique source-node station, and all projected
+numeric values must be finite.
+
+| exact legacy path | expected trimmed header | unique row key | observed inventory |
+| --- | --- | --- | --- |
+| `reference/cantilever beam/cantilever beam displacements.csv` | `Frame, Part Instance Name, Node Label, U-U1, U-U2, U-U3, UR-UR1, UR-UR2, UR-UR3` | `(Frame, Part Instance Name, Node Label)` | 11 rows; header/key/finite/arity checks observed |
+| `reference/cantilever beam/cantilever beam reactions.csv` | `Frame, Part Instance Name, Node Label, RF-RF1, RF-RF2, RF-RF3, RM-RM1, RM-RM2, RM-RM3` | `(Frame, Part Instance Name, Node Label)` | 11 rows; header/key/finite/arity checks observed |
+| `reference/cantilever beam/cantilever beam elemental forces.csv` | `Frame, Part Instance Name, Node Label, SF-SF1, SM-SM1, SM-SM2, SM-SM3` | `(Frame, Part Instance Name, Node Label)` | 11 rows; header/key/finite/arity checks observed |
+
+The wide-row key becomes unique canonical component rows after adding `quantity` and `component`.
+Missing, extra, duplicate, nonfinite, header/schema or identity mismatch stops comparison as
+`needs-reference-artifacts` or `schema-mismatch`. No bad or near-zero row may be silently dropped.
+
+For the elemental-force CSV, source node station is not an element-end identity. A boundary
+station uses its only incident endpoint. An interior station may collapse exactly two endpoints
+only when chain connectivity, section and local axes are consistent and the station has no
+concentrated force/moment. The two positive-local-x section-cut values must first agree within the
+approved component tolerance. If they agree, choose the endpoint with smaller stable internal
+element ID; never average. Reversed orientation, branch, section jump, local-axis discontinuity or
+loaded interior station requires an element-aware future schema and is a `schema-mismatch` under
+this legacy schema.
+
+## Coverage Matrix
+
+The authoritative comparison source is FESA HDF5, not an extracted FESA CSV. Dataset paths use
+the canonical V0 step identity.
+
+| verification quantity | requirement ids | model_id | FESA HDF5 dataset | legacy CSV and components | row identity/location | tolerance | verification method | status |
+| --- | --- | --- | --- | --- | --- | --- | --- | --- |
+| nodal displacement/rotation | 003, 029-031, 036-042 | `cantilever-beam-b33` | `/steps/Step-1/frames/0/nodal/displacement` | `reference/cantilever beam/cantilever beam displacements.csv`: `U-U1/U-U2/U-U3 -> UX/UY/UZ`, `UR-UR1/UR-UR2/UR-UR3 -> URX/URY/URZ` | preserved instance + source node; global nodal | `1e-9 + 1e-6*reference_scale` per displacement/rotation component | HDF5-to-read-only CSV after artifact/row-set precheck | ready for implementation planning; comparison not run |
+| nodal reaction force | 007, 027, 029-031, 036-042 | `cantilever-beam-b33` | `/steps/Step-1/frames/0/nodal/reaction` | `reference/cantilever beam/cantilever beam reactions.csv`: `RF-RF1/RF-RF2/RF-RF3 -> RF1/RF2/RF3` | preserved instance + source node; global nodal | `1e-3 + 1e-6*reference_scale` per force component | HDF5-to-read-only CSV plus global equilibrium | ready for implementation planning; comparison not run |
+| nodal reaction moment | 007, 027, 029-031, 036-042 | `cantilever-beam-b33` | `/steps/Step-1/frames/0/nodal/reaction` | `reference/cantilever beam/cantilever beam reactions.csv`: `RM-RM1/RM-RM2/RM-RM3 -> RM1/RM2/RM3` | preserved instance + source node; global nodal | `1e-3 + 1e-6*reference_scale` per moment component | HDF5-to-read-only CSV plus moment equilibrium | ready for implementation planning; comparison not run |
+| section axial force | 031, 036-042 | `cantilever-beam-b33` | `/steps/Step-1/frames/0/element/section_resultant` | `reference/cantilever beam/cantilever beam elemental forces.csv`: `SF-SF1 -> N` | positive-local-x endpoint projected to eligible source node station | `1e-3 + 1e-6*reference_scale` for `N` | endpoint consistency, deterministic station selection, HDF5-to-CSV | ready for implementation planning; comparison not run |
+| section moments/torsion | 031, 036-042 | `cantilever-beam-b33` | `/steps/Step-1/frames/0/element/section_resultant` | `reference/cantilever beam/cantilever beam elemental forces.csv`: `SM-SM1 -> My`, `SM-SM2 -> Mz`, `SM-SM3 -> T` | positive-local-x endpoint projected to eligible source node station; beam local | `1e-3 + 1e-6*reference_scale` separately for `My`, `Mz`, `T` | endpoint consistency, deterministic station selection, HDF5-to-CSV | ready for implementation planning; comparison not run |
+| equilibrium end action | 031, 035, 043 | analytical models and physics portfolio | `/steps/Step-1/frames/0/element/end_force_local` | Abaqus CSV N/A for direct outward-action comparison | element endpoint `xi=-1,+1`; local outward action `[FX,FY,FZ,MX,MY,MZ]` | analytical normalized `1e-12`; residual `1e-10` | unit/analytical end-sign tests and later physics sanity | planned |
+| generalized strain/resultant | 029, 031, 035 | code and analytical models | `/steps/Step-1/frames/0/element/generalized_strain` and `/steps/Step-1/frames/0/element/generalized_resultant` | Abaqus CSV N/A | two Gauss points; beam local | matrix/formulation normalized `1e-12`, analytical relative `1e-9` | formulation/unit/HDF5 schema tests | planned |
+| axial stress | 029, 032, 035 | axial/local-z analytical models | `/steps/Step-1/frames/0/element/stress_s11` | stress CSV N/A; Abaqus beam stress reference comparison N/A | element, Gauss point, input section point or `fesa-default` centroid | analytical relative `1e-9`; exact unit/row schema | unit/analytical recovery and HDF5 schema tests | planned; reference N/A |
+
+For every matched reference group,
+`reference_scale=max(abs(Abaqus reference rows))` for the same model, step/frame, quantity and
+component, and `row_tolerance=absolute_floor+1e-6*reference_scale`. Abaqus values alone set the
+scale. A zero scale uses only the floor. Every row decision and max absolute, component-scale
+normalized, RMS, norm and worst-row/component metrics must be reported.
+
+### Complete must-requirement coverage
+
+Every approved `must` requirement is connected below to a model/test/quantity or an explicit
+non-reference governance check. `N/A` means that an Abaqus CSV is not the applicable evidence;
+it does not waive the requirement.
+
+| requirement | model/test/quantity or explicit N/A | planned verification |
+| --- | --- | --- |
+| `FESA-REQ-LS3DEB-001` | `smoke-b33-cli`; `neg-b33-input-contract` second-step case | positive single-step and structured rejection test |
+| `FESA-REQ-LS3DEB-002` | all analytical B33 records | model-validation and formulation scope tests; CSV N/A except approved benchmark |
+| `FESA-REQ-LS3DEB-003` | all code/analytical records; displacement/reaction rows | exact DOF/component-order tests |
+| `FESA-REQ-LS3DEB-004` | axial, torsion and both bending records | four independent analytical solution tests |
+| `FESA-REQ-LS3DEB-005` | `smoke-b33-cli`, `cantilever-beam-b33` | B33 semantic mapping and artifact type precheck |
+| `FESA-REQ-LS3DEB-006` | `neg-b33-input-contract` B31 case | exact `unsupported-element-formulation` test |
+| `FESA-REQ-LS3DEB-007` | four cantilevers and prescribed-displacement record | DOF 1..6 load/BC and nonzero `dc` tests |
+| `FESA-REQ-LS3DEB-008` | `an-b33-line-load-kernel`; negative `*DLOAD` case | closed-form vector and unsupported parser tests; reference CSV N/A |
+| `FESA-REQ-LS3DEB-009` | `smoke-b33-cli`, keyword table tests, approved legacy input | exact positive keyword inventory |
+| `FESA-REQ-LS3DEB-010` | parser code-verification cases | case/comment/source-label preservation tests; CSV N/A |
+| `FESA-REQ-LS3DEB-011` | analytical load/BC decks and invalid arity/target cases | target expansion and row grammar tests |
+| `FESA-REQ-LS3DEB-012` | both bending and rotated-space records | property/axis mapping and transform checks |
+| `FESA-REQ-LS3DEB-013` | all analytical records; invalid property cases | `G` calculation and positive property tests |
+| `FESA-REQ-LS3DEB-014` | `neg-b33-input-contract` geometry cases; `NR-T05` | exact scale-aware length/projection boundary tests |
+| `FESA-REQ-LS3DEB-015` | multi-instance semantic fixture and all HDF5/reference identities | stable source/internal identity tests |
+| `FESA-REQ-LS3DEB-016` | multi-instance semantic fixture | distinct deterministic identity test; reference CSV N/A |
+| `FESA-REQ-LS3DEB-017` | invalid instance-transform case | exact diagnostic test |
+| `FESA-REQ-LS3DEB-018` | invalid nested/dependent cases | structured unsupported tests |
+| `FESA-REQ-LS3DEB-019` | `cantilever-beam-b33` input and allowlist table cases | warning/no-op and no semantic-effect tests |
+| `FESA-REQ-LS3DEB-020` | unknown-keyword negative case and `smoke-b33-cli` | error plus mandatory-output independence test |
+| `FESA-REQ-LS3DEB-021` | Domain/AnalysisModel code-verification fixture | non-copy/non-mutation ownership tests; CSV N/A |
+| `FESA-REQ-LS3DEB-022` | DOF/scatter/reconstruction code-verification fixture | DofManager ownership and exact mapping tests; CSV N/A |
+| `FESA-REQ-LS3DEB-023` | `smoke-b33-cli` and HDF5 state fixture | required/excluded state allocation tests; CSV N/A |
+| `FESA-REQ-LS3DEB-024` | `cv-b33-patch-rigid-assembly`, `NR-T11` | repeated thread-count CSR determinism test; CSV N/A |
+| `FESA-REQ-LS3DEB-025` | math/adapter dependency fixtures | storage/layout and public dependency review; CSV N/A |
+| `FESA-REQ-LS3DEB-026` | orchestration event-trace fixture | exact factorize-before-load order test; CSV N/A |
+| `FESA-REQ-LS3DEB-027` | `an-b33-prescribed-displacement` | effective RHS, reconstruction and residual reaction test |
+| `FESA-REQ-LS3DEB-028` | `smoke-b33-cli` writer failure/success fixtures | authoritative output and atomicity tests; CSV N/A |
+| `FESA-REQ-LS3DEB-029` | HDF5 rows in this Coverage Matrix | exact path/shape/component schema test |
+| `FESA-REQ-LS3DEB-030` | `smoke-b33-cli`; `cantilever-beam-b33` provenance | ordinary unit label and external SI metadata tests |
+| `FESA-REQ-LS3DEB-031` | all code/analytical models and three legacy CSV quantities | recovery component/location and mandatory-output tests |
+| `FESA-REQ-LS3DEB-032` | axial/local-z analytical stress; HDF5 `stress_s11` | stress unit/analytical/schema tests; Abaqus stress comparison N/A |
+| `FESA-REQ-LS3DEB-033` | `smoke-b33-cli`, diagnostic negative cases | CLI exit-code/field/order integration tests; CSV N/A |
+| `FESA-REQ-LS3DEB-034` | every implementation model/test | per-step RED/GREEN/VERIFY and full MSVC/CTest evidence; model CSV N/A |
+| `FESA-REQ-LS3DEB-035` | `NR-T01` through `NR-T11` and analytical inventory | exact numerical criteria in model records |
+| `FESA-REQ-LS3DEB-036` | `cantilever-beam-b33` and comparison-policy unit fixtures | Abaqus-only component scale and exact formula tests |
+| `FESA-REQ-LS3DEB-037` | same comparison fixtures, including zero-scale groups | exact SI floors and zero-scale tests |
+| `FESA-REQ-LS3DEB-038` | malformed reference cases in `neg-b33-input-contract` | pre-tolerance fail-fast and no-clamp/no-drop tests |
+| `FESA-REQ-LS3DEB-039` | verification-report schema fixture | every row decision and aggregate/worst metrics test |
+| `FESA-REQ-LS3DEB-040` | exact legacy Artifact Bundle Contract | inventory plus `git diff --exit-code -- reference/` process check |
+| `FESA-REQ-LS3DEB-041` | approved artifact precheck | four files, B33, exact headers, unique keys, finite values |
+| `FESA-REQ-LS3DEB-042` | three comparison quantities and station normalization | exact component mapping, endpoint consistency and no-average tests |
+| `FESA-REQ-LS3DEB-043` | gate audit; later physics portfolio | reference execution N/A at this step; enforce build/test -> comparison -> physics -> release order |
+| `FESA-REQ-LS3DEB-044` | process/Git diff audit and limitations review | no reference execution/mutation and no out-of-scope support claim |
+
+## Artifact Acceptance Checklist
+
+Read-only inventory inspection on `2026-08-09` established the following pre-implementation facts:
+
+- all four exact legacy paths exist;
+- the input declares `TYPE=B33`;
+- each CSV trimmed header matches the documented `abaqus-cae-report-csv-v0` inventory;
+- each CSV has 11 data rows with a unique `(Frame, Part Instance Name, Node Label)` key;
+- every projected numeric field is finite and every row has the header arity;
+- generator, source commit, SI units, coordinates, step/increment/time and tolerance provenance are
+  recorded in the approved design and this contract;
+- absent `metadata.json` is allowed by project-wide policy; legacy `README.md` and stress CSV are accepted N/A exceptions;
+- no reference value was recalculated and no comparison was performed.
+
+Before an actual comparison, tooling must repeat all artifact checks, verify the exact Frame and
+instance identities, compare the complete projected row sets, and stop on any failure. The Step AC
+must also show no working-tree diff under `reference/`. Passing this checklist is not a reference
+comparison pass.
+
+## Open Issues and Downstream Handoff
+
+### Open issues
+
+- No missing artifact or user decision blocks implementation planning for the approved legacy
+  model.
+- `NR-O01` (official oneMKL PARDISO contract) and `NR-O02` (deterministic duplicate-reduction
+  algorithm) remain implementation-planning inputs, not reference artifact defects.
+- Future reversed, branched, loaded-interior or section-jump reference models require an
+  element-aware canonical CSV schema; the legacy node-station schema must not be generalized.
+
+### Implementation Planning Agent
+
+Use this order for tests that must fail before their production implementation:
+
+1. Hermite/DOF/sign and `B` checks.
+2. Gauss/closed stiffness, rigid modes, rank and energy.
+3. Rotation/local-axis and signed line-load kernel.
+4. Axial, torsion, local-y and local-z analytical cantilevers.
+5. Nonzero prescribed displacement, SPD/residual and deterministic assembly.
+6. Parser invalid-input portfolio and CLI/HDF5 output contract.
+7. Legacy artifact precheck, row projection and tolerance/report policy.
+
+Keep reference comparison after the full MSVC build/test gate and do not require new Abaqus
+artifacts for code/analytical fixtures.
+
+### Reference Verification Agent
+
+Run `ARTIFACT CHECK -> HDF5 ROW PROJECTION -> EXACT ROW-SET CHECK -> ENDPOINT CONSISTENCY ->
+COMPONENT-SCALE COMPARE -> REPORT`. Use only the exact legacy files and the HDF5 paths/component
+mappings in the Coverage Matrix. Do not synthesize `SF2/SF3` or stress rows, clamp values, omit
+rows, average interior endpoints, or change the approved tolerance.
+
+### Physics Evaluation Agent
+
+Only after reference comparison passes, check global force/moment equilibrium, reaction sign,
+displacement direction, bending symmetry, outward end action versus positive-face section
+resultant consistency, and normalized residual. The approved reference model is one local-z
+bending cantilever; broader physical coverage comes from the analytical portfolio, not an inflated
+claim about the single CSV bundle.
+
+### I/O Definition Agent
+
+No upstream contract revision is requested. If a future reference model needs an element-aware row
+identity, define and approve that schema separately without changing the read-only legacy aliases.

docs/reference-models/linear-static-mitc4-shell-reference-models.md

@@ -0,0 +1,122 @@
+# Linear Static MITC4 Shell Reference Cases
+
+## Metadata
+
+- feature_id: `linear-static-mitc4-shell`
+- source_requirement: `docs/requirements/linear-static-mitc4-shell.md`
+- source_io_definition: `docs/io-definitions/linear-static-mitc4-shell-io.md`
+- status: `approved-for-implementation-planning`
+- owner_agent: `reference-model-agent`
+- date: `2026-08-13`
+- artifact_policy: `read-only-existing-files`
+- authoritative_fesa_output: `results.h5`
+
+## 1. Purpose and boundary
+
+This document is the lightweight inventory and comparison contract for the sole
+approved full-integration S4 reference case. Abaqus supplies an external displacement reference;
+it does not define FESA element equations, integration, stabilization, recovery, or
+implementation structure. FESA and Abaqus are not required to operate identically.
+
+Reference readiness requires only:
+
+- the declared Abaqus `.inp` file and displacement CSV for each case;
+- the FESA `results.h5` generated from that case's `.inp`;
+- deterministic source-instance/node/component matching;
+- the approved tolerance and decision rule in Section 5.
+
+README, `metadata.json`, canonical naming, legacy-alias approval, Abaqus version or
+generation provenance, duplicated unit/coordinate/model/step/frame/material/section
+descriptions, and a CSV schema-version record are not required. If `metadata.json`
+later exists, it is optional read-only context and does not override the declared
+input, CSV, row mapping, or tolerance.
+
+## 2. Read-only case inventory
+
+| case_id | source label | role | exact path | SHA-256 | observed content |
+| --- | --- | --- | --- | --- | --- |
+| `shell-s4` | `S4` | input | `reference/shell/shell.inp` | `4005851E1AB22FD3A16AC17A8D5DA3E051233F69F37419079F3553AD134ECFCF` | `TYPE=S4`; one linear-static case |
+| `shell-s4` | `S4` | required reference | `reference/shell/shell displacements.csv` | `C81D94E0B4A849F87AA0F79C83A79B94D5661AC79E44ED826919AB432C87746B` | 49 data rows; U and UR components |
+
+The existing reaction and stress CSVs in `reference/shell/` are optional inspection
+evidence only. Existing files under `reference/shellR/` are also optional inspection
+evidence and are not consumed by acceptance comparison. They are not pass/fail inputs.
+No agent may rename, rewrite, normalize, repair, regenerate, or restore any reference
+artifact unless a later phase explicitly authorizes that operation.
+
+## 3. Required CSV mapping
+
+Trim surrounding whitespace from header names, then apply this exact projection:
+
+| Abaqus CSV column | normalized identity/value | FESA HDF5 source |
+| --- | --- | --- |
+| `Part Instance Name` | `instance_name` | `/model/nodes.instance_name` |
+| `Node Label` | `source_node_label` | `/model/nodes.source_label` |
+| `U-U1` | `U1` | `/steps/Step-1/frames/0/nodal/displacement[:,0]` (`UX`) |
+| `U-U2` | `U2` | `/steps/Step-1/frames/0/nodal/displacement[:,1]` (`UY`) |
+| `U-U3` | `U3` | `/steps/Step-1/frames/0/nodal/displacement[:,2]` (`UZ`) |
+| `UR-UR1` | `UR1` | `/steps/Step-1/frames/0/nodal/displacement[:,3]` (`URX`) |
+| `UR-UR2` | `UR2` | `/steps/Step-1/frames/0/nodal/displacement[:,4]` (`URY`) |
+| `UR-UR3` | `UR3` | `/steps/Step-1/frames/0/nodal/displacement[:,5]` (`URZ`) |
+
+The normalized row key is
+`(case_id,instance_name,source_node_label,component)`. Stable comparison order is
+case `shell-s4`; then FESA instance declaration order; stable source-node order; and
+component order `[U1,U2,U3,UR1,UR2,UR3]`.
+
+## 4. Precheck
+
+Before numerical comparison, each case shall satisfy all of the following:
+
+1. The declared input, displacement CSV, and FESA `results.h5` exist.
+2. The six required displacement headers map exactly as Section 3 specifies.
+3. Each required CSV and HDF5 value is finite.
+4. Each normalized row key is unique.
+5. CSV and HDF5 normalized row-key sets are exactly equal.
+
+Missing, extra, duplicate, nonfinite, header-mismatched, or source-identity-mismatched
+required rows fail reference verification before tolerance evaluation. Values are not
+zero-clamped and mismatched rows are not omitted, averaged, or synthesized.
+
+## 5. Tolerance and decision rule
+
+For every matched row:
+
+```text
+tolerance = 1.0e-5
+absolute_error_i = abs(fesa_value_i - abaqus_value_i)
+```
+
+The fixed `1.0e-5` value is expressed in the model's user-consistent length unit for
+`U1/U2/U3` and is dimensionless for `UR1/UR2/UR3`. Neither a component reference scale
+nor a row-specific denominator changes the value. Reference scale may be reported as
+non-decision diagnostic information. The separate B33 mixed tolerance is unchanged.
+
+- Every matched `U1/U2/U3` row must satisfy `absolute_error_i <= tolerance`.
+  Any U exceedance fails that case and the feature reference comparison.
+- `UR1/UR2/UR3` uses the same fixed value. Every exceedance produces a deterministic
+  warning containing the case, source row, component, error, and tolerance, but does
+  not change pass/fail.
+
+The comparison report records every U/UR row decision, maximum absolute error,
+fixed-tolerance-normalized error, RMS error, vector-norm error, worst source
+row/component, and every UR warning.
+
+## 6. Coverage and handoff
+
+The S4 case is the complete required reference inventory for this feature:
+
+- `shell-s4` checks the approved full-integration `S4 -> FESA-MITC4` input path against Abaqus U.
+- `S4R -> FESA-MITC4` support is verified by parser, common-kernel,
+  deterministic-assembly and HDF5 source-metadata tests without consuming an Abaqus
+  S4R reference artifact.
+
+They do not prove Abaqus formulation equivalence or general MITC4 accuracy outside
+the modeled cases. Additional flat/thin/thick/distorted/curved models, mesh studies,
+drilling sweeps, drilling-energy criteria, `NR-O03`, and `NR-O04` are not required
+before Implementation Planning or feature completion.
+
+Numerical Review may use this inventory as downstream comparison input, but missing
+bundle-administration data shall not change a mathematically consistent formulation
+verdict. The revised Numerical Review passes the formulation and authorizes
+Implementation Planning; this does not authorize implementation or Harness execution.

docs/reference-papers/MITC4/AContinuumMechanicsBasedFourNodeShell/AContinuumMechanicsBasedFourNodeShell_001.md

@@ -0,0 +1,955 @@
+<!-- source-page: 1 -->
+
+# A continuum mechanics based four-node shell element for general non-linear analysis
+
+Eduardo N. Dvorkin and Klaus-Jürgen Bathe
+
+Department of Mechanical Engineering,
+
+Massachusetts Institute of Technology, Cambridge, MA 02139, USA
+
+(Received December 1983)
+
+# ABSTRACT
+
+A new four-node (non-flat) general quadrilateral shell element for geometric and material non-linear analysis is presented. The element is formulated using three-dimensional continuum mechanics theory and it is applicable to the analysis of thin and thick shells. The formulation of the element and the solutions to various test and demonstrative example problems are presented and discussed.
+
+# INTRODUCTION
+
+The finite element analysis of general shell structures has been a very active field of research for a large number of years $^{14,29}$ . However, despite the fact that many different shell elements have already been proposed, the search for a shell element capable of representing the general nonlinear behaviour of shells with arbitrary geometry and loading conditions in an effective and reliable manner is still continuing very actively.
+
+During recent years it has become apparent that two approaches for the development of shell elements are very appropriate: (1) the use of simple elements, based on the discrete-Kirchhoff approach for the analysis of thin shells $^{2,5-9}$ ; (2) the use of degenerated isoparametric elements in which fully three-dimensional stress and strain conditions are degenerated to shell behaviour $^{2,3,5,7,17,19,24,29}$ .
+
+The latter approach has the advantage of being independent of any particular shell theory, and this approach was used by Bathe and Bolourchi $^{3}$ to formulate a general shell element for geometric and material non-linear analysis. This element has been employed very successfully when used with 9 or, in particular, 16 nodes. However, the 16-node element is quite expensive, and although it is possible to use in some analyses only a few elements to represent the total structure (see later examples) in other analyses still a fairly large number of elements need by employed $^{5}$ .
+
+Considering general shell analyses, much emphasis has been placed onto the development of a versatile, reliable and cost-effective 4-node shell element $^{16,17,22,28}$ . Such element would complement the above high-order 16-node element and may be more effective in certain analyses. The difficulties in the development of such element lie in that the element should be applicable in a reliable manner to thin and thick shells of arbitrary geometries for general non-linear analysis.
+
+The objective in this paper is to present a simple 4-node general shell element with the following properties: the element is formulated using three-dimensional stress and strain conditions without use of a shell theory; the element is applicable to thin and thick shells and can be employed to model arbitrary geometries; the element is applicable to the conditions of large displacements and rotations but small strains, and can be used effectively in materially non-linear analysis.
+
+The formulation of the element is quite simple and transparent, and the element has good predictive capability without containing spurious zero energy modes.
+
+In the next section of the paper we discuss some basic considerations with respect to the assumptions used, and in the following section we present the element formulation for non-linear analysis. The results obtained in numerical solutions that demonstrate the properties of the element are given in the final section.
+
+# BASIC CONSIDERATIONS
+
+The formulation of the 4-node shell element represents an extension of the shell element discussed previously $^{2,3}$ , and we therefore use the same notation as in those references. Also, to focus attention onto some key issues of the formulation, we consider in this section only linear analysis conditions.
+
+The geometry of the element (see Figure 1) is described using $^{2}$ :
+
+$$
+{ } ^ { l } x _ { i } = \sum _ { k = 1 } ^ { 4 } h _ { k } { } ^ { l } x _ { i } ^ { k } + \frac { r _ { 3 } } { 2 } \sum _ { k = 1 } ^ { 4 } a _ { k } h _ { k } { } ^ { l } V _ { n i } ^ { k } \tag {1}
+$$
+
+![](images/page-001_d5a8b8dfa6fbec52dcaa04baf84bcf6c3e6094dcbdc7affb122aa54bf942eed1.jpg)
+
+<details>
+<summary>text_image</summary>
+
+r2
+2
+node 1
+r1
+3
+g3
+g2
+g1
+oVn4
+a4
+4
+oVn^k
+u3^k
+u2^k
+oV2^k
+node k
+oV1^k
+αk
+oV1^k = e2 × 0Vn^k / |e2 × 0Vn^k |
+oV2^k = 0Vn^k × 0V1^k
+</details>
+
+Figure 1 Four-node shell element
+
+<!-- source-page: 2 -->
+
+![](images/page-002_ff020b598ebf94ae65e6bc78efebdc2f3b74a4d3a7eec6bb1611ec0d8c770c3e.jpg)
+
+<details>
+<summary>text_image</summary>
+
+r₃
+r₂
+2
+A
+I
+q₃
+q₂
+q₁
+B
+D
+r₁
+3
+C
+4
+</details>
+
+![](images/page-002_6cb23535ce5ce32d6a992b2e0ab5048f0b4e374b4f3923a30cde0f385d0c7b5a.jpg)
+
+![](images/page-002_d08941e2c28a89d87966f44f673a97c182c7f8e7e7a8463c4dc64d3a59eda4f5.jpg)  
+$\tilde{\varepsilon}_{13}$ interpolation
+
+![](images/page-002_f0e3ac3a321ba459c27856613fb953d2e49581e7c39cd42eb6a6c0cd5f67612c.jpg)
+
+![](images/page-002_a5d95902e898986b8afdfd449bb9b0b86be37c1ae18a1cc360bfc197ca4bb023.jpg)  
+$\tilde{\varepsilon}_{23}$ interpolation   
+Figure 2 Interpolation functions for the transverse shear strains
+
+where the $h_{k}(r_{1},r_{2})$ are the two-dimensional interpolation functions corresponding to node k; the $r_{i}$ are the natural coordinates; and $^{l}x_{i}=$ Cartesian coordinates of any point in the element; $^{l}x_{i}^{k}=$ Cartesian coordinates of nodal point k; $^{l}V_{nl}^{k}=$ components of director vector at node k (which is not necessarily normal to the midsurface of the element); and $a_{k}$ is the shell thickness at node k, measured along the vector $^{l}V_{n}^{k}$ . The left superscript is zero for the initial geometry of the element and is equal to 1 for the deformed element geometry. Note that the thickness of the element varies and the element is in general non-flat.
+
+The displacements of any particle with natural coordinates $r_{i}$ of the shell element in the stationary Cartesian coordinate system are:
+
+$$
+u _ {i} = \sum_ {k = 1} ^ {4} h _ {k} u _ {i} ^ {k} + \frac {r _ {3}}{2} \sum_ {k = 1} ^ {4} a _ {k} h _ {k} \left(- ^ {0} V _ {2 i} ^ {k} \alpha_ {k} + ^ {0} V _ {1 i} ^ {k} \beta_ {k}\right) \tag {2}
+$$
+
+where the $u_{i}^{k}$ are the nodal point displacements into the Cartesian coordinate directions, and the $\alpha_{k}$ and $\beta_{k}$ are the rotations of the director vector ${}^{0}V_{n}^{k}$ about the ${}^{0}V_{1}^{k}$ and ${}^{0}V_{2}^{k}$ axes (see Figure 1).
+
+A basic problem inherent in the use of the above interpolation of the displacements, and the derivation of the strain-displacement matrices therefrom, is that the element 'locks' when it is thin. This is due to the fact that with these interpolations the transverse shear strains cannot vanish at all points in the element, when it is subjected to a constant bending moment. Hence, although the basic continuum mechanics assumptions contain the Kirchhoff shell assumptions, the finite element discretization is not able to represent these assumptions rendering the element not applicable to the analysis of thin plates or shells $^{2,5,7}$ . To solve this deficiency, various remedies based on selective and reduced integration have been proposed $^{17,22,23}$ but there is still much room for more effective and reliable elements for general non-linear analysis.
+
+Considering our element formulation - because the problem lies in the representation of the transverse shear strains - we proceed to not evaluate these shear strains from the displacements in (2), but to introduce separate interpolations for these strain components. Since we consider non-flat shell elements, the separate interpolations are performed effectively in a convected coordinate system†.
+
+The choice of the interpolation for the transverse shear strain components is the key assumption in our element formulation, because adequate coupling between the element displacements and rotations must be introduced and the element should not exhibit any spurious zero energy modes. For our element we use (see Figure 2):
+
+$$
+\begin{array}{l} \tilde {\varepsilon} _ {1 3} = \frac {1}{2} (1 + r _ {2}) \tilde {\varepsilon} _ {1 3} ^ {\mathrm{A}} + \frac {1}{2} (1 - r _ {2}) \tilde {\varepsilon} _ {1 3} ^ {\mathrm{C}} \\ \tilde {\varepsilon} _ {2 3} = \frac {1}{2} \left(1 + r _ {1}\right) \tilde {\varepsilon} _ {2 3} ^ {\mathrm{D}} + \frac {1}{2} \left(1 - r _ {1}\right) \tilde {\varepsilon} _ {2 3} ^ {\mathrm{B}} \tag {3} \\ \end{array}
+$$
+
+Since the kinematic relations for the above shear strains are not satisfied using (3), we impose them using Lagrange multipliers $^{2,27}$ to obtain,
+
+$$
+\Pi^ {*} = \frac {1}{2} \int_ {V} \tilde {\tau} ^ {i j} \tilde {\varepsilon} _ {i j} \mathrm{d} V + \int_ {V} \lambda^ {1 3} \left(\tilde {\varepsilon} _ {1 3} - \tilde {\varepsilon} _ {1 3} ^ {\mathrm{DI}}\right) \mathrm{d} V + \tag {4}
+$$
+
+$$
+\int_ {V} \lambda^ {2 3} \left(\tilde {\varepsilon} _ {2 3} - \tilde {\varepsilon} _ {2 3} ^ {\mathrm{DI}}\right) \mathrm{d} V - \mathscr {W}
+$$
+
+where the $\tilde{\tau}^{ij}$ are the contravariant components of the Cauchy stress tensor $^{13,15}$ , the $\tilde{\varepsilon}_{ij}$ are the covariant components of the infinitesimal strain tensor, the $\lambda^{13}$ and $\lambda^{23}$ are the Lagrange multipliers, the $\tilde{\varepsilon}_{13}^{DI}$ and $\tilde{\varepsilon}_{23}^{DI}$ are the transverse shear strains evaluated using the displacement interpolations in (2), and W is the potential of the external loads. For the Lagrange multipliers we choose the following interpolations,
+
+$$
+\lambda^ {1 3} = \lambda^ {A} \delta (r _ {1}) \delta (1 - r _ {2}) + \lambda^ {C} \delta (r _ {1}) \delta (1 + r _ {2})
+$$
+
+$$
+\lambda^ {2 3} = \lambda^ {\mathrm{D}} \delta \left(r _ {2}\right) \delta \left(1 - r _ {1}\right) + \lambda^ {\mathrm{B}} \delta \left(r _ {2}\right) \delta \left(1 + r _ {1}\right) \tag {5}
+$$
+
+where $\delta(\ldots)$ is the Dirac-delta function. This represents a weakening of the Lagrange multiplier constraint in (4) $^{10}$ . Substituting from (5) into (4) and invoking that $\delta\Pi^{*}=0$ gives the distinct constrains:
+
+$$
+\left. \tilde {\varepsilon} _ {1 3} \right| _ {\text { at   A }} = \left. \tilde {\varepsilon} _ {1 3} ^ {\mathrm{DI}} \right| _ {\text { at   A }} \quad \left. \tilde {\varepsilon} _ {1 3} \right| _ {\text { at   C }} = \left. \tilde {\varepsilon} _ {1 3} ^ {\mathrm{DI}} \right| _ {\text { at   C }} \tag {6}
+$$
+
+$$
+\tilde {\varepsilon} _ {2 3} \left| _ {\text {at D}} = \tilde {\varepsilon} _ {2 3} ^ {\mathrm{DI}} \right| _ {\text {at D}} \quad \tilde {\varepsilon} _ {2 3} \left| _ {\text {at B}} = \tilde {\varepsilon} _ {2 3} ^ {\mathrm{DI}} \right| _ {\text {at B}}
+$$
+
+Hence, the complete element stiffness matrix is calculated using the functional:
+
+$$
+\Pi^ {*} = \frac {1}{2} \int_ {V} \tilde {\tau} ^ {i j} \tilde {\varepsilon} _ {i j} \mathrm{d} V - \mathcal {W} \tag {7}
+$$
+
+<!-- source-page: 3 -->
+
+![](images/page-003_f95c601761b2d3e08c15c9560b9b44d0e52d2e50af8c3719ef6481f69875f563.jpg)
+
+<details>
+<summary>text_image</summary>
+
+r2
+r3
+g2
+g3
+r1
+e3
+e2
+e1
+g1
+e3 = g3 / |g3|; e1 = g2 × e3 / |g2 × e3|; e2 = e3 × e1
+</details>
+
+Figure 3 Local Cartesian coordinate system used
+
+with stress and strain components in convected coordinates and (1) and (2) to evaluate the strain components $\tilde{\varepsilon}_{11}$ , $\tilde{\varepsilon}_{22}$ and $\tilde{\varepsilon}_{12}$ ; (3) to evaluate the strain components $\tilde{\varepsilon}_{13}$ , $\tilde{\varepsilon}_{23}$ ; and (6) to express the variables $\tilde{\varepsilon}_{13}^{\mathrm{A}}$ , $\tilde{\varepsilon}_{13}^{\mathrm{C}}$ , $\tilde{\varepsilon}_{23}^{\mathrm{D}}$ , and $\tilde{\varepsilon}_{23}^{\mathrm{B}}$ in terms of the nodal point displacements and rotations of (2).
+
+Considering the representation that we have chosen for the transverse shear strains, we can make the following three important observations:
+
+(1) The element is able to represent the six rigid body modes. The element contains the rigid body modes because zero strains are calculated in the formulation when the element nodal point displacements and rotations correspond to an element rigid body displacement. This can be verified by using (1) to (6) to evaluate the strains, but more easily we can use the fact that the 4-node shell element of reference 3 satisfies the rigid body mode criterion. Hence, for a rigid body displacement the $\tilde{\varepsilon}_{13}^{DI}$ and $\tilde{\varepsilon}_{23}^{DI}$ are zero, from which it follows that also the shear strains in (3) are zero, and the rigid body mode criterion is satisfied.
+
+(2) The element can approximate the Kirchhoff–Love hypothesis of negligible shear deformation effects and can be used for thin shells. Various demonstrative solutions are given in the fourth section.
+
+(3) Based on our studies the element does not contain any spurious zero energy modes (using a 'full' numerical integration). We reach this observation by studying the strains along the element sides. If the element were to contain a spurious zero energy mode, the strains along every side should vanish for a displacement pattern (to be identified) other than the displacements corresponding to a true rigid body mode. However, such displacement pattern could not be identified.
+
+Considering the practical use of the element the interpolation employed for the transverse shear strains shows that $\tilde{\varepsilon}_{13}$ is constant with $r_{1}$ and in general discontinuous at $r_{1}=\pm1$ (between elements), and similarly $\tilde{\varepsilon}_{23}$ is constant with $r_{2}$ and in general discontinuous at $r_{2}=\pm1$ . As a consequence, the accuracy with which transverse shear stresses are predicted depends to a significant degree on the mesh used and the geometric distortions of the elements. However, our experience is
+
+that the bending stress predictions are relatively little affected by element distortions (see examples).
+
+To employ (7), we also need to use the appropriate constitutive relations:
+
+$$
+\tilde {\tau} ^ {i j} = \tilde {C} ^ {i j k l} \tilde {\varepsilon} _ {k l} \tag {8}
+$$
+
+where $\tilde{C}^{ijkl}$ is the fourth-order contravariant constitutive tensor in the convected coordinates $r_{i}$ . The constitutive law is known in the local Cartesian system of orthonormal base vectors $\hat{e}_{i}, i=1,2,3$ , with the condition $\hat{\tau}^{33}$ equal to zero $^{2}$ , (see Figure 3). Denoting this constitutive tensor by $\hat{C}^{mnop}$ , the constitutive tensor for (8) is obtained using the transformation:
+
+$$
+\tilde {C} ^ {i j k l} = \left(\mathbf {g} ^ {i} \cdot \hat {\mathbf {e}} _ {m}\right) \left(\mathbf {g} ^ {j} \cdot \hat {\mathbf {e}} _ {n}\right) \left(\mathbf {g} ^ {k} \cdot \hat {\mathbf {e}} _ {0}\right) \left(\mathbf {g} ^ {l} \cdot \hat {\mathbf {e}} _ {p}\right) \hat {C} ^ {m n o p} \tag {9}
+$$
+
+where the $g^{i}$ are the contravariant base vectors of the convected coordinates $r_{i}$ . These vectors are calculated using the covariant base vectors $g_{i}$ , where:
+
+$$
+\mathbf {g} _ {i} = \frac {\partial^ {0} \mathbf {x}}{\partial r _ {i}} \tag {10}
+$$
+
+with $^{0}x$ from (1) and the following relations,
+
+$$
+g _ {i j} = \mathbf {g} _ {i} \cdot \mathbf {g} _ {j} \tag {11}
+$$
+
+and
+
+$$
+\mathbf {g} ^ {i} = g ^ {i j} \mathbf {g} _ {j} \tag {12}
+$$
+
+$$
+g ^ {i j} = \frac {D ^ {i j}}{| \mathbf {J} | ^ {2}}
+$$
+
+where $D^{ij}$ is the cofactor of the term $g_{ij}$ in the matrix of the metric tensor and $|J|$ is the determinant of the Jacobian matrix at the point considered.
+
+# TOTAL LAGRANGIAN FORMULATION
+
+The large displacement formulation of the shell element is based on the derivation given in ref. 2 (Section 6.3.5), and the concepts and interpolations presented in the previous section.
+
+The geometry of the element at any time t is defined as in (1) but using the nodal point coordinates, $^{t}x_{i}^{k}$ , and director vectors $^{t}V_{n}^{k}$ , at time $t,\dagger$
+
+$$
+{ } ^ { t } x _ { i } = h _ { k } { } ^ { t } x _ { i } ^ { k } + \frac { r _ { 3 } } { 2 } a _ { k } h _ { k } { } ^ { t } V _ { n i } ^ { k } \tag {13}
+$$
+
+where we imply summation over k. The displacements, $u_{i}$ , and incremental displacements, $u_{i}$ , of a particle of the element at time t are hence given by:
+
+$$
+{ } ^ { t } u _ { i } = h _ { k } { } ^ { t } u _ { i } ^ { k } + \frac { r _ { 3 } } { 2 } a _ { k } h _ { k } ( { } ^ { t } V _ { n i } ^ { k } - { } ^ { 0 } V _ { n i } ^ { k } ) \tag {14}
+$$
+
+$$
+u _ {i} = h _ {k} u _ {i} ^ {k} + \frac {r _ {3}}{2} a _ {k} h _ {k} \left(- ^ {t} V _ {2 i} ^ {k} \alpha_ {k} + ^ {t} V _ {1 i} ^ {k} \beta_ {k}\right)
+$$
+
+where the $^{t}u_{i}^{k}$ are the nodal point displacements at time $t$ , the $u_{i}^{k}$ are the incremental nodal point displacements from the configuration at time $t$ , and the variables $^{t}V_{2i}^{k}, ^{t}V_{1i}^{k}, \alpha_{k}$ and $\beta_{k}$ are defined as in (2) but referred to the configuration at time $t$ .
+
+This kinematic description implies the following hy-
+
+<!-- source-page: 4 -->
+
+potheses: the director vectors remain straight during the deformations; the 'thickness' of the element measured along the director vectors remains constant during the deformations; hence only small strain conditions are considered.
+
+Using the assumptions in (13) and (14) the geometric and material non-linear response is analysed using an incremental formulation $^{2}$ , in which the configuration is sought for time (load step) ' $t+\Delta t$ ', when the configuration for time t is known. The basis of this incremental formulation is the use of the virtual work principle applied to the configuration at time $t+\Delta t$ . In essence, two approaches can be employed leading to the updated Lagrangian and the total Lagrangian formulations. These approaches are, from a continuum mechanics point of view, equivalent, and in the following we develop the governing finite element relations for the total Lagrangian formulation.
+
+The principle of virtual work applied to the configuration at time $t + \Delta t$ is:
+
+$$
+\int_ {0 V} ^ {t + \Delta t} \tilde {S} _ {0} ^ {i j} \delta_ {0} ^ {t + \Delta t} \tilde {\varepsilon} _ {i j} ^ {0} \mathrm{d} V = ^ {t + \Delta t} \mathcal {R} \tag {15}
+$$
+
+where the $^{t+\Delta t}_{0}\tilde{S}^{ij}$ are the contravariant components of the second Piola-Kirchhoff stress tensor at time $t+\Delta t$ and referred to the configuration at time 0, and the $^{t+\Delta t}_{0}\tilde{E}_{ij}$ are the covariant components of the Green-Lagrange strain tensor at time $t+\Delta t$ and referred to time 0. Both sets of tensor components are measured in the convected coordinate system $r_{i}, i=1,2,3$ . The external virtual work is given by $^{t+\Delta t}\mathcal{R}$ and includes the work due to the applied surface tractions and body forces.
+
+For the incremental solution, the stresses and strains are decomposed into the known quantities, ${}_{0}^{t}\tilde{S}^{ij}$ and ${}_{0}^{t}\tilde{e}_{ij}$ , and unknown increments, ${}_{0}\tilde{S}^{ij}$ and ${}_{0}\tilde{e}_{ij}$ , so that
+
+$$
+{ } _ { 0 } ^ { t + \Delta t } \tilde { S } ^ { i j } = { } _ { 0 } ^ { t } \tilde { S } ^ { i j } + { } _ { 0 } \tilde { S } ^ { i j } \tag {16}
+$$
+
+$$
+{ } ^ { t + \Delta t } _ { 0 } \tilde { \varepsilon } _ { i j } = { } _ { 0 } ^ { t } \tilde { \varepsilon } _ { i j } + { } _ { 0 } \tilde { \varepsilon } _ { i j } \tag {17}
+$$
+
+In addition, the strain increment can be written as a linear part, $_{0}\tilde{e}_{ij}$ , and a non-linear part, $_{0}\tilde{\eta}_{ij}$ , hence
+
+$$
+_ 0 \tilde {\varepsilon} _ {i j} = _ {0} \tilde {e} _ {i j} + _ {0} \tilde {\eta} _ {i j} \tag {18}
+$$
+
+Substituting from (16) to (18) into (15) and using the linearized expressions $_{0}\bar{S}^{ij}=_{0}\bar{C}^{ijkl}_{0}\tilde{e}_{kl}$ and $\delta_{0}\tilde{\varepsilon}_{ij}=\delta_{0}\tilde{e}_{ij}$ we obtain the linearized equation of motion:
+
+$$
+\begin{array}{l} \int_ {0 _ {V}} ^ {0} \tilde {C} ^ {i j k l} _ {0} \tilde {e} _ {k l} \delta_ {0} \tilde {e} _ {i j} ^ {0} \mathrm{d} V + \int_ {0 _ {V}} ^ {t} \tilde {S} ^ {i j} \delta_ {0} \tilde {\eta} _ {i j} ^ {0} \mathrm{d} V \tag {19} \\ = ^ {t + \Delta t} \mathcal {R} - \int_ {0 V} ^ {t} \tilde {S} ^ {i j} \delta_ {0} \tilde {e} _ {i j} ^ {0} \mathrm{d} V \\ \end{array}
+$$
+
+This equation is the basic equilibrium relation employed to develop the governing finite element matrices. For the actual solution of problems it is frequently important to use equilibrium iterations, but the finite element matrices and vectors used in these iterations can be derived directly from the matrices obtained using (19) $^{2}$ . Note that $_{0}\tilde{C}^{ijkl}$ is now obtained using (9) with the condition $_{0}^{t}\hat{S}^{33}=0$ , which implies the more natural condition $^{t}\hat{\tau}^{33}=0$ only in the small strain case.
+
+The basic problem of the finite element discretization of (19) lies in expressing the strain terms of (19) in terms of the finite element interpolations. Using the definition of the Green-Lagrange strain components:
+
+$$
+{ } _ { 0 } ^ { t } \tilde { \varepsilon } _ { i j } = \frac { 1 } { 2 } ( { } ^ { t } \mathbf { g } _ { i } \cdot { } ^ { t } \mathbf { g } _ { j } - { } ^ { 0 } \mathbf { g } _ { i } \cdot { } ^ { 0 } \mathbf { g } _ { j } ) \tag {20}
+$$
+
+and the relations in (13) and (14) we obtain:
+
+$$
+{ } _ { 0 } \tilde { e } _ { i i } = h _ { k , i } { } ^ { t } \mathbf { g } _ { i } \cdot \mathbf { u } _ { k } + \frac { r _ { 3 } } { 2 } a _ { k } h _ { k , i } ( - \alpha _ { k } { } ^ { t } \mathbf { g } _ { i } \cdot { } ^ { t } \mathbf { V } _ { 2 } ^ { k } + \beta _ { k } { } ^ { t } \mathbf { g } _ { i } \cdot { } ^ { t } \mathbf { V } _ { 1 } ^ { k } ) \tag {21a}
+$$
+
+$$
+_ {0} \tilde {\eta} _ {i i} = \frac {1}{2} h _ {k, i} h _ {p, i} \mathbf {u} _ {k} \cdot \mathbf {u} _ {p} + \frac {r _ {3}}{2} h _ {k, i} h _ {p, i} a _ {p} \left(- \alpha_ {p} ^ {t} \mathbf {V} _ {2} ^ {p} \cdot \mathbf {u} _ {k} + \beta_ {p} ^ {t} \mathbf {V} _ {1} ^ {p} \cdot \mathbf {u} _ {k}\right) +
+$$
+
+$$
+\begin{array}{r l} \frac {(r _ {3}) ^ {2}}{8} h _ {k, i} h _ {p, i} a _ {k} a _ {p} (- \alpha_ {k} ^ {t} \mathbf {V} _ {2} ^ {k} + \beta_ {k} ^ {t} \mathbf {V} _ {1} ^ {k}) \cdot (- \alpha_ {p} ^ {t} \mathbf {V} _ {2} ^ {p} + \beta^ {p t} \mathbf {V} _ {1} ^ {p}) & (i = 1, 2) \\ & (2 1 b) \end{array}
+$$
+
+with the notation $h_{k,i} = \frac{\partial h_k}{\partial r_i}, \mathbf{u}_k^{\mathrm{T}} = [u_1^k \quad u_2^k \quad u_3^k]$ , and
+
+$$
+{ } _ { 0 } \tilde { e } _ { 1 2 } = \frac { 1 } { 2 } \left[ h _ { k , 2 } { } ^ { t } \mathbf { g } _ { 1 } \cdot \mathbf { u } _ { k } + h _ { k , 1 } { } ^ { t } \mathbf { g } _ { 2 } \cdot \mathbf { u } _ { k } + \right.
+$$
+
+$$
+\frac {r _ {3}}{2} h _ {k, 2} a _ {k} \left(- \alpha_ {k} ^ {t} \mathbf {V} _ {2} ^ {k} \cdot^ {t} \mathbf {g} _ {1} + \beta_ {k} ^ {t} \mathbf {V} _ {1} ^ {k} \cdot^ {t} \mathbf {g} _ {1}\right) +
+$$
+
+$$
+\frac {r _ {3}}{2} h _ {k, 1} a _ {k} (- \alpha_ {k} ^ {t} \mathbf {V} _ {2} ^ {k} \cdot^ {t} \mathbf {g} _ {2} + \beta_ {k} ^ {t} \mathbf {V} _ {1} ^ {k} \cdot^ {t} \mathbf {g} _ {2}) ] \tag {22a}
+$$
+
+$$
+_ 0 \tilde {\eta} _ {1 2} = \frac {1}{2} \left[ h _ {k, 1} h _ {p, 2} \mathbf {u} _ {k} \cdot \mathbf {u} _ {p} + \right.
+$$
+
+$$
+\frac {r _ {3}}{2} h _ {k, 1} h _ {p, 2} a _ {p} \left(- \alpha_ {p} ^ {\prime} \mathbf {V} _ {2} ^ {p} \cdot \mathbf {u} _ {k} + \beta_ {p} ^ {\prime} \mathbf {V} _ {1} ^ {p} \cdot \mathbf {u} _ {k}\right) +
+$$
+
+$$
+\frac {r _ {3}}{2} h _ {k, 1} h _ {p, 2} a _ {k} \left(- \alpha_ {k} ^ {t} \mathbf {V} _ {2} ^ {k} \cdot \mathbf {u} _ {p} + \beta_ {k} ^ {t} \mathbf {V} _ {1} ^ {k} \cdot \mathbf {u} _ {p}\right) +
+$$
+
+$$
+\frac {(r _ {3}) ^ {2}}{4} h _ {k, 1} h _ {p, 2} a _ {k} a _ {p} \left(- \alpha_ {k} ^ {t} \mathrm{V} _ {2} ^ {k} + \beta_ {k} ^ {t} \mathrm{V} _ {1} ^ {k}\right) \cdot \left(- \alpha_ {p} ^ {t} \mathrm{V} _ {2} ^ {p} + \beta_ {p} ^ {t} \mathrm{V} _ {1} ^ {p}\right) ] \tag {22b}
+$$
+
+Further, we obtain for the transverse shear strains, using (3) and (6):
+
+$$
+{ } _ { 0 } \tilde { e } _ { 1 3 } = \frac { 1 } { 8 } ( 1 + r _ { 2 } ) \left[ ^ { t } g _ { 3 i } ^ { \mathrm{A} } ( u _ { i } ^ { 1 } - u _ { i } ^ { 2 } ) + \right.
+$$
+
+$$
+\frac {1}{2} ^ {t} g _ {1 i} ^ {A} \left(- \alpha_ {1} a _ {1} ^ {t} V _ {2 i} ^ {1} + \beta_ {1} a _ {1} ^ {t} V _ {1 i} ^ {1} - \alpha_ {2} a _ {2} ^ {t} V _ {2 i} ^ {2} + \beta_ {2} a _ {2} ^ {t} V _ {1 i} ^ {2}\right) ] +
+$$
+
+$$
+\frac {1}{8} (1 - r _ {2}) \left[ ^ {t} g _ {3 i} ^ {C} \left(u _ {i} ^ {4} - u _ {i} ^ {3}\right) + \frac {1}{2} ^ {t} g _ {1 i} ^ {C} \left(- \alpha_ {4} a _ {4} ^ {t} V _ {2 i} ^ {4} + \right. \right.
+$$
+
+$$
+\left. \beta_ {4} a _ {4} ^ {t} V _ {1 i} ^ {4} - \alpha_ {3} a _ {3} ^ {t} V _ {2 i} ^ {3} + \beta_ {3} a _ {3} ^ {t} V _ {1 i} ^ {3}) \right] \tag {23a}
+$$
+
+$$
+{ } _ { 0 } \tilde { \eta } _ { 1 3 } = \frac { 1 } { 3 2 } ( 1 + r _ { 2 } ) \left[ ( - \alpha _ { 1 } a _ { 1 } { } ^ { t } V _ { 2 i } ^ { 1 } + \beta _ { 1 } a _ { 1 } { } ^ { t } V _ { 1 i } ^ { 1 } - \right.
+$$
+
+$$
+\left. \alpha_ {2} a _ {2} ^ {t} V _ {2 i} ^ {2} + \beta_ {2} a _ {2} ^ {t} V _ {1 i} ^ {2}) \left(u _ {i} ^ {1} - u _ {i} ^ {2}\right) \right] +
+$$
+
+$$
+\frac {1}{3 2} (1 - r _ {2}) \left[ \left(- \alpha_ {4} a _ {4} ^ {\prime} V _ {2 i} ^ {4} + \beta_ {4} a _ {4} ^ {\prime} V _ {1 i} ^ {4} - \right. \right.
+$$
+
+$$
+\left. \alpha_ {3} a _ {3} ^ {t} V _ {2 i} ^ {3} + \beta_ {3} a _ {3} ^ {t} V _ {1 i} ^ {3}) \left(u _ {i} ^ {4} - u _ {i} ^ {3}\right) \right] \tag {23b}
+$$
+
+and
+
+$$
+{ } _ { 0 } \tilde { e } _ { 2 3 } = \frac { 1 } { 8 } ( 1 + r _ { 1 } ) \left[ ^ { t } g _ { 3 i } ^ { \mathrm{D} } ( u _ { i } ^ { 1 } - u _ { i } ^ { 4 } ) + \right.
+$$
+
+$$
+\frac {1}{2} ^ {t} g _ {2 i} ^ {\mathrm{D}} \left(- \alpha_ {1} a _ {1} ^ {t} V _ {2 i} ^ {1} + \beta_ {1} a _ {1} ^ {t} V _ {1 i} ^ {1} - \alpha_ {4} a _ {4} ^ {t} V _ {2 i} ^ {4} + \beta_ {4} a _ {4} ^ {t} V _ {1 i} ^ {4}\right) ] +
+$$
+
+$$
+\frac {1}{8} (1 - r _ {1}) _ {L} ^ {t} g _ {3 i} ^ {B} (u _ {i} ^ {2} - u _ {i} ^ {3}) + \frac {1}{2} ^ {t} g _ {2 i} ^ {B} (- \alpha_ {2} a _ {2} ^ {t} V _ {2 i} ^ {2} +
+$$
+
+$$
+\left. \beta_ {2} a _ {2} ^ {t} V _ {1 i} ^ {2} - \alpha_ {3} a _ {3} ^ {t} V _ {2 i} ^ {3} + \beta_ {3} a _ {3} ^ {t} V _ {1 i} ^ {3}) \right] \tag {24a}
+$$
+
+<!-- source-page: 5 -->
+
+$$
+\begin{array}{l} _ 0 \tilde {\eta} _ {2 3} = \frac {1}{3 2} (1 + r _ {1}) \left[ \left(- \alpha_ {1} a _ {1} ^ {\prime} V _ {2 i} ^ {1} + \beta_ {1} a _ {1} ^ {\prime} V _ {1 i} ^ {1} - \right. \right. \\ \left. \alpha_ {4} a _ {4} ^ {t} V _ {2 i} ^ {4} + \beta_ {4} a _ {4} ^ {t} V _ {1 i} ^ {4}) \left(u _ {i} ^ {1} - u _ {i} ^ {4}\right) \right] + \\ \frac {1}{3 2} (1 - r _ {1}) \left[ \left(- \alpha_ {2} a _ {2} ^ {t} V _ {2 i} ^ {2} + \beta_ {2} a _ {2} ^ {t} V _ {1 i} ^ {2} - \right. \right. \\ \alpha_ {3} a _ {3} ^ {\prime} V _ {2 i} ^ {3} + \beta_ {3} a _ {3} ^ {\prime} V _ {1 i} ^ {3}) (u _ {i} ^ {2} - u _ {i} ^ {3}) ] \\ \end{array}
+$$
+
+(24b)
+
+Note that, since we assume the thickness of the shell to be constant, the strain $t_{0}\tilde{\varepsilon}_{33}$ through the element thickness is zero.
+
+The expressions in (21) to (24) are substituted into (19) which in the standard manner yields the linear strain incremental stiffness matrix ${}^{t}_{0}K_{L}$ , the non-linear strain (or geometric) incremental stiffness matrix ${}^{t}_{0}K_{NL}$ and the nodal point force vector ${}^{t}_{0}F$ in the finite element incremental equilibrium relations $^{2}$ ,
+
+$$
+(_ {0} ^ {t} \mathbf {K} _ {L} + _ {0} ^ {t} \mathbf {K} _ {N L}) \mathbf {u} = ^ {t + \Delta t} \mathbf {R} - _ {0} ^ {t} \mathbf {F} \tag {25}
+$$
+
+The element matrices in (25) correspond to five degrees of freedom per node (see Figure 1) but in some applications it is convenient to use instead of $\alpha_{k}$ and $\beta_{k}$ three rotations about the global coordinate axes (see examples). In this case, we simply transform the matrices of (25) in the standard manner $^{2}$ .
+
+# NUMERICAL TESTS AND EXAMPLE SOLUTIONS
+
+We have implemented our shell element in the ADINA computer program and have performed various numerical tests to study the predictive capabilities of the element. The following solutions were all obtained using $2 \times 2$ Gauss integration in the $r_{3}=0$ surface of the element, and 2 and 4 point Gauss integration in the $r_{3}$ direction, for elastic and elastoplastic analyses, respectively.
+
+# Some simple tests
+
+As a first step to test the element, the eigenvalues of the stiffness matrices of undistorted and distorted elements were calculated. In all cases, as expected, the element displayed the six rigid body modes and no spurious zero energy modes.
+
+Patch tests. For the patch test $^{2,18}$ the mesh shown in Figure 4a was used. In the first analysis (Figure 4b) the mesh was loaded with the constant moment indicated and a constant curvature (linear distribution of rotations) was obtained for both plate thicknesses in the two plate directions. The transverse displacements predicted by the model were, as expected, those of Kirchhoff–Love plate theory at nodes 7 and 8.
+
+In the second analysis (Figure 4c) the rotational degrees of freedom were deleted and the mesh was subjected to shear forces. As expected, for both plate thicknesses a linear distribution of transverse displacements was obtained.
+
+In the third analysis (Figure 4d) the mesh was subjected to an external twisting moment. In the thin plate analysis, constant curvatures were obtained in both plate directions and the transverse displacements agreed with the analytical thin plate theory solution. In the thick plate analysis, a slight non-symmetry in the displacement response (the third digit) was obtained due to the unsymmetric representation of the transverse shear deformations. This non-symmetry is not observed, if the shear deformations are suppressed (which corresponds to thin
+
+![](images/page-005_a48de6bf3f03750b20738b9903df25da0d15abf6d3d92458cdd4f606a0f75c3d.jpg)
+
+<details>
+<summary>text_image</summary>
+
+x₂
+1
+(Q,1Q)
+7(10,1Q)
+3(4,7.)
+5(8,7.)
+10.
+4(2,2)
+6
+(8,3)
+2
+(Q,Q)
+8(10,Q)
+x₁
+10.
+</details>
+
+(a) Patch test mesh
+
+![](images/page-005_00510176490cef82f49b70141ea71894cb95c13d476fc9a8c2bcced4d290419c.jpg)
+
+<details>
+<summary>text_image</summary>
+
+u_{1-2-3}=0
+β=0
+BENDING
+u_{1-3}=0
+β=0
+</details>
+
+(b) Constant curvature patch test
+
+![](images/page-005_578dbb8081c2c49793ec95f7bdcfd44b9148f8302223b63bb98f8236dc704aa6.jpg)
+
+<details>
+<summary>text_image</summary>
+
+u₃=0
+SHEAR
+u₁₋₂=0
+α=Ω=0
+u₃=0
+</details>
+
+(c) Constant shear patch test (zero rotations)
+
+![](images/page-005_1012548cf5134eca3c0e9354dd072c4ec5a4b225b6cc50fdc277d9688d9c026e.jpg)
+
+<details>
+<summary>text_image</summary>
+
+u₃=0
+TWISTING
+u₁₋₂ = 0
+u₃=0
+u₃=0
+</details>
+
+(d) Constant twist patch test   
+Figure 4 Patch tests. $E = 2.1 \times 10^{6}$ ; $v = 0.3$ ; thickness $= \begin{cases} 1.0 \\ 0.001 \end{cases}$
+
+<!-- source-page: 6 -->
+
+![](images/page-006_561f992b28f0957f27f23d84b3ef820569f70b8004e6f194f1f363d45439d344.jpg)
+
+<details>
+<summary>text_image</summary>
+
+x₃
+4
+3
+x₂
+M/2
+1.0
+1
+2
+M/2
+x₁
+L={100,10.}
+</details>
+
+(a) One element case. Node 1: $x = 0$ ; $u_{2-3} = 0$ . Node 4: $x = 0$ ; $u_{1-2-3} = 0$
+
+![](images/page-006_16f6a8ca84210938f4fae40ea7c42718158fa4014f8f772cadfa18f393160368.jpg)
+
+<details>
+<summary>text_image</summary>
+
+x₃
+L
+0.3L
+x₂
+x₁
+0.3L
+</details>
+
+(b) Two element case   
+Figure 5 Cantilever subjected to tip bending moment. $E=2.1 \times 10^{6}$ ; v=0.3; thickness=0.1.
+
+plate theory) by choosing a large value for the shear correction factor $k$ (or when using rectangular elements in the mesh) $^2$ .
+
+Finally, it should be noted that the patch test is of course passed for the three membrane stress states ( $\tau_{11}$ , $\tau_{22}$ and $\tau_{12}$ constants).
+
+Cantilever linear analyses. A cantilever of unit width, thickness 0.1 and lengths 10 and 100 was subjected to a tip bending moment. The structure was modelled using one single element and two distorted elements as shown in Figure 5. The results obtained in these analyses for the displacements and rotations at the cantilever tip and the stresses were those of Bernoulli beam theory.
+
+Next, the cantilever in Figure 6a was analysed for the transverse tip load shown. Using 4 equal size elements to idealize the cantilever, again good results were obtained when compared with beam theoretical results (see Figure 6b and Table 1).
+
+Finally, the elements modelling the cantilever were distorted as shown in Figure 6c for a thin and a thick cantilever. The results given in Figure 6d and Table 2 show that the transverse displacements and normal bending stresses are almost insensitive to the element distortions. However, the calculated transverse shear stresses (not shown in the Figure) are not accurate.
+
+Linear analyses of a simply-supported plate. A simply-supported plate was considered for a static and a frequency analysis using a consistent mass matrix. To model one quarter of the plate the $4 \times 4$ mesh of equal elements (Figure 7a) was used. Figure 7b and Tables 3 and 4 give a comparison of the numerically and analytically predicted results. The same plate was also analysed using the distorted element mesh also shown in Figure 7a and the results of Figure 7b and Tables 3 and 4 were obtained.
+
+$$
+E = 2. 1 \times 1 0 ^ {6}; v = 0. 0; \text { thickness } = 0. 1; P = 1. 0
+$$
+
+![](images/page-006_38ebcfb83a18e241db3810921bae82e46545bac6903cd665b2e6790bf82066be.jpg)
+
+<details>
+<summary>text_image</summary>
+
+x3
+elem. 1
+elem. N
+P/2
+x2
+α=0
+u1-2-3=0
+α=0
+u2-3=0
+P/2
+1.0
+x1
+10.
+</details>
+
+(a) Cantilever subjected to transverse tip load
+
+![](images/page-006_dec6db2921847506cee29537cb7e1fb8f97613d01edbef9a15d4bcd2bdcf06ef.jpg)
+
+<details>
+<summary>line</summary>
+| x₂   | τ₂₂     | τ₂₃     |
+| ---- | ------- | ------- |
+| 0    | 3464.10 | 10      |
+| L    | 0       | 10      |
+| x₂   | 0       | 10      |
+</details>
+
+(b) Solution using non-distorted elements
+
+![](images/page-006_572bd2c8413d9ea55265b5ffb1ebc5848a2ae8c33b16ef03b5392bb163b374c0.jpg)
+
+<details>
+<summary>flowchart</summary>
+
+```mermaid
+graph TD
+    A["0. 2.5 4.5 7.5 10. B"] -->|x₁| B["0. 2. 5. 7. 10. A"]
+    B --> C["x₂"]
+```
+</details>
+
+(c) Distorted mesh - plan view
+
+![](images/page-006_b868b07d372b77a5c662be3a2db817454282936b40b91ee4720442982a1fad6a.jpg)  
+(d) Solution using distorted mesh - two thicknesses and loads   
+Figure 6 Response of a cantilever subjected to transverse tip load, stresses shown are those at the Gauss integration stations $r_{3}=0.57735$ ; $\tau_{pp}$ , is the principal stress in the distorted mesh, and its direction was always less than 11 degrees from the $x_{2}$ axis. ——, Analytical (Bernoulli); ○, shell element (N=4)
+
+Table 1 Cantilever tip transverse displacement: non-distorted meshes of N elements 
+
+<table><tr><td>N</td><td> $u_{3\text{TIP}}^{\text{FEM}} \left/ \left( \frac{\text{PL}^3}{3\text{EI}} + \frac{\text{PL}}{\text{AG}} \right) \right.$ </td></tr><tr><td>1</td><td>0.750</td></tr><tr><td>4</td><td>0.984</td></tr></table>
+
+Table 2 Cantilever tip transverse displacements 
+
+<table><tr><td>Thickness</td><td> $\eta|_{point B}$ </td><td> $\eta|_{point A}$ </td></tr><tr><td>0.1</td><td>0.989</td><td>0.996</td></tr><tr><td>2.0</td><td>1.0013</td><td>0.995</td></tr></table>
+
+$\eta = (u_{3}$ distorted mesh)/(u3 non-distorted mesh)
+
+<!-- source-page: 7 -->
+
+![](images/page-007_fc638e677479023b3329468c72e192e8c07bc681f3891a39caebca185648552b.jpg)
+
+<details>
+<summary>text_image</summary>
+
+L/2
+12.50
+x₂
+x₁
+12.50
+L/2
+</details>
+
+(a) Non-distorted and distorted meshes ( $\Delta=2.50$ )
+
+![](images/page-007_26fe881157d94642d5935f90d7e3b59d6a7fe50f64a26e0ab1352a0b0c6aae9e.jpg)
+
+<details>
+<summary>line</summary>
+
+| x₁ | τ₂₂/qL² |
+|----|---------|
+| 0  | 20      |
+| 10 | 18      |
+| 20 | 16      |
+| 30 | 14      |
+| 40 | 12      |
+| 50 | 0       |
+</details>
+
+![](images/page-007_1df20afc31504b59377219a264749fb20ccc8fa41de4382d1727d6d7363d97fc.jpg)
+
+<details>
+<summary>line</summary>
+
+| x₁  | τ₁₁/qL² |
+| --- | ------- |
+| 0   | 20      |
+| 10  | 18      |
+| 20  | 15      |
+| 30  | 12      |
+| 40  | 8       |
+| 50  | 4       |
+</details>
+
+(b) Static response due to constant pressure loading, stresses are given along line $x_{2}=0$ , $x_{3}=0.028868$ . ——, analytical (Kirchhoff plate); ○, non-distorted mesh; □, distorted mesh.   
+Figure 7 Linear analysis of a simply-supported plate
+
+Table 3 Non-dimensional displacements at centre of simply-supported plate: distorted and non-distorted meshes 
+
+<table><tr><td>Model</td><td> $u_{3}^{\text{FEM}}/u_{3}^{\text{thin plate}}$ </td><td>at centre</td></tr><tr><td>non-dist.</td><td>0.995</td><td></td></tr><tr><td>dist.</td><td>0.992</td><td></td></tr></table>
+
+Table 4 Non-dimensional frequencies f (cycles/sec) for a simply-supported plate: distorted and non-distorted meshes 
+
+<table><tr><td>Mode shape</td><td> $f^{FEM}/f^{thin plate}$ </td></tr><tr><td>1-1</td><td>1.02</td></tr><tr><td>1-3</td><td>1.18</td></tr><tr><td>3-3</td><td>1.17</td></tr></table>
+
+Analysis of a rhombic cantilever. The rhombic cantilever shown in Figure 8, fixed at one side and subjected to constant pressure was analysed using a $4 \times 4$ element mesh. In Table 5, the results for the transverse displacements at six locations are compared against the solutions obtained using the DKT triangular element $^{6}$ , experimental measurements $^{1}$ and using the 16-node isoparametric element (with $4 \times 4 \times 2$ Gauss integration). In all cases a one step geometric non-linear analysis with equilibrium iterations was performed. Good correspondence between the experimental results and the solution obtained using our new 4-node element is observed.
+
+# Linear analysis of a cylindrical (Scordelis–Lo) shell
+
+The shell structure shown in Figure 9a has frequently been used to test the performance of shell elements $^{12}$ . Figure 9b shows the solutions obtained with our elements. In each of the solutions uniform meshes with equal sized elements were employed over one-quarter of the shell. Solutions obtained using the 3-node DKT triangular element $^{25}$ and the 16-node isoparametric element $^{25}$ are also shown.
+
+# Linear analysis of a pinched cylinder
+
+The pinched cylinder problem shown in Figure 10a was also frequently analysed to test shell elements. Figure 10b and Tables 6 and 7 show the convergence behaviour obtained with our new element, when comparing the finite element solutions $^{11,21}$ . Note that using the isoparametric shell element $^{3}$ also a fairly large number of degrees of freedom are required to predict the response of the cylinder accurately.
+
+# Large deflection analysis of a cantilever
+
+The cantilever shown in Figure 11a was analysed for its large displacement and large rotation response. This is a typical problem considered to test the geometric nonlinear behaviour of beam and shell elements $^{25}$ . Figure 11a also shows the models used in the analysis.
+
+The first two models are single element, cubic and parabolic isoparametric degenerate shell element models. Model I predicts the response of the cantilever very accurately, whereas model II yields an accurate response solution in linear analysis but locks once the element is curved in the non-linear response solution. This observation is in accordance with the results reported elsewhere $^{5}$ .
+
+The same nodal point layouts were next employed for models III and IV using our new 4-node shell element. Figures 11b–11d give the results obtained with these models. It is seen that model III yields an accurate large displacement response prediction, and even model IV yields quite accurate results up to about 60 degrees of rotation. The computer time required in these analyses were only little different using models I, III and IV.
+
+Another important result is shown in Table 8. As reported earlier $^{5}$ , the cubic shell element is sensitive to 'in-plane' distortions, and hence it is interesting to study the effect of using a distorted element mesh in the analysis of the cantilever (see Figures 12a and 12b). Table 8 summarizes the results obtained using the one cubic element and three 4-node elements with a nodal layout that corresponds to distorting the elements. It is seen that the predictive capability of our new 4-node element is considerably less sensitive to the element distortions.
+
+<!-- source-page: 8 -->
+
+![](images/page-008_5da32209f9cc0a6196f1164fc9ce754f4ae6c38f136e9ce5053c93e0be7c0c81.jpg)
+
+<details>
+<summary>text_image</summary>
+
+x₂
+3
+2
+1
+45°
+6
+5
+4
+12
+x₁
+12
+u₁₋₂₋₃ = α = β = 0
+</details>
+
+4 x 4 mesh - 4-node elements
+
+![](images/page-008_340afbf55b4f809ae3ac12c13d5aba569d93c5d818819279e228ce3c5951471c.jpg)
+
+<details>
+<summary>text_image</summary>
+
+4 x 4 mesh - DKT elements
+2 x
+</details>
+
+![](images/page-008_b658945d9e061f5d0f1bcb162247b3e5701759c6319100d3bed3030913ba93e2.jpg)
+
+<details>
+<summary>text_image</summary>
+
+2 x 2 mesh - 16-node elements
+(Int. 4x4x2)
+</details>
+
+Figure 8 Response of rhombic cantilever subjected to constant pressure. q=0.26066; $E=10.5\times10^{6}$ ; thickness=0.125; r=0.3   
+Table 5 
+
+<table><tr><td rowspan="2">Element</td><td rowspan="2">Mesh</td><td rowspan="2">CPU timeCPU time of DKT</td><td colspan="6">Deflection at location</td></tr><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td></tr><tr><td>DKT</td><td>4×4</td><td>1.00</td><td>0.293</td><td>0.196</td><td>0.114</td><td>0.118</td><td>0.055</td><td>0.024</td></tr><tr><td>4-node</td><td>4×4</td><td>approx. 2</td><td>0.272</td><td>0.183</td><td>0.106</td><td>0.102</td><td>0.046</td><td>0.019</td></tr><tr><td>16-node</td><td>2×2</td><td>approx. 6 $\frac{1}{2}$ </td><td>0.266</td><td>0.182</td><td>0.110</td><td>0.105</td><td>0.048</td><td>0.019</td></tr><tr><td>Experimental $^1$ </td><td></td><td></td><td>0.297</td><td>0.204</td><td>0.121</td><td>0.129</td><td>0.056</td><td>0.022</td></tr></table>
+
+![](images/page-008_e1cf53288253eab932778ca78bfedae1ad8dc7144444b1e7b165c443e4bf982d.jpg)
+
+<details>
+<summary>text_image</summary>
+
+diaphragm
+φ
+R
+A
+D
+B
+C
+L
+y
+z
+</details>
+
+(a) Cylindrical shell
+
+![](images/page-008_18f29259871d03f105eb75c2aa4c103e6d193978c0ab18cd8c222680ec1d647e.jpg)
+
+<details>
+<summary>line</summary>
+
+| Number of d.o.f. | w_B  | Grid Size |
+| ---------------- | ---- | --------- |
+| 2 x 1            | 3.45 | (2 x 1)   |
+| 5 x 5            | 3.45 | (5 x 5)   |
+| 8 x 8            | 3.50 | (8 x 8)   |
+| 12 x 12          | 3.55 | (12 x 12) |
+</details>
+
+(b) Convergence of displacement at point B   
+Figure 9 Linear analysis of a cylinder shell subjected to dead weight. The $2 \times 1$ result refers to the solution obtained with two 16-node shell elements spanning from C to B. The $16 \times 16$ result refers to the use of 512 equal triangular DKT elements. R=300; L=600; $\phi=40^{\circ}$ ; thickness=3.0; $E=3 \times 10^{6}$ ; v=0.0; specific weight=0.208333, ——, reference solutions; ●—●, present study; □, 16-node element (Int. $4 \times 4 \times 2$ ); ∇, DKT element
+
+Geometric non-linear response of a shallow spherical shell
+
+Figure 13a shows the spherical shell that was also analysed $^{3}$ with one cubic shell element, modelling one-quarter of the shell. To test our new 4-node shell element, the same nodal point layout was used $^{3}$ , giving a mesh of nine elements. Figure 13b shows the response calculated, including the post-buckling response (not reported in ref. 3) with the automatic load stepping algorithm $^{4}$ . Good correspondence with the analytical solution of Leicester $^{20}$ and the solution of Horrigmoe $^{16}$ was obtained. The solution with the 16-node element was almost twice as expensive as the 4-node element solution (using in both cases the same parameters for the automatic step-by-step solution algorithm).
+
+Linear buckling analysis and large deflection response of a simply-supported stiffened plate
+
+The stiffened plate shown in Figure 14a was analysed for its buckling reresponse. Since we expect the buckling mode to be symmetric $^{26}$ only one-quarter of the plate is modelled using symmetry boundary conditions. The model consists of nine 4-node shell elements and three 2-node isoparametric beam elements. At the nodes where a shell element connects to a beam element, three rotational degrees of freedom aligned with the global axes are considered for the shell element. In order to avoid locking of the isoparametric beam elements, one point Gauss integration along the beam axes was used. This does not introduce spurious zero energy modes in the model although the bending stiffness of the beam is underestimated.
+
+The linearized buckling problem was solved as described in reference 4(37) and we obtained:
+
+$$
+\frac {\sigma_ {\mathrm{cr}} (\text { finite   element   solution })}{\sigma_ {\mathrm{cr}} (\text { analytical   solution })} = 1. 0 2
+$$
+
+<!-- source-page: 9 -->
+
+![](images/page-009_caf3c4b08aca827d2c811c83e3da163e5ea94265b15cea98c674f800ed5888ca.jpg)
+
+<details>
+<summary>text_image</summary>
+
+L/2
+P
+L/2
+D
+C
+R
+A
+B
+end
+diaphragm
+end
+diaphragm
+P
+</details>
+
+(a) Pinched cylinder. $R / t = 100, L / R = 2$
+
+![](images/page-009_8cf79691768477d08f742f3a168d99cbba823b5ec17c33c1039cfaa10981a892.jpg)
+
+<details>
+<summary>line</summary>
+
+| Time Point | Etw/P (Top) | Etw/P (Bottom) | Etu/P (Top) | Etu/P (Bottom) |
+| ---------- | ----------- | -------------- | ----------- | -------------- |
+| D          | 0           | 0              | 0           | 0              |
+| C          | -50         | -150           | 0           | 0              |
+| A          | -100        | -150           | 0           | 0              |
+| C          | -150        | -150           | 0           | 0              |
+</details>
+
+(b) Displacements: —, analytical solution; +, present study (20×20 mesh).   
+Figure 10 Linear analysis of a pinched cylinder; u=axial displacement, w=radial displacement
+
+Table 6 Convergence study for 4-node element: pinched cylinder 
+
+<table><tr><td>Mesh for 1/8th of shell</td><td>Number of d.o.f.</td><td> $\hat{w}_{C}^{FEM}/\hat{w}_{C}^{analyt}$ </td></tr><tr><td>5×5</td><td>130</td><td>0.51</td></tr><tr><td>10×10</td><td>510</td><td>0.83</td></tr><tr><td>20×20</td><td>2020</td><td>0.96</td></tr></table>
+
+$\hat{w}_{C}$ (series solution) = -164.24 by Lindberg et al. $\hat{w}_{C} = \frac{w_{C}Et}{P}$
+
+Table 7 Comparison between displacements for 4-node and 16-node elements: pinched cylinder 
+
+<table><tr><td>Element</td><td>Mesh for  $\frac{1}{8}$ th of shell</td><td>Number of d.o.f.</td><td> $\hat{w}_{C}^{FEM}/\hat{w}_{C}^{analyt}$ </td></tr><tr><td>4-node</td><td>20×20</td><td>2020</td><td>0.96</td></tr><tr><td>16-node</td><td>10×10</td><td>4530</td><td>0.98</td></tr></table>
+
+Next, an initial imperfection with the shape of the first buckling mode and a maximum amplitude of 1/5 of the plate thickness was introduced. Figure 14b shows the large deflection response of this model as calculated using the automatic load stepping scheme of reference 4 with a tight energy convergence tolerance.
+
+# Analysis of elastoplastic response of a circular plate
+
+The thin circular plate shown in Figure 15a was analysed for its elastoplastic response, when subjected to a concentrated load at its centre. The plate is simply-supported with its edges restrained from moving in its plane.
+
+In a first solution, the plate model shown in Figure 15a was used to analyse the plate assuming small displacements (materially-non-linear-only conditions). Figure 15c shows that the theoretical collapse load is overestimated, but for the coarse mesh used, the predicted response is quite reasonable.
+
+In a second solution, large displacements and elastoplastic conditions were assumed and in this case the stiffening behaviour of the plate shown in Figure 15c was predicted. In order to have a comparison, also the model of five axisymmetric 8-node elements shown in Figure 15b was solved. Figure 15c shows that both models predict in essence the same response; however, in this case relatively little plasticity was developed for the range of displacements considered.
+
+# CONCLUSIONS
+
+A new four-node non-flat general non-linear shell element has been presented with the following important element properties: (1) the element is formulated using three-dimensional continuum mechanics theory; hence the use of the element is not restricted by application of a specific shell theory; (2) the element is reliable and has good predictive capability in the analysis of thick and thin shells; (3) the amount of computations required to calculate the element stiffness matrix are very closely those that are used in standard isoparametric formulations. The computer time used could be reduced considerably in elastic analysis by using analytical integration through the element thickness.
+
+In this paper we have presented the formulation and some applications of the element. The solution results obtained are most encouraging, but a formal mathematical convergence study of the element would be very valuable, and we are currently pursuing such research.
+
+Finally, it should be noted that the element presented here provides a very attractive basic formulation that could be extended to large strain analysis and analysis of composite shells. Also, the concepts applied here to formulate a 4-node element could equally well be employed in an effective manner to formulate higher-order shell elements.
+
+# ACKNOWLEDGEMENTS
+
+We are grateful for the financial support by the U.S. Army contract no. DAAK11-82-K-0005 and the ADINA users group for this work.
+
+Note added in proof. — We have just learned — and regret not to have known of it earlier — that R. H. MacNeal [J. Nucl. Eng. Design, 70, 3–12 (1982)] proposed a plate element for linear analysis that is very close to the element presented above.
+
+<!-- source-page: 10 -->
+
+![](images/page-010_1a4e5447eff6132d258a7e2b08738cb779d2a112055027502b4da88578c508e0.jpg)
+
+<details>
+<summary>text_image</summary>
+
+z
+b
+y
+u
+φ
+w
+M
+x
+L
+</details>
+
+![](images/page-010_2fca9c66a0ea26af571892007ae9ad3e046dc7a6fe618069b5b1cf18dfffd4d7.jpg)
+
+<details>
+<summary>text_image</summary>
+
+Int 4x2x2
+I
+Int 3x2x2
+II
+III
+IV
+</details>
+
+(a) Finite element models: $b = 1.0$ ; $t = 1.0$ ; $L = 12.0$ ; $E = 1800$ ; $v = 0.0$
+
+![](images/page-010_a9a3dc752fe05a0fe3390b5c9d12147c22e06c9b8be587266fdf0659be489412.jpg)
+
+<details>
+<summary>line</summary>
+
+| η = ML / 2π EI | u/L    | w/L    | φ/2π   |
+| -------------- | ------ | ------ | ------ |
+| 0.0            | 0.0000 | 0.0000 | 0.0000 |
+| 0.05           | 0.0500 | 0.1000 | 0.0250 |
+| 0.10           | 0.1000 | 0.2000 | 0.0500 |
+| 0.15           | 0.1500 | 0.3000 | 0.0750 |
+| 0.20           | 0.2000 | 0.4000 | 0.1000 |
+| 0.25           | 0.2500 | 0.5000 | 0.1250 |
+| 0.30           | 0.3000 | 0.6000 | 0.1500 |
+</details>
+
+(c) Response of model III
+
+![](images/page-010_ac31feb014ad68fd431cdc04e17196a071969d0a0ad53fb93a246a6fd68c1b00.jpg)
+
+<details>
+<summary>line</summary>
+
+| η = ML / 2πEI | u/L    | w/L    | φ/2π   |
+| ------------- | ------ | ------ | ------ |
+| 0.00          | 0.0000 | 0.0000 | 0.0000 |
+| 0.05          | 0.0500 | 0.1000 | 0.0250 |
+| 0.10          | 0.1000 | 0.2000 | 0.0500 |
+| 0.15          | 0.1500 | 0.3000 | 0.0750 |
+| 0.20          | 0.2000 | 0.4000 | 0.1000 |
+| 0.25          | 0.2500 | 0.5000 | 0.1250 |
+| 0.30          | 0.3000 | 0.6000 | 0.1500 |
+</details>
+
+(b) Response of model I
+
+![](images/page-010_f956249974be0a7100fffa5b018c13399784ee4d88f2f9c71e73ed966eb2ddf5.jpg)
+
+<details>
+<summary>line</summary>
+
+| η = ML/2πEI | u/L    | w/L    | φ/2π   |
+| ----------- | ------ | ------ | ------ |
+| 0.0         | 0.0000 | 0.0000 | 0.0000 |
+| 0.05        | 0.0500 | 0.1000 | 0.0200 |
+| 0.10        | 0.1000 | 0.2000 | 0.0500 |
+| 0.15        | 0.1500 | 0.3000 | 0.1000 |
+| 0.20        | 0.2000 | 0.4000 | 0.1500 |
+| 0.25        | 0.2500 | 0.5000 | 0.2000 |
+| 0.30        | 0.3000 | 0.6000 | 0.2500 |
+</details>
+
+(d) Response of model IV   
+Figure 11 Large deflection analysis of a cantilever using non-distorted elements. —, Analytical solution, ●, □, ▽, respective model response
+
+# REFERENCES
+
+1 Adini, A. Analysis of shell structures by the finite element method, PhD Dissertation, Department of Civil Engineering, University of California, Berkeley (1961)   
+2 Bathe, K. J. Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, New Jersey (1982)
+
+3 Bathe, K. J. and Bolourchi, S. A geometric and material nonlinear plate and shell element, J. Comput. Struct., 11, 23–48 (1979)   
+4 Bathe, K. J. and Dvorkin, E. N. On the automatic solution of nonlinear finite element equations, J. Comput. Struct. 17, (5–6), 871–879 (1983)   
+5 Bathe, K. J., Dvorkin, E. N. and Ho, L. W. Our discrete-Kirchhoff and isoparametric shell elements for nonlinear analysis – an assessment, J. Comput. Struct., 16, (1–4), 89–98 (1983)

docs/reference-papers/MITC4/AContinuumMechanicsBasedFourNodeShell/AContinuumMechanicsBasedFourNodeShell_002.md

@@ -0,0 +1,173 @@
+<!-- source-page: 11 -->
+
+![](images/page-011_ce5ce4625df64c46433bc92128a90eb39be61afbd4c2315e7e0c0071db43588a.jpg)
+
+<details>
+<summary>text_image</summary>
+
+3.
+Int 4x2x2
+</details>
+
+(a)   
+Model I - distorted
+
+![](images/page-011_039915932f73557d586a445907a46b35c323592070cc7fd250afef7c523be1ae.jpg)
+
+<details>
+<summary>text_image</summary>
+
+4.
+4.
+</details>
+
+(b)   
+Model III - distorted   
+Figure 12: Large deflection analysis of a cantilever using distorted elements
+
+Table 8 Results for large deflection analysis of a cantilever using distorted elements 
+
+<table><tr><td rowspan="2"></td><td colspan="3">Model I (distorted)</td><td colspan="3">Model III (distorted)</td></tr><tr><td>step 2</td><td>step 5</td><td>step 8</td><td>step 2</td><td>step 5</td><td>step 8</td></tr><tr><td> $\phi^{FEM}/\phi^{analyt}$ </td><td>0.13</td><td>0.13</td><td>0.13</td><td>0.95</td><td>0.84</td><td>0.76</td></tr><tr><td> $u^{FEM}/u^{analyt.}$ </td><td>0.01</td><td>0.01</td><td>0.01</td><td>0.89</td><td>0.68</td><td>0.56</td></tr><tr><td> $w^{FEM}/w^{analyt}$ </td><td>0.10</td><td>0.11</td><td>0.12</td><td>0.95</td><td>0.86</td><td>0.81</td></tr><tr><td> $\phi^{analyt}$ </td><td>18°</td><td>45°</td><td>72°</td><td>18°</td><td>45°</td><td>72°</td></tr></table>
+
+![](images/page-011_23b0df71e88de62769bd055734ee603af4fcfa7adf7da03a944a9206496022b7.jpg)
+
+<details>
+<summary>text_image</summary>
+
+P
+2a
+h
+2a
+R1
+R2
+</details>
+
+(a) Spherical shell
+
+![](images/page-011_6d1d03aec07b27283cc63c39e2ea41ab7c89aa78366687854f02d2fe26fcfd54.jpg)
+
+<details>
+<summary>line</summary>
+
+| Central deflection, Wc | Central load, (P/1000) |
+| ---------------------- | ---------------------- |
+| 0                      | 0                      |
+| 50                     | 30                     |
+| 100                    | 45                     |
+| 150                    | 50                     |
+| 200                    | 40                     |
+| 250                    | 35                     |
+| 300                    | 55                     |
+</details>
+
+(b) Non-linear load displacement curve.   
+Figure 13 Geometric non-linear response of a spherical shell. O, Horrigmoe; —, Leicester; ●, nine 4-node elements; □, one 16-node element Int 4×4×2
+
+![](images/page-011_c2174153f8463396ae83e28f9b093efd21de5102a9dd440d8d175f192ab5eff0.jpg)
+
+<details>
+<summary>text_image</summary>
+
+ε
+ε
+102.
+54.
+0.54
+0.5
+4
+</details>
+
+(a) Stiffened plate
+
+![](images/page-011_cf304ccd3c6278299800e4191548a141c23c268e4c96d4d53b4accd146b583fb.jpg)
+
+<details>
+<summary>line</summary>
+
+| Vertical displac. of center | τ/τ_CR |
+| --------------------------- | ------ |
+| 0.004                       | 0.95   |
+| 0.008                       | 1.00   |
+| 0.012                       | 1.00   |
+| 0.016                       | 1.00   |
+| 0.020                       | 1.00   |
+</details>
+
+(b) Large deflection response   
+Figure 14 Non-linear response of a stiffened plate. $E=2.1\times10^{6}$ ; v=0.3
+
+6 Bathe, K. J. and Ho, L. W. A simple and effective element for analysis of general shell structures, J. Comput. Struct., 13, 673–682 (1980)   
+7 Bathe, K. J. and Hô, L. W. Some results in the analysis of thin shell structures, Nonlinear Finite Element Analysis in Structural Mechanics, (Ed. W. Wunderlich et al.), Springer-Verlag, Berlin (1981)   
+8 Batoz, J. L., Bathe, K. J. and Ho, L. W. A study of three-node triangular plate bending elements, Int. J, Num. Meth. Eng., 15, 1771–1812 (1980)   
+9 Batoz, J. L. and Ben Tahar, M. Evaluation of a new quadrilateral plate bending element, Int. J. Num. Meth. Eng., 18, 1655–1677 (1982)   
+10 Bercovier, M., Hasbani, Y., Gilon, Y., and Bathe, K., J., On a finite element procedure for nonlinear incompressible elasticity, Hybrid and Mixed Finite Element Methods, (Ed, S. M. Atluri et al.), John Wiley, New York (1983)   
+11 Flügge, W. Stresses in Shells, 2nd edn, Springer-Verlag, Berlin (1973)   
+12 Forsberg, K. and Hartung, R. An evaluation of finite difference and finite element techniques for analysis of general shells, Symp. High Speed Computing of Elastic Structures, IUTAM, Liège (1970)   
+13 Fung, Y. C. Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, New Jersey (1965)   
+14 Gallagher, R. H. Problems and progress in thin shell finite element analysis, Finite Elements in Thin Shells and Curved Members, (Ed. D. G. Ashwell and R. H. Gallagher), John Wiley, New York (1976)   
+15 Green, A. E. and Zerna, W. Theoretical Elasticity, 2nd edn, Oxford University Press (1968)   
+16 Horrigmoe, G. Finite element instability analysis of free-form shells, Report 77-2, Division of Structural Mechanics, The Norwegian Institute of Technology, University of Trondheim, Norway (1977)   
+17 Hughes, T. J. R. and Liu, W. K. Nonlinear finite element analysis of shells: Part I, Three-dimensional shells, J. Comput. Meth. Appl. Mech. Eng., 26, 331–362 (1981)
+
+<!-- source-page: 12 -->
+
+![](images/page-012_4cb42a5782816bc4cedbd4393a3f6987776bde88664fcddcdc6d74f32812e067.jpg)
+
+<details>
+<summary>text_image</summary>
+
+hinged
+immovable edge
+</details>
+
+(a) 4-node shell model
+
+![](images/page-012_7914d5c2d5d8cf5d37f7c6a7e743ff25301e4b7687afbf07d510d3d86e254568.jpg)
+
+<details>
+<summary>text_image</summary>
+
+t
+R
+</details>
+
+(b) Axisymmetric model
+
+18 Irons, B. M. and Razzaque, A. Experience with the patch test for convergence of finite elements. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, (Ed. A. K. Aziz), Academic Press, New York (1972)   
+19 Kråkeland, B. Nonlinear analysis of shells using degenerate isoparametric elements, Finite Elements in Nonlinear Mechanics, Vol. 1, (Ed. P. G. Bergan et al.), Tapir Publishers (Norwegian Institute of Technology, Trondheim, Norway) (1978)   
+20 Leicester, R. H. Finite deformations of shallow shells, Proc. Am. Soc. Civil Eng., 94, (EM6), 1409–1423 (1968)   
+21 Lindberg, G. M., Olson, M. D. and Cowper, G. R. New developments in the finite element analysis of shells, Q. Bull. Div. Mech. Eng. and the National Aeronautical Establishment, National Research Council of Canada, Vol. 4 (1969)   
+22 MacNeal, R. H. A simple quadrilateral shell element, J. Comput. Struct. 8, 175–183 (1978)   
+23 Noor, A. K. and Peters, J. M. Mixed models and reduced/selec-
+
+![](images/page-012_3a106631a364ac4a83c9b22dfb1ea729baf8c2940fd538340267a37203fe1421.jpg)
+
+<details>
+<summary>line</summary>
+
+| Vertical displac. of center | P     |
+| --------------------------- | ----- |
+| 0                           | 0     |
+| 1                           | 1500  |
+| 2                           | 2500  |
+| 3                           | 1000  |
+| 4                           | 1200  |
+| 5                           | 1300  |
+| 6                           | 1400  |
+| 7                           | 1500  |
+| 8                           | 1600  |
+| 9                           | 1700  |
+| 10                          | 1700  |
+</details>
+
+(c) Elastoplastic load-displacement curve   
+Figure 15 Response of elastic-perfectly plastic circular plate subjected to a concentrated load, P, at its centre. TLF abbreviates use of total Lagrangian formulation and MNO abbreviates use of materially non-linear-only formulation. R=100, t=1; $E=2.1\times10^{6}$ ; $E_{T}=0.0$ ; $\nu=0.3$ ; $\sigma_{\nu}=1000$ . Circular plate response; —, axisymmetric model;   
+●, 4-node shell model
+
+tive integration displacement models for nonlinear analysis of curved beams, Int. J. Num. Meth. Eng., 17, 615–631 (1981)   
+24 Ramm, E. and Sattele, J. M. Elasto-plastic large deformation shell analysis using degenerated elements, Nonlinear Finite Element Analysis of Plates and Shells, (Ed. T. J. R. Hughes), AMD-Vol. 48, Am. Soc. Mech. Eng., New York (1981)   
+25 Report AE 83-5, ADINA System Verification Manual, ADINA Engineering, Västerås, Sweden and Watertown, Mass. (1983)   
+26 Timoshenko, S. P. and Gere, J. M. Theory of Elastic Stability, 2nd edn, McGraw-Hill, New York (1961)   
+27 Washizu, K. Variational Methods in Elasticity and Plasticity, Pergamon Press, Oxford and New York (1968)   
+28 Wempner, G., Talaslidis, D. and Hwang, C.-M. A simple and efficient approximation of shells via finite quadrilateral elements, J. Appl. Mech., 49, 115–120 (1982)   
+29 Zienkiewicz, O. C. The Finite Element Method, McGraw-Hill, New York (1977)