add reference for S4R element

.agents/skills/harness/SKILL.md

@@ -0,0 +1,172 @@
+---
+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.
+
+## 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.
+
+### 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 해당 step을 갱신한다.
+   - 성공: `status`를 `completed`로 바꾸고 한 줄 `summary` 기록
+   - 수정 3회 후 실패: `status`를 `error`로 바꾸고 `error_message` 기록
+   - 사용자 개입 필요: `status`를 `blocked`로 바꾸고 `blocked_reason` 기록 후 중단
+
+## 금지사항
+
+- 이 step의 범위 밖 기능을 추가하지 마라. 이유: step의 독립성을 깨뜨린다.
+- 기존 테스트를 깨뜨리지 마라. 이유: 이전 동작을 회귀시킨다.
+````
+
+## E. 실행
+
+```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/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

@@ -43,7 +43,9 @@ Execution contract:
 - 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.
 - 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 +71,19 @@ 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

@@ -55,11 +55,11 @@ Required Implementation Plan sections:
 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.
 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.
 

.codex/agents/release-agent.toml

@@ -62,7 +62,7 @@ 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.

.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

@@ -26,10 +26,12 @@ Read these first:
 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`.
+6. VERIFY: run the targeted command, then the full MSVC build/test commands resolved from `.harness/config.json` or the Harness defaults.
 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.
+8. 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.
+9. Let Stop perform the final whole-project MSVC build/test before the Step ends.
+10. For failure triage, classify as `configure | compile | link | test | reference-comparison | harness | environment | upstream-contract`.
+11. Fix implementation-owned failures only and keep changes traceable to the implementation plan.
 
 ## Output Contract
 
@@ -43,17 +45,19 @@ 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
@@ -73,6 +77,7 @@ ctest --test-dir build/msvc-debug --output-on-failure -C Debug
 - 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/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 +10,86 @@
 - 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.
+- 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.
 - 문서와 구현은 full Abaqus compatibility를 주장하지 않는다. 기능별로 승인된 Abaqus keyword subset만 지원한다.
 - 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 artifact의 정확한 경로와 파일명은 기능별 reference model contract를 따른다. 신규 모델은 `reference/<model-id>/<model-id>_*.csv` canonical 이름을 사용한다.
+- 승인된 B33 baseline은 예외적으로 `reference/cantilever beam/`의 기존 space-containing 파일명을 read-only legacy alias로 사용한다.
 - 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: 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.
+
+## 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 +102,11 @@
   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 +122,39 @@
 | 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
+## 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 +39,26 @@ 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.
+**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 +77,107 @@ 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.
+**결정**: Agent는 Abaqus, Nastran 또는 reference solver를 직접 실행하지 않는다. reference artifact 생성, 수정, 복원은 명시 승인된 phase에서만 수행한다. 신규 bundle의 provenance는 `metadata.json`에 기록한다. 승인된 `cantilever-beam-b33` legacy baseline은 source commit과 generator, units, coordinate system, schema, tolerance를 설계 및 Reference Model Contract가 대신 기록하므로 이 baseline에 한해서 `metadata.json`과 `README.md`가 N/A다.
 
 **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 준비가 느려질 수 있다. Legacy 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.

docs/ARCHITECTURE.md

@@ -9,206 +9,278 @@ FESA의 아키텍처 목표는 Abaqus `.inp` subset을 내부 semantic model로
 - 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
+  <model-id>/              # approved read-only Abaqus input/CSV bundle
+.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 +288,12 @@ 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
 ```
 
@@ -231,41 +305,54 @@ Schema requirements:
 - 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.
 - 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, invalid geometry/property | Domain record와 mapper, element kernel, DofManager scatter/pattern, SparseAssembler, ResultRecovery | rigid modes/rank/energy, patch·analytical test, rotated coordinates, reference/physics | 기존 TYPE을 비슷한 kernel에 alias, 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.

docs/HARNESS.md

@@ -0,0 +1,124 @@
+# 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
+```
+
+## 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 +1,607 @@
+# 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
+  --dangerously-bypass-hook-trust
+  --cd <repository-root>
+  -
+```
+
+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/PRD.md

@@ -15,41 +15,73 @@ 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 HDF5 row를 승인된 Abaqus reference CSV identity에 투영해 tolerance를 판정하고, 별도로 equilibrium과 물리적 타당성을 검토한다.
+
+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, units/coordinates/identity, 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, reference comparison과 physics sanity가 수치·물리 타당성을 각각 증명한다. Reference가 N/A이면 그 이유와 대체 evidence를 명시한다.
 
 ## 기능 요구조건
 | ID | 요구조건 | Acceptance Criteria | Verification Method |
@@ -58,38 +90,56 @@ 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 Abaqus reference CSV rows와 비교 가능한 deterministic row mapping을 제공해야 한다. | displacement와 reaction은 node identity, B33 section resultant는 정규화된 node station identity로 비교하고 stress reference comparison은 N/A로 기록한다. | 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-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 read-only baseline으로 유지해야 한다. | `reference/cantilever beam/` 파일을 rename, rewrite, 보정하지 않고 exact legacy path로 읽으며 B33 element type과 expected headers를 artifact check에서 확인한다. | 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.
 - 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.
+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: FESA `results.h5`의 displacement, reaction, section resultant rows가 승인된 B33 CSV와 documented identity 및 component-scale 혼합 tolerance 안에 있다. Beam stress comparison은 명시적 N/A다.
+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

@@ -12,6 +12,7 @@
 - Abaqus나 Nastran을 Agent가 직접 실행하지 않는다. `reference/<model-id>/`에 저장된 `model.inp`, `metadata.json`, Abaqus reference CSV files를 검증 기준으로 사용한다.
 - 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.
 
 ## 전체 Agent 구성
 
@@ -168,15 +169,20 @@ 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
@@ -301,7 +307,8 @@ flowchart TD
 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:
@@ -352,11 +359,12 @@ 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.
 

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
 
@@ -34,10 +35,10 @@ 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.
@@ -98,9 +99,17 @@ 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.
@@ -148,7 +157,8 @@ 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 +173,11 @@ 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 +1,10 @@
 # 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.
+
 ## 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/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
 
@@ -184,6 +184,6 @@ 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

@@ -15,7 +15,7 @@ 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.
 
 수행하지 않는다:
 - C++ 코드를 구현하지 않는다.
@@ -80,8 +80,8 @@ 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
 
@@ -107,11 +107,17 @@ 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

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. 이 legacy bundle에서
+`metadata.json`과 `README.md`는 N/A이고 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/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/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/reference-models/linear-static-3d-euler-beam-reference-models.md

@@ -0,0 +1,420 @@
+# 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.
+
+Only for this approved legacy bundle:
+
+- `metadata.json`: N/A
+- `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 jointly replace those missing files by recording 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. Their absence therefore does
+not change the legacy 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
+    <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. `metadata.json` and `README.md` are mandatory.
+A quantity CSV may be omitted only when the upstream acceptance contract explicitly records N/A
+and gives its verification replacement. Missing required files keep that model at
+`needs-reference-artifacts`.
+
+## Metadata JSON Contract
+
+`metadata.json` is N/A only for `cantilever-beam-b33`. Every later bundle shall include at least:
+
+```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.
+
+## 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;
+- legacy `metadata.json`, `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-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)