# MITC4 비선형 정적 해석 검증과 한계

본 문서는 당시 revision의 검증·판정 기록이다. 본문에 남긴 원본 보고서 이름과 SHA-256은
통합 전 자료의 식별자이며 정리된 현재 파일의 byte hash를 뜻하지 않는다. 원문은 Git
`858e87b`의 해당 기능 폴더에서 확인할 수 있다. 현재 진입점과 대응 기록은 [README](README.md)를 따른다.

아래 날짜·revision·명령·수치는 당시 실제 실행 기록이다. 문서 정리에서 solver를 다시 실행하지 않았다.
현재 계약은 [요구사항](requirements.md), [정식화](formulation.md), [I/O](io.md), [공통 tolerance](../TOLERANCE.md)를 따른다. [과거 release 판정](release.md)의 재검증 경계도 유지한다.

<a id="build-test"></a>

<a id="build-test--nonlinear-static-newton-raphson-build-and-test-report"></a>
## Nonlinear Static Newton-Raphson Build and Test Report

<a id="build-test--metadata"></a>
### Metadata

| key | value |
| --- | --- |
| feature_id | `nonlinear-static-newton-raphson` |
| owner_agent | `implementation-agent` |
| working directory | `C:\git\FESADev\.worktrees\nonlinear-static-newton-raphson` |
| configuration | `windows-msvc-ninja-debug`, x64 Debug |
| compiler | MSVC `cl.exe` from VS 18, toolset `14.51.36231` |
| generator | Ninja |
| dependency configuration | `FESA_GTEST_SOURCE_DIR=C:/git/googletest`; MKL `2026.1`; TBB `2023.1`; HDF5 `2.1.1` |
| final classification | none; all commands passed |

<a id="build-test--fresh-command-log"></a>
### Fresh command log

| stage | command | exit | duration | output tail |
| --- | --- | ---: | ---: | --- |
| configure | `cmake --preset windows-msvc-ninja-debug` | 0 | 1.066 s | `Configuring done`; `Generating done`; build files written to `.harness/build-ninja-msvc-debug` |
| build | `cmake --build --preset windows-msvc-ninja-debug` | 0 | 0.113 s | `ninja: no work to do.` |
| discovery | `ctest --preset windows-msvc-ninja-debug --show-only=json-v1` | 0 | 0.219 s | 302 tests discovered |
| focused control/log | `ctest --preset windows-msvc-ninja-debug -R "^(NonlinearConvergence|NewtonIterationLog)\." --output-on-failure` | 0 | 0.471 s | 14/14 passed |
| focused procedure/writer | `ctest --preset windows-msvc-ninja-debug -R "^(NonlinearStaticProcedure|NonlinearHdf5ResultsWriter)\." --output-on-failure` | 0 | 2.524 s | 7/7 passed |
| nonlinear reference | `ctest --preset windows-msvc-ninja-debug -R "^NonlinearStaticReference\." --output-on-failure` | 0 | 905.404 s | 9/9 passed |
| extended reference | `ctest --preset windows-msvc-ninja-debug -R "^(NonlinearStaticReference|ReferenceTolerance|Mitc4Reference)\." --output-on-failure` | 0 | 930.617 s | 9/9 matched tests passed |
| full CTest | `ctest --preset windows-msvc-ninja-debug --output-on-failure` | 0 | 956.498 s | 302/302 passed; integration 16, unit 256, reference 30 |

The full CTest output reported no failed-test inventory. The build emitted no compiler/linker
output beyond `ninja: no work to do.`; the build tree audit found no new `warning C####` or
`: warning:` record. The only diagnostic setup issue was that standalone HDF5 inspection tools
need Intel `libmmd.dll` on `PATH`; this did not affect the staged test executables, CMake build, or
CTest and is not a product failure.

<a id="build-test--results-and-handoff"></a>
### Results and handoff

The selected `.harness/config.json` preset was used throughout. All commands were run from the
repository root in an x64 VsDevCmd environment. The final status is
`pass-for-physics-evaluation`; no Harness Python command was required because this Step did not
change Python, hooks, or agent configuration.

This Step changed documentation and its own phase status only. It did not modify C++ production,
tests, CMake, Harness configuration, tolerance, reference artifacts, or output data. The immutable
reference artifact audit before and after comparison was identical; see `reference-comparison.md`.

<a id="reference-comparison"></a>

<a id="reference-comparison--nonlinear-static-newton-raphson-reference-comparison"></a>
## Nonlinear Static Newton-Raphson Reference Comparison

<a id="reference-comparison--verdict"></a>
### Verdict

`blocking-pass-with-review-only-findings`. FESA HDF5 is the authoritative solver output. The
Abaqus CSV files are read-only external comparison evidence; the observed agreement does not imply
Abaqus S4 internal formulation, integration, stabilization, or recovery equivalence.

Overall handoff status: `pass-for-physics-evaluation`. This handoff classification records that
all blocking comparisons passed; the detailed verdict above remains
`blocking-pass-with-review-only-findings` because the six local RF/RM findings are review-only.

The literal execution order was `ARTIFACT CHECK -> COMPARE -> CLASSIFY -> REPORT`.

The `COMPARE` commands were
`ctest --preset windows-msvc-ninja-debug -R "^NonlinearStaticReference\." --output-on-failure`
(exit 0, 905.404 s, 9/9 passed), followed by
`ctest --preset windows-msvc-ninja-debug -R "^(NonlinearStaticReference|ReferenceTolerance|Mitc4Reference)\." --output-on-failure`
(exit 0, 930.617 s, 9/9 matched tests passed). The fresh full CTest run then passed 302/302;
its command and output tail are recorded in `build-test.md`.

<a id="reference-comparison--artifact-check"></a>
### Artifact check

Every input, displacement CSV, reaction CSV, and stress-inventory CSV was readable, finite where
required, unique by declared source key, and identical before and after all copied-input executions.

| case / role | exact path | bytes | pre/post UTC mtime | SHA-256 |
| --- | --- | ---: | --- | --- |
| fine primary input | `reference/shellNL-meshfine/shellNL-meshfine.inp` | 56,516 | `2026-08-25T13:53:49.1919675Z` | `40DF1CE77311C8D799564A21A60F3BDEBB8148D52CAE22B7292FDFAD32018220` |
| fine U | `reference/shellNL-meshfine/shellNL-meshfine displacements.csv` | 111,184 | `2026-08-25T14:06:00.1262830Z` | `740819FF8AED0E279961581F7CDBFA12784CFBA3A488C35A652E80103F64433F` |
| fine local reaction | `reference/shellNL-meshfine/shellNL-meshfine reactions.csv` | 108,951 | `2026-08-25T14:05:06.2950127Z` | `AEB01C98C596792B0E5F2B86A81945CAB0BEB0C6969CFC6738C6F81DF1F94363` |
| fine stress inventory | `reference/shellNL-meshfine/shellNL-meshfine stresses.csv` | 1,036,869 | `2026-08-25T14:04:24.2027682Z` | `6D6213AB5DB9D6B1F5FBD641367D08BACC805967B6C5A95BCE0E1A5395377782` |
| coarse companion input | `reference/shellNL/shellNL.inp` | 4,778 | `2026-08-23T16:36:23.9302881Z` | `4BF3ECB0F7F1E8462C573E993DBC97AC5D920C91CF6F23AD4C6891D77FFBADA2` |
| coarse U | `reference/shellNL/shellNL displacements.csv` | 7,542 | `2026-08-23T16:36:23.9282815Z` | `4E0F99CA9372B1ADF7FAF102F43BC0B887DC743FDEDA378E4342D2CF8E0C0786` |
| coarse local reaction | `reference/shellNL/shellNL reactions.csv` | 7,443 | `2026-08-23T16:36:23.9292877Z` | `001CB1541A9E94424E5E650509D46BC8724970DF4DE47184D9DB09C7938AB069` |
| coarse stress inventory | `reference/shellNL/shellNL stresses.csv` | 54,720 | `2026-08-23T16:36:23.9302881Z` | `5500E5114B1C44887528E30CEC054A1EB0F68BE3F4B8CE81FA59FC74A881483F` |
| linear control input | `reference/shell/shell.inp` | 4,770 | `2026-08-23T16:36:23.9272805Z` | `4005851E1AB22FD3A16AC17A8D5DA3E051233F69F37419079F3553AD134ECFCF` |
| linear U | `reference/shell/shell displacements.csv` | 5,592 | `2026-08-23T16:36:23.9262810Z` | `C81D94E0B4A849F87AA0F79C83A79B94D5661AC79E44ED826919AB432C87746B` |
| linear reaction inventory | `reference/shell/shell reactions.csv` | 5,524 | `2026-08-23T16:36:23.9262810Z` | `0E34EEC27E700C3C0C744C1DAFD8A3B95EFEF34B8616FE96665876586FE82D41` |
| linear stress inventory | `reference/shell/shell stresses.csv` | 43,502 | `2026-08-23T16:36:23.9272805Z` | `2B75A5B0DEB045A283C9BB7E9B1153B79F7537FF487214BF4A23316B59B660A7` |

Fine and coarse required nonlinear CSV rows had exact `Frame=Increment     10: Step Time =    1.000`.
The HDF5 `/steps/Step-1/accepted_frames` table had exactly one factor-one row: frame 9, increment
10, load factor 1.0, two Newton iterations. Reference copies and generated artifacts were confined
to these build-local directories:

| case | copied input | generated results / log |
| --- | --- | --- |
| fine | `.harness/build-ninja-msvc-debug/reference/nonlinear-static-reference/shellNL-meshfine/shellnl-meshfine-s4-final-72767400538200-0/shellNL-meshfine.inp` | `.harness/build-ninja-msvc-debug/reference/nonlinear-static-reference/shellNL-meshfine/shellnl-meshfine-s4-final-72767400538200-0/shellNL-meshfine_results.h5`, SHA-256 `2E9817E173D73FD91C2D34864B69A1EC37483CB25951FB7CCE85895A6C87D2C6`; `.harness/build-ninja-msvc-debug/reference/nonlinear-static-reference/shellNL-meshfine/shellnl-meshfine-s4-final-72767400538200-0/shellNL-meshfine_log.txt`, SHA-256 `1DB6FE4AAA2F1443ACC7F9B3F919CC8DD873C90392121DAB6509F1693435DA27` |
| coarse | `.harness/build-ninja-msvc-debug/reference/nonlinear-static-reference/shellNL/shellnl-s4-final-73175241456500-1/shellNL.inp` | `.harness/build-ninja-msvc-debug/reference/nonlinear-static-reference/shellNL/shellnl-s4-final-73175241456500-1/shellNL_results.h5`, SHA-256 `130E2E7B73B022F216A7A34C88D58114A62595ADD556A0D202B8A7FAC7391F39`; `.harness/build-ninja-msvc-debug/reference/nonlinear-static-reference/shellNL/shellnl-s4-final-73175241456500-1/shellNL_log.txt`, SHA-256 `3D5C4F1B20384655F9012ADE842B99E3B06B3799FC9AB16DD6FD141E18B77906` |
| linear | `.harness/build-ninja-msvc-debug/reference/nonlinear-static-reference/shell/shell-s4-linear-limit-72742739390700-2/shell.inp` | `.harness/build-ninja-msvc-debug/reference/nonlinear-static-reference/shell/shell-s4-linear-limit-72742739390700-2/shell_results.h5`, SHA-256 `8AEE34D5BC80382D7E6DE85C51F0F8BCBF451CD5F5C7B8DDA6C585EB22B31763`; `.harness/build-ninja-msvc-debug/reference/nonlinear-static-reference/shell/shell-s4-linear-limit-72742739390700-2/shell_log.txt`, zero bytes, SHA-256 `E3B0C44298FC1C149AFBF4C8996FB92427AE41E4649B934CA495991B7852B855` |

<a id="reference-comparison--compare-and-classify"></a>
### Compare and classify

Rows were matched by `(case_id, accepted_state, canonical_instance_name, source_node_label,
component)`, never CSV order. Required HDF5 projections were factor-one
`/steps/Step-1/frames/9/nodal/displacement`, `generalized_internal_force`,
`generalized_external_force`, `generalized_residual`, `reaction`, `/model/nodal_constraint_mask`,
and `/global/equilibrium`; the linear control uses `/steps/Step-1/frames/0/nodal/displacement`.
All required source keys, components, uniqueness and finite checks passed before tolerance.

External families use `docs/TOLERANCE.md`: reference-only scale, near-zero band `0.01*S`, row
relative limit `0.05`, and family RMS limit `0.01`. `rows passed` is the deterministic per-row
decision count; U is blocking and UR is warning-only.

| family | disposition | rows passed | scale | max abs | max relative | relative RMS | result |
| --- | --- | ---: | ---: | ---: | ---: | ---: | --- |
| fine.translation | blocking | 2187/2187 | 2.57957054e-05 | 1.6193812501e-07 | 6.27771648e-03 | 2.27230258e-04 | pass |
| fine.rotation | warning-only | 2187/2187 | 6.58704994e-06 | 3.0109969916e-08 | 3.54510604e-02 | 4.68253850e-04 | pass |
| coarse.translation | blocking | 147/147 | 2.37408203e-05 | 1.9037855439e-07 | 8.57111694e-03 | 1.03327572e-03 | pass |
| coarse.rotation | warning-only | 147/147 | 7.60725743e-06 | 6.8828551252e-08 | 4.69071871e-02 | 2.97713732e-03 | pass |
| linear.translation | blocking | 147/147 | 2.37408203e-05 | 1.9037853492e-07 | 8.57111604e-03 | 1.03327567e-03 | pass |
| linear.rotation | warning-only | 147/147 | 7.60725743e-06 | 6.8828549627e-08 | 4.69071860e-02 | 2.97713730e-03 | pass |

Worst absolute rows were fine U `PART-1-1/node 2/U3`, fine UR
`PART-1-1/node 442/UR1`, coarse U `PART-1-1/node 2/U3`, coarse UR
`PART-1-1/node 37/UR1`, linear U `PART-1-1/node 2/U3`, and linear UR
`PART-1-1/node 44/UR1`. No warning-only family failed.

The eight blocking internal families are independent of Abaqus CSV tolerance.

| family | rows | numerator | scale | metric | gate | result |
| --- | ---: | ---: | ---: | ---: | --- | --- |
| fine.global_force_balance | 3 | 2.6775524023e-07 | 1.2773012379e+05 | 2.09625758e-12 | `<=1e-8` | pass |
| fine.global_moment_balance | 3 | 1.3258637157e-04 | 4.8292847478e+05 | 2.74546602e-10 | `<=1e-8` | pass |
| fine.accepted_free_force_residual | 1875 | 3.8659904671e-03 | 1.0000000000e+05 | 3.86599047e-08 | `<=1e-2` | pass |
| fine.accepted_free_moment_residual | 1875 | 1.3760745787e-06 | 0 | exact-zero typed `<=1e-3` | exact-zero branch | pass |
| coarse.global_force_balance | 3 | 8.2512269735e-07 | 1.0000000439e+05 | 8.25122661e-12 | `<=1e-8` | pass |
| coarse.global_moment_balance | 3 | 4.1788609354e-05 | 2.9558678960e+05 | 1.41375091e-10 | `<=1e-8` | pass |
| coarse.accepted_free_force_residual | 75 | 3.1462885132e-02 | 1.0000000000e+05 | 3.14628851e-07 | `<=1e-2` | pass |
| coarse.accepted_free_moment_residual | 75 | 3.3292052422e-06 | 0 | exact-zero typed `<=1e-3` | exact-zero branch | pass |

The constrained-reaction resultant remains a distinct review summary: fine force
`[1.2306822228e-12, -3.5943123478e-12, 1.0000000000e+05]`, moment
`[2.7057467378e-11, -5.6934368331e-10, -1.3258637157e-04]`; coarse force
`[7.9591888635e-12, 7.2906680693e-12, 1.0000000000e+05]`, moment
`[-1.7826096155e-10, -2.5829649530e-10, -4.1788609352e-05]`.

Local reaction RF/RM source-key/inventory/finite prechecks passed, but the following direct
row/RMS findings remain review-only and therefore do not change the blocking classification.

| review family | rows passed | relative RMS | worst absolute row | finding |
| --- | ---: | ---: | --- | --- |
| coarse in-plane RF | 4/48 | 1.1437709953e-01 | node 3/RF1, 5.3914239451e-01 | review-only failure |
| coarse RF3 | 4/24 | 4.8448360241e-02 | node 31/RF3, 7.1995422354e+02 | review-only failure |
| coarse physical RM1/RM2 | 32/48 | 2.7464126167e-02 | node 22/RM1, 1.0484921048e+03 | review-only failure |
| fine in-plane RF | 12/208 | 1.1971372918e-01 | node 1/RF2, 1.5298653299e-01 | review-only failure |
| fine RF3 | 92/104 | 5.3476362434e-03 | node 9/RF3, 4.6176964624e+01 | review-only row failure |
| fine physical RM1/RM2 | 112/208 | 3.3719303859e-03 | node 52/RM2, 3.1549617088e+01 | review-only row failure |

`RM3` and stress were not numerically compared. Artifact inventory, byte size, timestamp, and
SHA-256 equality before/after all runs prove that no reference artifact changed.

<a id="physics-evaluation"></a>

<a id="physics-evaluation--nonlinear-static-newton-raphson-physics-evaluation"></a>
## Nonlinear Static Newton-Raphson Physics Evaluation

<a id="physics-evaluation--1-metadata"></a>
### 1. Metadata

| key | value |
| --- | --- |
| feature_id | `nonlinear-static-newton-raphson` |
| source reference comparison report | `docs/nonlinear-static-newton-raphson/verification.md` |
| source reference comparison SHA-256 | `22867B0F2E3C06C5AB908485D94160CA33CBAF1274EE099847979FA511ECC241` |
| source reference model | `docs/nonlinear-static-newton-raphson/reference-model.md` |
| source reference model SHA-256 | `B2E6845AB59A32F78261B7A47506C27F7BF4B61401B34BC5DE3DAD4F03D6ADDA` |
| status | `pass-for-release-agent` |
| owner_agent | `physics-evaluation-agent` |
| date | `2026-08-28` |

이 평가는 승인된 물리 acceptance scope와 이미 생성된 accepted-state evidence만 사용한다.
Abaqus 또는 다른 reference solver를 실행하지 않았고, 외부 solver의 내부 정식화·적분·안정화·
결과 복구 동등성을 주장하지 않는다.

<a id="physics-evaluation--2-input-evidence"></a>
### 2. Input Evidence

<a id="physics-evaluation--21-gate-entry-audit"></a>
#### 2.1 Gate-entry audit

- `implementation-report.md`와 `build-test.md`의 Stage 6 owner classification은
  `pass-for-physics-evaluation`이며 full CTest `302/302`, nonlinear reference `9/9` 통과를
  기록한다.
- Corrected required source `reference-comparison.md`는 overall handoff status를
  `pass-for-physics-evaluation`로 명시한다. Detailed verdict
  `blocking-pass-with-review-only-findings`는 모든 blocking numerical family가 통과하고 six
  local RF/RM findings만 review-only라는 세부 분류로 함께 유지된다. 두 status는 서로
  모순되지 않으며 `PHYS-STATUS-001`은 해소되었다.
- `requirements.md` metadata의 `status: draft`, `approved_by: pending user re-approval` 및
  `FESA-REQ-NSNR-069`의 historical `draft` 표시는 내용상 physics blocker가 아니다.
  당시 Authoritative `coordination.md` Stage 1 record는 당시 requirements SHA-256
  `89C1AB5F1BEDB7C5F6AD0726ED62F0982181EA8746EDE4661183FD3D18A2408E`가
  `2026-08-27` 사용자에게 명시적으로 재승인되었고 Stage 1이 `passed`임을 기록한다.
  따라서 이 stale metadata를 승인 부재로 재해석하지 않는다.

<a id="physics-evaluation--22-solver-outputs-and-logs"></a>
#### 2.2 Solver outputs and logs

| case | checked authoritative/generated evidence | SHA-256 / observed identity |
| --- | --- | --- |
| `shellnl-meshfine-s4-final` | build-local `shellNL-meshfine_results.h5` | `2E9817E173D73FD91C2D34864B69A1EC37483CB25951FB7CCE85895A6C87D2C6`; accepted frames 10; unique factor-one frame 9/increment 10; 2 iterations per increment |
| `shellnl-meshfine-s4-final` | build-local `shellNL-meshfine_log.txt` | `1DB6FE4AAA2F1443ACC7F9B3F919CC8DD873C90392121DAB6509F1693435DA27`; 20 entered-iteration records; each increment continues once and accepts on iteration 2 |
| `shellnl-s4-final` | build-local `shellNL_results.h5` | `130E2E7B73B022F216A7A34C88D58114A62595ADD556A0D202B8A7FAC7391F39`; accepted frames 10; unique factor-one frame 9/increment 10; 2 iterations per increment |
| `shellnl-s4-final` | build-local `shellNL_log.txt` | `3D5C4F1B20384655F9012ADE842B99E3B06B3799FC9AB16DD6FD141E18B77906`; 20 entered-iteration records; each increment continues once and accepts on iteration 2 |
| `shell-s4-linear-limit` | build-local `shell_results.h5`, `shell_log.txt` | HDF5 `8AEE34D5BC80382D7E6DE85C51F0F8BCBF451CD5F5C7B8DDA6C585EB22B31763`; zero-byte log `E3B0C44298FC1C149AFBF4C8996FB92427AE41E4649B934CA495991B7852B855` |

HDF5는 `reference-comparison.md`에 적힌 build-local exact path에서 직접 읽었다. Optional FESA
debug CSV view는 선언되거나 필요하지 않아 사용하지 않았다. Factor-one
`nodal/displacement`, `global/equilibrium`, `global/energy`, direct shell stress와
`accepted_frames`를 확인했다.

<a id="physics-evaluation--23-read-only-reference-evidence"></a>
#### 2.3 Read-only reference evidence

Canonical reference bundle은 `reference-comparison.md`가 inventoried한 12개 exact file을 사용했다.

- `reference/shellNL-meshfine/`: input, displacement, reaction, stress inventory
- `reference/shellNL/`: input, displacement, reaction, stress inventory
- `reference/shell/`: linear input, displacement, reaction inventory, stress inventory

각 SHA-256은 `reference-model.md`와 `reference-comparison.md` inventory에 일치한다. 비교량은
fine/coarse/linear `U1/U2/U3` blocking, `UR1/UR2/UR3` warning-only, fine/coarse local
`RF1/RF2/RF3`와 physical spatial `RM1/RM2` review-only다. `RM3`와 stored element-corner
stress는 numerical comparison에서 제외되었다.

Reference model의 목적은 중앙 `DOF 3=-100000` fixed-global dead load를 받고 둘레의 all-six
DOF가 고정된 `10 x 10`, thickness `0.5` square plate의 coarse/fine nonlinear response와
linear-limit source identity를 검증하는 것이다. Nonlinear cases는 `0.1` 간격으로 factor one까지
진행한다.

<a id="physics-evaluation--3-physics-checks"></a>
### 3. Physics Checks

| physics check | result | evidence and interpretation |
| --- | --- | --- |
| global equilibrium | `pass` | Fine normalized force `2.09625758e-12`, moment `2.74546602e-10`; coarse force `8.25122661e-12`, moment `1.41375091e-10`. 네 값 모두 approved inclusive `<=1e-8`다. HDF5 `/global/equilibrium`은 `location=global-balance-error`, current arm, global origin `[0,0,0]`, spatial moment 의미를 가진다. |
| reaction consistency | `pass` | Applied `F3=-100000`에 대해 constrained-reaction resultant `F3`는 fine/coarse 모두 약 `+100000`이고 다른 force components는 roundoff 수준이다. Applied-plus-reaction force/moment와 accepted free force/moment residual이 각각 blocking gate를 통과했다. Local RF/RM six-family discrepancy는 승인 계약상 review-only nodal redistribution evidence이며 global reaction/resultant identity를 대체하지 않는다. |
| displacement direction | `pass` | Downward load에 대해 node 2 final `U3`는 fine `-2.56338e-5`, coarse `-2.35504e-5`; reference도 각각 `-2.57957054e-5`, `-2.37408203e-5`다. HDF5 path는 factor `0.1..1.0`에서 fine `-2.56338e-6 .. -2.56338e-5`, coarse `-2.35504e-6 .. -2.35504e-5`로 부호 반전·jump·rollback 없이 진행한다. |
| symmetry / expected zero | `pass` | Center node 2의 factor-one `U1/U2`와 rotations는 fine/coarse에서 약 `1e-17` 이하로, centered load와 symmetric all-edge constraint의 expected-zero response와 일치한다. Fresh physics-focused CTest에서 finite rigid objectivity, zero internal force, rigid translation nullspace와 no-moment tangent symmetry checks가 통과했다. |
| element force balance | `covered-by-approved-invariants` | 승인 HDF5에는 standalone element nodal-action balance dataset이 없고 external element-force comparison도 요구되지 않는다. 대신 complete element residual/tangent same-trial identity, patch recovery, stable assembly covariance tests와 accepted global/free equilibrium gate가 문서화된 expectation을 충족한다. 별도 element-force output을 invent하지 않았다. |
| stress/strain | `pass-sanity-evidence` | HDF5 direct fixed-reference Gauss stress는 finite다. Element 1/GP1의 `[S11,S22,S12]`는 fine bottom `[-264846,-77843.6,914.879]`, middle `[1.94695,0.530775,-0.0224511]`, top `[264850,77844.8,-914.925]`; coarse도 bottom/top sign이 반대이고 middle이 작아 centered plate bending sign/thickness pattern과 일치한다. Stored CSV는 corner/SPOS-SNEG identity로 위치가 달라 numerical stress comparison이 승인되지 않았으므로 이를 tolerance pass로 재분류하지 않는다. |
| rigid body mode | `pass` | 둘레 all-six-DOF support가 global rigid-body motion을 제거하고, accepted path에 비정상 large translation 또는 singular/nonfinite 증상이 없다. Fresh focused tests에서 proper triad/director, finite rigid objectivity, zero internal force, rigid nullspace와 invalid branch rejection을 확인했다. |
| energy/residual | `pass-sanity-evidence` | Factor-one physical strain energy는 fine `1.28169`, coarse `1.17752`로 finite positive이며 near-linear relation `0.5*100000*abs(U3_center)`와 일치한다. 이는 secondary sanity evidence이고 승인 energy convergence gate는 아니다. Fine/coarse accepted free force/moment residual은 NSNR-069 blocking gate를 통과했고 log에는 nonfinite/failed accepted state가 없다. |
| model coverage | `pass` | Fine 729-node/676-element primary, coarse 49-node/36-element companion, linear control과 internal linear-limit/tangent/objectivity/patch/rollback portfolio가 승인 NSNR-030 scope를 덮는다. Stored response는 weak geometric-nonlinear regime이고 original-style MITC4의 curved/distorted membrane-locking risk는 알려진 한계지만 Numerical Review가 이번 release의 additional benchmark/convergence gate로 승인하지 않았으므로 model-coverage gap을 새로 만들지 않는다. |

Fresh physics-focused verification command:

```powershell
ctest --preset windows-msvc-ninja-debug -R '^(NonlinearMitc4Shell|NonlinearMitc4Recovery|NonlinearMitc4Residual|NonlinearMitc4Tangent|NonlinearMitc4Objectivity|NonlinearMitc4Patch|FiniteRotation|NonlinearStaticProcedure)\.' --output-on-failure
```

Result: `23/23` passed, exit `0`, total real time `5.12 s`.

<a id="physics-evaluation--4-failure-classification"></a>
### 4. Failure Classification

- blocking classification: 없음
- resolved finding: `PHYS-STATUS-001`; corrected `reference-comparison.md`가 required overall
  `pass-for-physics-evaluation` handoff와 detailed
  `blocking-pass-with-review-only-findings` verdict의 관계를 명시했다.
- observed failures: `equilibrium-failure`, `reaction-inconsistency`,
  `displacement-direction-failure`, `symmetry-failure`, `stress-location-failure`,
  `element-force-inconsistency`, `rigid-body-mode-suspected`, `nonfinite-result`,
  `model-coverage-gap`, `upstream-contract`, `environment` 모두 없음.

<a id="physics-evaluation--5-evaluation-verdict"></a>
### 5. Evaluation Verdict

- verdict: `pass-for-release-agent`
- physics evidence disposition: documented equilibrium, reaction, displacement, symmetry/objectivity,
  stress/strain sanity, rigid-body, residual/path and model-coverage checks show no physical failure.
- pass disposition: documented physical expectations passed and no physics/model-coverage/I/O/upstream
  blocker remains.
- release meaning: this verdict authorizes Release Agent evaluation through Coordinator only. It is
  not Release approval, publish/deploy/package/tag authorization, or external-solver equivalence.

<a id="physics-evaluation--6-handoff-recommendation"></a>
### 6. Handoff Recommendation

- handoff: `Release Agent`, always through `Coordinator Agent`
- recommendation: Release Agent는 current approved hashes, Stage 6
  `pass-for-physics-evaluation`, 이 문서의 `pass-for-release-agent`, known limitations와
  review-only findings를 사용해 release readiness만 audit한다.
- boundary: Physics Evaluation Agent는 release readiness, final release checklist, release notes,
  publish/deploy/package/tag를 승인하지 않는다.

<a id="physics-evaluation--8-open-issues"></a>
### 8. Open Issues

| id | severity | issue | gate effect |
| --- | --- | --- | --- |
| `PHYS-META-001` | nonblocking | `requirements.md`의 draft/pending metadata가 authoritative Coordinator/user reapproval record와 stale함 | 현재 hash의 explicit approval로 physics authority는 해소됨; Release traceability audit에서 투명하게 유지 |
| `PHYS-LOCAL-001` | nonblocking | six local RF/RM families have review-only discrepancies | approved disposition 유지; global force/moment balance와 free residual을 blocking evidence로 사용 |
| `PHYS-STRESS-001` | nonblocking | stored corner/SPOS-SNEG stress와 FESA direct Gauss recovery 위치가 다르고 fine optional stress row 하나의 node label이 malformed | stress numerical comparison 제외 유지; artifact를 repair하지 않음 |
| `PHYS-LIMIT-001` | known limitation | stored cases are weak geometric-nonlinear plate responses; original MITC4 has known curved/distorted membrane-locking risk | approved current portfolio에서는 blocker 아님; broader claim 금지 |