# Step 4: MITC4 Stiffness and Drilling Stabilization

## 담당 역할과 필수 스킬

- 담당 역할: `implementation-agent`
- 필수 스킬: `harness`, `fesa-cpp-msvc-tdd`

## 읽어야 할 파일

- `/.agents/skills/harness/SKILL.md`, `/.codex/skills/fesa-cpp-msvc-tdd/SKILL.md`
- `/AGENTS.md`, `/docs/PRD.md`, `/docs/ARCHITECTURE.md`, `/docs/ADR.md`
- `/docs/HARNESS.md`, `/docs/HARNESS_WORKFLOW.md`, `/.codex/hooks.json`
- `/docs/linear-static-mitc4-shell/implementation-plan.md`
- `/docs/linear-static-mitc4-shell/requirements.md` Requirements 031-038/050-056
- `/docs/linear-static-mitc4-shell/research.md`
- `/docs/linear-static-mitc4-shell/formulation.md` Sections 10-14, 17
- `/docs/linear-static-mitc4-shell/numerical-review.md` Sections 5.7, 6.1-6.2
- `/docs/linear-static-mitc4-shell/io.md`
- `/docs/linear-static-mitc4-shell/reference-model.md`
- phase indexes, `step4.md`, completed Step 3 kernel/header/test and summary

## 작업

1. `MITC4-KERNEL-001..006`를 production edit 전에 작성한다.
2. Common `2x2x2` integration으로 physical `K20`을 만들고 deterministic
   20-to-24 congruence로 global-coordinate `K24 physical`을 만든다.
3. `R+`는 eight physical tangent-rotation diagonal의 finite positive values만
   사용하고 `k_ref=min(R+)`, `k_d=1e-3*k_ref`,
   `K_drill=T_d^T(k_d I4)T_d`를 정확히 구현한다.
4. Empty/nonfinite `R+`는 structured deterministic failure다.
5. Scaled symmetry <=1e-12, transform energy <=1e-12, physical rigid action <=1e-10,
   physical rank 14, stabilized rank 18/nullity 6, positive non-rigid energy,
   membrane/bending/shear/twist patch fields를 독립 test로 검증한다.

## Acceptance Criteria

```powershell
$requiredBuildPaths=@("C:/git/googletest","C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl","C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb","C:/Program Files/HDF_Group/HDF5/2.1.1/cmake")
foreach($p in $requiredBuildPaths){if(-not(Test-Path -LiteralPath $p)){throw "Missing $p"}}
cmake --fresh -S . -B .harness/build -G "Visual Studio 18 2026" -A x64 `
  "-DFESA_GTEST_SOURCE_DIR=C:/git/googletest" `
  "-DMKL_DIR=C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl" `
  "-DTBB_DIR=C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb" `
  "-DHDF5_DIR=C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"
cmake --build .harness/build --config Debug --target fesa_unit_tests
ctest --test-dir .harness/build -C Debug -R "Mitc4ShellKernel|Mitc4ShellPatch|Mitc4ShellDrilling" --output-on-failure
```

Expected missing stiffness/drilling RED를 확인한 뒤 minimal GREEN. 이후:

```powershell
cmake --build .harness/build --config Debug --target fesa_unit_tests
ctest --test-dir .harness/build -C Debug -R "Mitc4ShellKernel|Mitc4ShellPatch|Mitc4ShellDrilling|Mitc4ShellKinematics" --output-on-failure
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
```

## 검증 및 상태 갱신

RED/VERIFY evidence와 exact formula를 summary에 기록하고 현재 Step 상태만 갱신한다.

## 금지사항

- Translational diagonal을 `R+`에 넣지 마라.
- Coefficient sweep, calibration, drill energy/result, physical recovery를 구현하지 마라.
- S4R reduced integration/hourglass와 future nonlinear tangent를 구현하지 마라.
- 직접 commit/hook 실행 또는 reference/upstream 변경을 하지 마라.