docs: approve MITC4 implementation handoff
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# Step 6: Shell DOF Scatter
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## 담당 역할과 필수 스킬
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- 담당 역할: `implementation-agent`
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- 필수 스킬: `harness`, `fesa-cpp-msvc-tdd`
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## 읽어야 할 파일
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- `/.agents/skills/harness/SKILL.md`, `/.codex/skills/fesa-cpp-msvc-tdd/SKILL.md`
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- `/AGENTS.md`, `/docs/PRD.md`, `/docs/ARCHITECTURE.md`, `/docs/ADR.md`
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- `/docs/HARNESS.md`, `/docs/HARNESS_WORKFLOW.md`, `/.codex/hooks.json`
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- `/docs/implementation-plans/linear-static-mitc4-shell-implementation-plan.md`
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- `/docs/requirements/linear-static-mitc4-shell.md` Requirements 005/025
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- `/docs/research/linear-static-mitc4-shell-research.md`
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- `/docs/formulations/mitc4-shell-formulation.md`
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- `/docs/numerical-reviews/linear-static-mitc4-shell-review.md`
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- `/docs/io-definitions/linear-static-mitc4-shell-io.md`
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- `/docs/reference-models/linear-static-mitc4-shell-reference-models.md`
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- phase indexes, `step6.md`, Step 0 shell model and Step 5 summary
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- `/include/fesa/fem/dof_manager.hpp`, `/src/fesa/fem/dof_manager.cpp`
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- `/tests/unit/fem/dof_manager_test.cpp`
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- `/tests/unit/constraints/essential_constraints_test.cpp`
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## 작업
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1. `MITC4-DOF-001..003` tests를 먼저 작성한다.
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2. 기존 node DOF order `[ux,uy,uz,urx,ury,urz]`를 유지한다.
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3. B33 12-entry scatter를 보존하면서 shell four-node/source-order 24-entry typed
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scatter와 sorted unique sparse pattern을 `DofManager` 단독 소유로 추가한다.
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4. Free/constrained numbering과 no/mixed/all constraint, nonzero prescribed value
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round trip을 shell-sized system에서 검증한다.
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5. All-constrained `0x0 Kff`가 valid하도록 existing constraint behavior를 보존한다.
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## Acceptance Criteria
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```powershell
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$requiredBuildPaths=@("C:/git/googletest","C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl","C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb","C:/Program Files/HDF_Group/HDF5/2.1.1/cmake")
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foreach($p in $requiredBuildPaths){if(-not(Test-Path -LiteralPath $p)){throw "Missing $p"}}
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cmake --fresh -S . -B .harness/build -G "Visual Studio 18 2026" -A x64 `
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"-DFESA_GTEST_SOURCE_DIR=C:/git/googletest" `
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"-DMKL_DIR=C:/Program Files (x86)/Intel/oneAPI/mkl/2026.1/lib/cmake/mkl" `
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"-DTBB_DIR=C:/Program Files (x86)/Intel/oneAPI/tbb/2023.1/lib/cmake/tbb" `
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"-DHDF5_DIR=C:/Program Files/HDF_Group/HDF5/2.1.1/cmake"
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cmake --build .harness/build --config Debug --target fesa_unit_tests
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ctest --test-dir .harness/build -C Debug -R "DofManager|EssentialConstraints" --output-on-failure
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```
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Current 12-entry-only behavior의 expected RED 뒤 minimal GREEN. 이후:
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```powershell
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cmake --build .harness/build --config Debug --target fesa_unit_tests
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ctest --test-dir .harness/build -C Debug -R "DofManager|EssentialConstraints|DomainModel" --output-on-failure
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cmake --build .harness/build --config Debug
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ctest --test-dir .harness/build -C Debug --show-only=json-v1
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ctest --test-dir .harness/build -C Debug --output-on-failure
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```
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## 검증 및 상태 갱신
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RED/VERIFY evidence를 기록하고 current Step의 Codex-owned fields만 갱신한다.
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## 금지사항
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- Node/Element에 equation id를 저장하지 마라.
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- Load/constraint ownership이나 sparse reduction을 이동하지 마라.
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- 기존 B33 scatter behavior를 제거하지 마라.
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- 직접 commit/hook 실행 또는 reference/upstream 변경을 하지 마라.
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