docs: add modular refactoring implementation plan
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# Step 15: Generic DofManager
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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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- 이 Step만 `RED -> observed failure -> minimal GREEN -> focused/full VERIFY`로 수행한다.
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## 읽어야 할 파일
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- `/AGENTS.md`
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- `/docs/CODINGSTYLE.md`
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- `/docs/ARCHITECTURE.md`
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- `/docs/ADR.md`
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- `/docs/cpp-object-oriented-modular-refactoring/implementation-plan.md`
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- Step 13 Domain/AnalysisModel files
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- Step 14 `element.h`, `element_factory.h`, concrete runtime elements
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- `/include/fesa/fem/dof_manager.h`, `/src/fesa/fem/dof_manager.cpp`
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- `/tests/unit/fem/dof_manager_test.cpp`
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- `/tests/unit/assembly/sparse_assembler_test.cpp`
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- `/phases/cpp-object-oriented-modular-refactoring/index.json`
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- `/phases/cpp-object-oriented-modular-refactoring/step15.md`
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## 작업
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Requirement `R-PIPELINE-001`의 DofManager portion과 `R-DUP-002`의 DOF invariant owner를
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구현한다.
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1. `dof_manager_test.cpp`에 `C-DOF-001`을 먼저 추가한다. A test-only fake `Element`
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supplies a layout not named B33 or MITC4; DofManager must number/scatter it in source order.
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2. Tests also corrupt duplicate/full/free/constrained/equation mappings through an approved test seam
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and expect `ValidateInvariants()` to reject each exact inconsistency.
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3. Current DofManager cannot consume fake base layouts or expose owner validation, producing RED.
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4. Candidate API:
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```cpp
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Status DofManager::Build(
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const AnalysisModel& analysis_model,
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const ElementView& elements);
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Result<std::vector<std::size_t>> DofManager::ElementScatter(
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const ElementDofLayout& layout) const;
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Status DofManager::ValidateInvariants() const;
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```
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5. Replace B33/MITC4 concrete scatter/pattern branches with the ordered layout. Node DOF ownership,
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constrained/free mappings, equation numbering and sparse pattern remain solely in DofManager.
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6. Preserve stable node/source/component order, no/mixed/all-constraint behavior, and valid 0 free
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equations. Do not store equation ids in Node/Element.
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7. Remove same-meaning `ValidateDofOrder` helpers from other modules only after their callers use
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`ValidateInvariants()` or an owner-issued immutable mapping.
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## Acceptance Criteria
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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 `
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-R "DofManager|EssentialConstraints|SparseAssembly" --output-on-failure
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$typeBranches = @(rg -n "EulerBeam3D|Mitc4Shell" src/fesa/fem/dof_manager.cpp)
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if ($typeBranches.Count -ne 0) { $typeBranches; throw "Concrete element branch remains" }
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rg -n "ValidateDofOrder" src/fesa
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& "C:/Program Files/LLVM/bin/clang-format.exe" --dry-run --Werror `
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include/fesa/fem/dof_manager.h src/fesa/fem/dof_manager.cpp `
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tests/unit/fem/dof_manager_test.cpp
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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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`ValidateDofOrder` scan must show no duplicate local definitions. Existing public compatibility
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wrappers may remain temporarily only if they delegate to DofManager and are removed by Step 20.
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## 검증 및 상태 갱신
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- RED fake-element/invariant failures, focused stable ordering, branch scan and full CTest를 summary에 기록한다.
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- Equation or sparse pattern ordering regression is `error`.
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- 성공 시 현재 Step만 `completed`로 갱신한다.
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- timestamp, retry, commit, advancement는 Executor 소유다.
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## 금지사항
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- Element에 equation ids or global CSR를 저장하지 마라.
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- DOF component order를 element kind switch로 재구성하지 마라.
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- Sparse assembly algorithm을 수정하지 마라. 이유: Step 16 소유다.
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- 직접 commit하거나 hook script를 수동 실행하지 마라.
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