refactor: extract math solver boundary

PROGRESS.md

@@ -13,10 +13,45 @@ Every new agent session must read this file together with `PLAN.md` before plann
 - Do not remove history unless the user explicitly asks for archival cleanup.
 
 ## Current Status
-Phase 1 has a completed rebaseline execution path in `phases/1-linear-static-mitc4-rebaseline`. Steps 0 through 15 are complete, and P1R-15 recorded a pass-with-documented-gaps evaluator closeout. The follow-up architecture refactor phase in `phases/1-structure-alignment-refactor` is underway because the current production implementation is concentrated in `include/fesa/fesa.hpp` instead of the module directories documented in `docs/ARCHITECTURE.md`; P1A-00, P1A-01, and P1A-02 are complete, so the next step is P1A-03 Math and solver adapter extraction. `quad_02_phase1.inp` is the normalized Phase 1-compatible input path for the stored `quad_02` S4 reference pair, while the original `quad_02.inp` remains preserved unsupported provenance. Core numeric aliases, DOF mapping, validation harness, model diagnostic context, the Phase 1 parser/domain subset, validation/singular diagnostics, DofManager/reaction foundation, minimum result model metadata, displacement CSV comparator foundation, MITC4 geometry/director scaffolding, MITC4 displacement/strain/tying row scaffolding, MITC4 material/transform/integration scaffolding, MITC4 stiffness/drilling/internal-force scaffolding, MITC4 patch/locking-sensitivity tests, full-space assembly, reduced projection, sparse-pattern scaffold, solver adapter injection, full-vector internal/reaction force state, active AnalysisModel construction, input-to-AnalysisState-to-U/RF result workflow, and the first stored Abaqus displacement regression have been revalidated. Full PRD Phase 1 completion still depends on the open architecture/reference gaps R-014, R-010, and R-013. The old `phases/1-linear-static-mitc4` path is historical and superseded after the MITC4 formulation reset.
+Phase 1 has a completed rebaseline execution path in `phases/1-linear-static-mitc4-rebaseline`. Steps 0 through 15 are complete, and P1R-15 recorded a pass-with-documented-gaps evaluator closeout. The follow-up architecture refactor phase in `phases/1-structure-alignment-refactor` is underway because the current production implementation is concentrated in `include/fesa/fesa.hpp` instead of the module directories documented in `docs/ARCHITECTURE.md`; P1A-00 through P1A-03 are complete, so the next step is P1A-04 IO parser extraction. `quad_02_phase1.inp` is the normalized Phase 1-compatible input path for the stored `quad_02` S4 reference pair, while the original `quad_02.inp` remains preserved unsupported provenance. Core numeric aliases, DOF mapping, validation harness, model diagnostic context, the Phase 1 parser/domain subset, validation/singular diagnostics, DofManager/reaction foundation, minimum result model metadata, displacement CSV comparator foundation, MITC4 geometry/director scaffolding, MITC4 displacement/strain/tying row scaffolding, MITC4 material/transform/integration scaffolding, MITC4 stiffness/drilling/internal-force scaffolding, MITC4 patch/locking-sensitivity tests, full-space assembly, reduced projection, sparse-pattern scaffold, solver adapter injection, full-vector internal/reaction force state, active AnalysisModel construction, input-to-AnalysisState-to-U/RF result workflow, and the first stored Abaqus displacement regression have been revalidated. Full PRD Phase 1 completion still depends on the open architecture/reference gaps R-014, R-010, and R-013. The old `phases/1-linear-static-mitc4` path is historical and superseded after the MITC4 formulation reset.
 
 ## Completed Work
 
+### 2026-05-05 - P1A-03 Math solver extraction completed
+Author: Codex
+
+Changed files:
+- `CMakeLists.txt`
+- `include/fesa/Core/Domain.hpp`
+- `include/fesa/Math/DenseMatrix.hpp`
+- `include/fesa/Math/LinearSolver.hpp`
+- `include/fesa/Math/Math.hpp`
+- `include/fesa/Math/SparsePattern.hpp`
+- `include/fesa/Math/Vector.hpp`
+- `include/fesa/fesa.hpp`
+- `tests/test_math_module_includes.cpp`
+- `phases/1-structure-alignment-refactor/index.json`
+- `PLAN.md`
+- `PROGRESS.md`
+
+Summary:
+- Extracted `Vec3` and vector helper functions into `include/fesa/Math/Vector.hpp`; `Core/Domain.hpp` now consumes `Vec3` from Math instead of defining it locally.
+- Extracted sparse pattern data structures into `include/fesa/Math/SparsePattern.hpp`.
+- Extracted `DenseMatrix` into `include/fesa/Math/DenseMatrix.hpp`.
+- Extracted `SolveResult`, `LinearSolver`, and `GaussianEliminationSolver` into `include/fesa/Math/LinearSolver.hpp`.
+- Added `fesa_math_module_tests`, a direct module include smoke test that does not include `fesa/fesa.hpp` and checks vector math, int64 sparse index/equation boundaries, dense matrix multiply, solver success, and singular-solver diagnostics.
+- Preserved `LinearSolver` as the adapter boundary and introduced no MKL, TBB, HDF5, or production sparse storage dependency.
+- Remaining large groups in `fesa.hpp` are IO parser, Assembly helpers (`buildReducedSparsePattern`, `recoverFullReaction`), MITC4 Element/Material helpers, Results/reference comparison, and Analysis workflow.
+
+Verification:
+- First ran `python scripts/validate_workspace.py` after adding the direct Math include test; it failed as expected because `fesa/Math/Math.hpp` did not yet expose Math primitives or solver types.
+- After extraction, `python scripts/validate_workspace.py` configured CMake, built `fesa_core`, `fesa_tests`, `fesa_core_module_tests`, and `fesa_math_module_tests`, and ran CTest successfully.
+- CTest result: 3 test executables passed.
+
+Follow-up:
+- Continue with P1A-04 IO parser extraction.
+- Keep R-014 open until P1A-09 independently accepts the final architecture alignment.
+
 ### 2026-05-05 - P1A-02 Core domain DOF extraction completed
 Author: Codex