refactor: extract math solver boundary

PLAN.md

@@ -13,7 +13,7 @@ Every new agent session must read this file together with `PROGRESS.md` before p
 - If an item becomes obsolete, move it to `PROGRESS.md` with a short reason instead of silently deleting it.
 
 ## Current Objective
-Execute the Phase 1 structure-alignment refactor in `phases/1-structure-alignment-refactor`, continuing with P1A-03 Math and solver adapter extraction. P1A-00 completed the architecture drift audit, P1A-01 created the module scaffold, and P1A-02 extracted Core/Util plus Phase 1 Boundary/Load/Property model ownership without changing solver behavior. This phase must align the current monolithic `include/fesa/fesa.hpp` implementation with the module ownership model in `docs/ARCHITECTURE.md` without changing solver behavior. Product-level Phase 1 reference gaps R-010 and R-013 remain open and must not be hidden by the refactor.
+Execute the Phase 1 structure-alignment refactor in `phases/1-structure-alignment-refactor`, continuing with P1A-04 IO parser extraction. P1A-00 completed the architecture drift audit, P1A-01 created the module scaffold, P1A-02 extracted Core/Util plus Phase 1 Boundary/Load/Property model ownership, and P1A-03 extracted Math primitives plus the solver adapter boundary without changing solver behavior. This phase must align the current monolithic `include/fesa/fesa.hpp` implementation with the module ownership model in `docs/ARCHITECTURE.md` without changing solver behavior. Product-level Phase 1 reference gaps R-010 and R-013 remain open and must not be hidden by the refactor.
 
 ## Required Reading For New Agents
 1. `AGENTS.md`
@@ -37,7 +37,7 @@ Execute the Phase 1 structure-alignment refactor in `phases/1-structure-alignmen
 ## Phase Files
 - Active phase directory: `phases/1-structure-alignment-refactor`
 - Execute with: `python scripts/execute.py 1-structure-alignment-refactor`
-- Step numbering is zero-based. `step0.md` is complete and wrote `phases/1-structure-alignment-refactor/step0-architecture-map.md`; `step1.md` is complete and created module scaffold headers, source directories, CMake source discovery, and umbrella compatibility smoke coverage; `step2.md` is complete and extracted Core/Util domain, diagnostics, DofManager ownership, AnalysisModel/AnalysisState, and Phase 1 Boundary/Load/Property model ownership; `step3.md` extracts Math and solver adapter boundaries; `step4.md` extracts the Abaqus parser into IO; `step5.md` extracts Results and reference comparison code; `step6.md` extracts MITC4 geometry/strain helpers; `step7.md` extracts MITC4 material/stiffness helpers; `step8.md` extracts Assembly and Analysis workflow; `step9.md` is the independent architecture evaluator closeout.
+- Step numbering is zero-based. `step0.md` is complete and wrote `phases/1-structure-alignment-refactor/step0-architecture-map.md`; `step1.md` is complete and created module scaffold headers, source directories, CMake source discovery, and umbrella compatibility smoke coverage; `step2.md` is complete and extracted Core/Util domain, diagnostics, DofManager ownership, AnalysisModel/AnalysisState, and Phase 1 Boundary/Load/Property model ownership; `step3.md` is complete and extracted Math primitives, sparse pattern data, dense matrix support, and solver adapter boundary; `step4.md` extracts the Abaqus parser into IO; `step5.md` extracts Results and reference comparison code; `step6.md` extracts MITC4 geometry/strain helpers; `step7.md` extracts MITC4 material/stiffness helpers; `step8.md` extracts Assembly and Analysis workflow; `step9.md` is the independent architecture evaluator closeout.
 - Completed phase directory: `phases/1-linear-static-mitc4-rebaseline`
 - Historical execution command: `python scripts/execute.py 1-linear-static-mitc4-rebaseline`
 - Step numbering is zero-based. `step0.md` is complete and recorded in `phases/1-linear-static-mitc4-rebaseline/step0-audit.md`; `step1.md` is complete and created the `quad_02_phase1.inp` normalized reference path; `step2.md` is complete and revalidated core harness guardrails; `step3.md` is complete and revalidated the Phase 1 parser/domain subset; `step4.md` is complete and strengthened validation/singular diagnostics; `step5.md` is complete and revalidated the DofManager/reaction foundation; `step6.md` is complete and revalidated the minimum result model plus displacement CSV comparator; `step7.md` is complete and revalidated MITC4 natural coordinates, tying points, center directors, and integration bases; `step8.md` is complete and revalidated degenerated-continuum displacement, direct covariant strain rows, and MITC shear tying rows; `step9.md` is complete and revalidated plane-stress material, convected-to-local transform, and `2 x 2 x 2` material integration scaffolding; `step10.md` is complete and revalidated MITC4 stiffness, internal force, six-DOF transform, and drilling stabilization; `step11.md` is complete and added MITC4 membrane, bending, shear, twist, drilling-sensitivity, and thin-cantilever locking-sensitivity tests; `step12.md` is complete and revalidated full-space assembly, reduced projection, deterministic sparse-pattern scaffold, solver adapter injection, and full-vector internal/reaction force state; `step13.md` is complete and revalidated active AnalysisModel construction plus input-to-AnalysisState-to-U/RF result workflow; `step14.md` is complete and added the first stored Abaqus displacement regression for `quad_02_phase1`; `step15.md` is complete and recorded the independent evaluator closeout in `phases/1-linear-static-mitc4-rebaseline/step15-evaluator-report.md`.
@@ -60,7 +60,7 @@ This phase is an architecture-preserving refactor. It must not change Phase 1 so
 | P1A-00 | completed | planner/evaluator | Audit `fesa.hpp` architecture drift and create a symbol-to-module migration map. | P1R-15 | Complete migration map and validation baseline |
 | P1A-01 | completed | generator | Create module directory scaffold, CMake source boundaries, and umbrella facade policy. | P1A-00 | Module include smoke tests and build stability |
 | P1A-02 | completed | generator | Extract Core/Util domain, diagnostics, aliases, DOF mapping, `AnalysisModel`, `DofManager`, and Phase 1 Boundary/Load/Property model ownership. | P1A-01 | Core has no dependency on higher layers; Boundary/Load/Property types are no longer hidden in the umbrella header; DOF tests unchanged |
-| P1A-03 | pending | generator | Extract Math and solver adapter boundaries. | P1A-02 | Linear solver interface remains adapter-ready; int64 paths unchanged |
+| P1A-03 | completed | generator | Extract Math and solver adapter boundaries. | P1A-02 | Linear solver interface remains adapter-ready; int64 paths unchanged |
 | P1A-04 | pending | generator | Extract Abaqus parser into IO. | P1A-02 | Parser subset and unsupported-feature diagnostics unchanged |
 | P1A-05 | pending | generator | Extract Results model, writer boundary, CSV loader, and reference comparator. | P1A-02, P1A-04 | `U`/`RF` schema and `quad_02_phase1` regression unchanged |
 | P1A-06 | pending | generator | Extract MITC4 geometry, director, strain, and tying helpers into Element. | P1A-03 | Geometry/strain tests and formulation signs unchanged |