# Sprint Contract: Math Solver Extraction

## Objective
Move math primitives, dense test matrix support, sparse pattern data, and linear solver interfaces into `Math` while keeping future MKL integration behind an adapter boundary.

## Required Reading
- /AGENTS.md
- /PROGRESS.md
- /PLAN.md
- /docs/README.md
- /docs/HARNESS_ENGINEERING.md
- /docs/ARCHITECTURE.md
- /docs/ADR.md
- /docs/NUMERICAL_CONVENTIONS.md
- /phases/1-structure-alignment-refactor/step0-architecture-map.md
- /phases/1-structure-alignment-refactor/step2.md

## Scope
- Extract vector/matrix helpers, `DenseMatrix`, sparse pattern structures, `SolveResult`, `LinearSolver`, and the deterministic test solver.
- Keep the production-facing solver dependency expressed through `LinearSolver`.
- Preserve int64 sparse index and equation-number boundaries.
- Keep MKL/PARDISO as a future adapter, not a Phase 1 dependency.

## Allowed Files
- `include/fesa/fesa.hpp`
- `include/fesa/Math/`
- `src/Math/`
- `include/fesa/Core/`
- `src/Core/`
- `tests/`
- `CMakeLists.txt`
- `phases/1-structure-alignment-refactor/index.json`
- `PLAN.md`
- `PROGRESS.md`

## Explicit Non-Goals
- Do not introduce MKL, TBB, HDF5, or production sparse storage.
- Do not change Gaussian solver numerical behavior except for mechanical relocation.
- Do not move MITC4, parser, results, assembly, or analysis logic except for include dependency repair.

## Tests To Write First
- Add or update include/link tests for the `Math` module.
- Preserve existing small linear algebra, sparse-pattern, solver-injection, and singular-solver diagnostic tests as characterization tests.

## Reference Artifacts
- None.

## Acceptance Commands
```bash
python scripts/validate_workspace.py
```

## Evaluator Checklist
- `Math` does not depend on `IO`, `Results`, `Element`, `Assembly`, or `Analysis`.
- `LinearSolver` remains an adapter boundary.
- All ids, equation ids, nonzero counts, and sparse indices remain int64.
- Solver failure diagnostics still propagate to analysis tests.
- No external library API leaks into solver core.

## Handoff Requirements
- Update this step status in `phases/1-structure-alignment-refactor/index.json`.
- Record moved math/solver files and any remaining math symbols still left in `fesa.hpp`.

## Do Not
- Do not optimize the solver while moving files.
- Do not replace deterministic tests with tolerance changes.