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.codex/skills/fesa-numerical-review/SKILL.md

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+---
+name: fesa-numerical-review
+description: Use when independently reviewing FESA FEM numerical review evidence, formulation correctness, stability risks, patch tests, locking, Jacobian handling, and implementation planning readiness.
+---
+
+# FESA Numerical Review
+
+Use this skill to review a formulation as a numerical algorithm contract before implementation planning.
+
+## Inputs
+
+Read these first:
+
+- `AGENTS.md`
+- `docs/SOLVER_AGENT_DESIGN.md`
+- `docs/numerical-reviews/README.md`
+- `docs/formulations/<feature-id>-formulation.md`
+- Related requirements and research documents when needed
+
+## Workflow
+
+1. Lead with findings and required revisions.
+2. Check dimensional consistency, signs, DOF ordering, constrained/free assumptions, and coordinate transforms.
+3. Review B matrix or kinematic operator consistency.
+4. Review constitutive matrix or stress update contract.
+5. Review Jacobian rules, determinant checks, derivative transforms, and distortion handling.
+6. Review integration rule, Gauss points, weights, and full/reduced/selective integration policy.
+7. Check element residual, internal force, external force, stiffness, tangent, symmetry, and positive definiteness expectations.
+8. Assess rigid body modes, patch test readiness, hourglass, shear locking, volumetric locking, singular Jacobian, conditioning, and convergence risk.
+9. Decide status: `pass-for-implementation-planning`, `needs-formulation-revision`, `needs-research`, `needs-reference-model`, or `blocked`.
+
+## Output Contract
+
+Produce or revise `docs/numerical-reviews/<feature-id>-review.md` with:
+
+- Metadata and source formulation
+- Review Verdict
+- Critical Findings
+- Numerical Risk Assessment
+- Consistency Checks
+- Verification Readiness
+- Required Revisions
+- Downstream Handoff
+
+## Boundaries
+
+- Do not implement code.
+- Do not edit formulations directly.
+- Do not design C++ APIs or file ownership.
+- Do not run Abaqus, Nastran, or any reference solver.
+- Do not generate reference CSVs.
+- Do not approve release readiness.
+- Do not decide reference comparison success.
+
+## Quality Gate
+
+- `pass-for-implementation-planning` means implementation planning may begin, not that the feature is complete.
+- Confirmed defects, risks, open questions, and test recommendations are separated.
+- Missing derivations are returned to Formulation Agent instead of being silently fixed.
+- Evidence gaps are routed to Research Agent or Reference Model Agent.
+
+## Handoff
+
+Send pass results to Implementation Planning Agent and Reference Model Agent. Send math defects to Formulation Agent, source gaps to Research Agent, and blocked decisions to Coordinator Agent.