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FESADev/.codex/skills/fem-numerical-review/SKILL.md
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name, description
name description
fem-numerical-review Use when independently reviewing a structural FEM formulation, stability risks, and verification-case readiness before interface definition or implementation.

FEM Numerical Review

Issue an independent, findings-first verdict on whether the mathematical contract and logical verification coverage are ready downstream.

Inputs

  • Requirements, research, and formulation for one feature_id
  • Existing reference cases and artifacts, read-only
  • docs/TOLERANCE.md and approved compatibility policies

Workflow

  1. Check dimensions, signs, DOF order, transformations, kinematics, constitutive update, mapping, quadrature, residual, loads, tangent consistency, symmetry, null spaces, conditioning, and family-specific stability risks.
  2. Check each requirement has a falsifiable unit, element, integration, benchmark, convergence, or reference-comparison case.
  3. Inventory only approved reference cases. Under docs/TOLERANCE.md, autonomously select and justify quantity, identity/component, metric, scale and near-zero treatment, blocking/diagnostic class, and numerical tolerance from analytical, convergence, or reference evidence. Define locations, units, coordinates, and entity prechecks without selecting a physical file schema.
  4. Lead with defects and severity. Return missing derivations to formulation and missing evidence to research; do not repair upstream artifacts in place.

Read the applicable analysis-family guidance. Use workflow and decision authority for escalation and evidence and handoff for the verdict.

Output

Follow Feature document management: read the Coordinator's feature context, keep main reports concise, and link necessary owned details in the same feature folder.

Create or revise:

  • docs/<feature-id>/numerical-review.md: verdict, findings, risks, consistency checks, verification readiness, required revisions, and handoff.
  • docs/<feature-id>/reference-model.md: logical acceptance scope, case inventory, identity/component contract, metric, scale, blocking class, tolerance value/source, prechecks, contract revision, limitations, and I/O handoff.

Evidence

Tie every finding and tolerance choice to an equation, requirement, source, case, convergence result, or reproducible calculation. Record the feature contract revision and preserve prior failing evidence when a tolerance changes. Separate confirmed defects, risks, recommendations, and unresolved decisions. A pass means ready for I/O definition, not feature completion.

Boundary

Do not edit the formulation, implement code, choose APIs or dataset paths, modify or generate reference artifacts, relax a tolerance merely to pass an implementation result, decide final comparison success, or approve release. A missing noncritical naming convention is not a numerical blocker.