MathModeling-skills: Skill for Claude Code

Purpose

Test the claims most likely to fail. Choose checks from the model's assumptions and decision risks rather than filling a generic checklist.

Preconditions

• Approved main and usable baseline executed.
• Run summary, method card, probe summary, and relevant outputs exist.
• Claim or decision to be tested is known.

Workflow

1. Identify load-bearing assumptions and claims.
2. Select applicable checks:
   • parameter or weight perturbation;
   • alternate split or resampling;
   • seed stability;
   • outlier/missing-data treatment;
   • constraint/capacity perturbation;
   • baseline comparison;
   • output concentration/rank stability;
   • error and uncertainty analysis.
3. State perturbation ranges and why they are meaningful before interpreting results.
4. Run checks with fixed seeds where stochastic.
5. Save compact metrics to:

robustness/Qx/qx_robustness_summary.json

1. In submission, also save:

robustness/Qx/qx_robustness_report.md

1. If the stability verdict affects method continuation or claim scope, invoke one choice card and log the human answer in qx_decisions.jsonl.

Summary Contract

Record:

• tested claim/assumption;
• input and result source paths;
• perturbation;
• metric and threshold if predeclared;
• observed value;
• status PASS, CONDITIONAL, or FAIL;
• limitation;
• fallback-trigger relevance.

Rules

• Do not run irrelevant checks merely to reach a count.
• Do not invent a threshold after seeing the result without labeling it exploratory.
• Do not convert stability metrics into the human confidence verdict.
• Do not create robustness-checker_modeler_decision.md.
• A failed robustness check is evidence for adjust/fallback/claim downgrade, not permission for AI to decide.

Verification

• Every major final claim has a supporting check or explicit limitation.
• Perturbations are justified and reproducible.
• Baseline and main comparisons remain metric-compatible.
• Concentration/degeneracy risks are revisited when relevant.
• Submission report sources its numbers from the summary and experiment artifacts.