MathModeling-skills: Skill for Claude Code

Purpose

Convert the framed problem and data profile into a small executable decision surface. Screen methods for load-bearing data, assumption, degeneracy, sensitivity, and scale risks before asking the human to choose.

This skill proposes and probes methods. The human chooses the method.

Preconditions

• G1 problem framing passed.
• Required output and evaluation criteria are known.
• Relevant data inventory or audit exists.
• planning/symbol_table.md and planning/model_assumptions.md exist when the problem needs them.

If these are missing, return to the producer skill rather than guessing.

Inputs

• Problem parse and classification.
• Data audit, including missingness, effective sample size, imbalance, cardinality, and distribution summaries.
• Literature analysis when available.
• Contest deadline, implementation language, interpretability needs, and compute limits.
• planning/session_config.json.
• Existing methods/Qx/qx_method_card.md and decision ledger when revising.

Workflow

1. Align the decision surface.

   • Invoke decision-prompt-builder before generating an open-ended shortlist.
   • Ask about human-owned trade-offs, not algorithm names.
   • Reuse answers already present in the decision ledger.

2. Derive method requirements.

   • Start from required output, hard constraints, data characteristics, validation criteria, explanation burden, and experiment budget.
   • Identify the failure modes that would make a method unusable.

3. Create a role-based shortlist.

   • One main_candidate: best fit to the chosen trade-off.
   • One usable_baseline: completes the real task and yields directly comparable outputs.
   • At most one conditional_fallback: differs in a meaningful mathematical way and has an explicit activation trigger.
   • If a simple reference cannot complete the real task, label it diagnostic_reference; it does not satisfy the baseline requirement.
   • Do not add a method merely to reach a candidate count.