MathModeling-skills

At a judgment point, emit the 2-3 questions only the human modeler can answer — framed as trade-offs, not answers — and refuse to answer them. The inverse of "AI answers, human confirms": here the AI asks, the human answers, then the AI assists with the consequences.

Manage the full mathematical modeling contest workflow and decide which skill should be used next.

Verify every skill that claims "completed" produced a substantive audit/review artifact on disk with ≥ 5 explicit pass items. Runs as part of the independent audit layer that does not trust any single skill's self-declaration of done.

Plan figures and tables that support the modeling logic, results, and paper narrative.

Generate publication-quality mathematical modeling figures with matplotlib, covering evaluation charts, prediction plots, optimization diagrams, mechanism schematics, heatmaps, and multi-panel layouts. Use when creating or revising figures for contest papers.

Extract, organize, and document unified model assumptions from the problem parse and candidate method pools, distinguishing necessary from simplifying assumptions.

Write mathematical modeling paper sections based only on available problem analysis, model plans, results, figures, and robustness reports.

Classify each subquestion into standard mathematical modeling problem types.

Parse a mathematical modeling problem into goals, objects, constraints, data, outputs, and subquestions.

Audit cross-media consistency of numbers, file names, symbols, and parameters across tex/code/results/data/appendix. Runs as an independent audit layer that does not trust any single skill's self-declaration of "done".

Help the modeler write a comprehensive final method explanation document that justifies the selected method, documents eliminated alternatives, defines assumptions, symbols, objectives, and solution steps for paper writing.

Generate multi-method experiment reports and final result analysis from model experiment outputs, comparing methods and providing actionable feedback for modelers and paper writers.

Design and run robustness, sensitivity, error, and baseline comparison checks.

Integrate the modeler's final method explanation and the programmer's final result analysis into a single comprehensive writer-facing solution package that the paper writer can directly use to draft paper sections.

Collect, stamp, and freeze the human modeler's decisions into one canonical per-subquestion decision log. The decision version of frozen_numbers.json — it does NOT originate decisions, it makes the human's judgments traceable, append-only, and the single source every downstream narrative is transcribed from.

Compare 2-4 candidate modeling schemes for each subproblem and recommend one execution route based on task type, data, interpretability, literature analysis, and contest constraints.

Audit, clean, summarize, and prepare contest data for modeling.

Review, debug, and verify MATLAB or Beita Tianyuan compatible modeling code against the validated method plan and expected artifacts.

Review, debug, and verify Python modeling code against the validated method plan and expected artifacts.

Audit the complete mathematical modeling solution before final submission and identify blocking issues.

Detect the language of generated modeling code and route review work to the Python or MATLAB reviewer without producing a separate saved artifact.

Generate executable MATLAB or Beita Tianyuan compatible modeling code from a validated method plan and cleaned data.

Polish mathematical modeling paper drafts for grammar, clarity, formula consistency, hedging calibration, overclaim detection, and contest formatting compliance. Use after paper-section-writer has drafted sections.

Generate executable Python modeling code from a validated method plan and cleaned data.

Manage and verify references for mathematical modeling contest papers, generating BibTeX entries, checking citation completeness, and ensuring all references are traceable to actual sources.

Build and maintain a unified global symbol table for all subquestions, ensuring consistent notation across the entire mathematical modeling solution.

Translate a validated method plan into language-neutral code logic, folder layout, and handoff notes before Python or MATLAB code generation.

Collect and analyze relevant papers, reports, and reference methods to inform method selection without fabricating references or copying models blindly.