math-reasoning

Mathematical Reasoning Perform rigorous mathematical reasoning and produce publication-quality LaTeX output. Input $0 — Task type: derive , prove , formalize , stats , notation , verify $1 — Context: equation, theorem statement, problem description, or data description Tasks derive — Step-by-step equation derivation Show every intermediate step. Justify each with the rule applied. Box final result with \boxed{} . Number important equations with \label{eq:name} . prove — Formal theorem proof Use appropriate technique: direct, contradiction, induction, construction, or cases. See references/proof-templates.md for LaTeX templates. formalize — Problem setting formalization Convert informal description into formal mathematical framework with: variable definitions, domain/range specifications, assumptions, objective function. stats — Statistical test selection Use the decision tree in references/notation-guide.md to select appropriate tests. Report p-values, effect sizes, confidence intervals. notation — Generate notation table Create a \begin{table} with all symbols used in the paper. Use standard ML notation from references/notation-guide.md . verify — Check mathematical correctness Verify: dimensional consistency, boundary cases, gradient computations, notation consistency across sections. References Standard ML notation + statistical tests: ~/.claude/skills/math-reasoning/references/notation-guide.md Proof templates and theorem environments: ~/.claude/skills/math-reasoning/references/proof-templates.md Rules Define ALL symbols before first use: "Let $\mathcal{X}$ denote..." Use consistent notation throughout the paper Number equations that are referenced later Use \tag{reason} for key derivation steps State assumptions explicitly Cite lemmas and prior results used in proofs