theory-audit - SKILL.md Agent Skill

name: theory-audit description: > Verify mathematical correctness and theoretical soundness of research papers. Checks derivation steps, notation consistency, assumption completeness, convergence arguments, and novelty assessment. Use after theory formulation or when reviewing mathematical content in LaTeX papers. allowed-tools: Read, Grep, Glob, Bash

Theory Audit

Verification Checklist

Run these checks sequentially. STOP at the first CRITICAL failure.

1. Notation Consistency Scan

# Extract all math symbols from LaTeX and check for redefinitions
grep -n '\\mathbf\|\\mathcal\|\\alpha\|\\beta\|\\lambda\|\\eta' workspace/paper/main.tex

Every symbol defined on first use
No symbol used with two different meanings
Vectors/matrices/scalars follow convention (see ieee-latex skill)

2. Derivation Completeness

For each equation block in the paper:

No skipped steps (can you get from Eq.(n) to Eq.(n+1)?)
Each step is mathematically valid
Assumptions required for each step are stated
Edge cases acknowledged (division by zero, empty sets, etc.)

3. Theorem/Lemma Verification

For each theorem or lemma:

All conditions are explicitly stated
Conditions are sufficient (not just necessary)
Proof is complete (no "it can be shown that...")
Connection to the main method is clear

4. Convergence & Stability

Loss function is bounded below
Gradient exists (differentiability stated)
Learning rate conditions stated (if relevant)
Any Lipschitz/smoothness assumptions are justified
Known failure modes acknowledged

5. Novelty Cross-Check

Compare against workspace/logs/literature_kb.json:

Not a trivial re-combination of methods A + B
Clear differentiation from closest existing work
Contribution statement is honest and accurate

Output Format

Write findings to workspace/logs/theory_audit.json:

{
  "timestamp": "...",
  "iteration": N,
  "status": "PASS | WARN | CRITICAL",
  "notation_issues": [],
  "derivation_gaps": [],
  "theorem_issues": [],
  "convergence_concerns": [],
  "novelty_assessment": "CONFIRMED | NEEDS_STRENGTHENING | INSUFFICIENT",
  "score": X  // 1-10
}