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
}