ai-asset-pricing: Skill for Claude Code

Audit Math Skill

Structured adversarial audit of mathematical content: proofs, derivations, definitions, assumptions, and formal environments. Works on any section containing formal math.

Examples

• /audit-math appendix-a -- full audit of Appendix A
• /audit-math methodology -- audit math content in the methodology section
• /audit-math 200-450 -- audit specific line range in main.tex

Input

The user provides one of:

• A section key (e.g., appendix-a, methodology, results)
• A line range (e.g., 200-450)
• If omitted, scans main.tex for sections containing formal environments and audits the first one found

Workflow

Step 1: Load Context

1. Read .claude/rules/notation-protocol.md for custom commands, core variables, subscript conventions, theorem environment numbering, and math writing rules (if it exists)
2. Read guidance/paper-context.md for key labels, formal environment ordering, and canonical results (if it exists)
3. Read .claude/rules/academic-writing.md for cross-reference style rules and terminology
4. Extract the target section from main.tex using %% BEGIN/END markers (or line range)

Step 2: Inventory Formal Environments

Build a registry of every formal environment in the target section:

• Definitions (\begin{definition})
• Assumptions (\begin{assumption})
• Lemmas (\begin{lemma})
• Propositions (\begin{proposition})
• Corollaries (\begin{corollary})
• Theorems (\begin{theorem})
• Proofs (\begin{proof})
• Remarks (\begin{remark})

For each, record: label, name (from [...] bracket), line number, and which assumptions/results it references.

If notation-protocol.md registers environment numbering, cross-check against it. Flag any missing or extra environments, misordered labels, or mismatched names.

Step 3: Assumption Dependency Audit

For each lemma, proposition, corollary, and theorem:

1. List the assumptions explicitly invoked in the statement (e.g., "Under Assumptions \ref{assum:iid} and \ref{assum:overlap}")
2. List the assumptions actually used in the proof
3. Flag hidden dependencies: assumptions used in the proof but not stated in the result
4. Flag unused declarations: assumptions stated in the result but never invoked in the proof
5. Flag implicit prerequisites: does the result depend on an earlier definition or lemma not cited?
6. Check that assumption references use \ref{assum:...} (not prose descriptions like "the independence assumption")