proof-obligation-and-assumption-audit

name	proof-obligation-and-assumption-audit
description	Use when checking mathematical paper results for assumptions, quantifiers, domains, dependency fit, edge cases, external theorem use, proof coverage, or theorem-to-claim consistency.

Proof Obligation And Assumption Audit

Audit whether a mathematical result is supported by its stated assumptions, dependencies, and proof coverage. This is a writing review, not automated theorem proving: it identifies obligations and risks that paper prose must not hide.

Inputs

• Theorem, proposition, lemma, corollary, algorithm guarantee, or experiment claim under review.
• Proof sketch or proof text, definitions, notation ledger, cited external results, and relevant source notes.
• Optional venue standards or reviewer comments.

If proof material is unavailable, mark the result provisional instead of rewriting it as proved.

Output Contract

Return a proof-obligation table with:

Field	Meaning
result	The theorem, lemma, proposition, or claim under review
assumptions	Quantifiers, domains, regularity, constraints, and boundary conditions
dependencies	Definitions, previous results, external theorems, experiments, or algorithms used
obligation	What the proof must establish or verify
coverage	covered, partial, missing, conflicting, or unclear
risk	Meaning-preserving issue, missing case, overclaim, citation-fit risk, or notation risk
action	Keep, soften, split, add assumption, cite precisely, prove, verify, or ask human

Workflow

1. Restate the result with all quantifiers, domains, and assumptions visible.
2. List proof obligations: existence, uniqueness, invariance, convergence, optimality, bounds, limiting cases, case splits, and dependency conditions.
3. Check every cited external theorem against its original assumptions and conclusion strength when sources are available.
4. Compare proof coverage to obligations; mark missing or partial cases without patching the mathematics.
5. Suggest wording changes only when they preserve the verified mathematical meaning.

Review Rules

• Do not strengthen a theorem to match the desired contribution.
• Do not weaken or drop assumptions without checking proof dependencies.
• Keep empirical evidence, heuristic arguments, conjectures, and formal proof status separate.
• Route notation conflicts to notation-and-variable-consistency before making semantic judgments that depend on symbols or dimensions.