Proof Checker: Rigorous Mathematical Verification & Fixing

Systematically verify a mathematical proof via cross-model adversarial review, fix identified gaps, re-review until convergence, and generate a detailed audit report with proof-obligation accounting.

Context: $ARGUMENTS

Constants

• MAX_REVIEW_ROUNDS = 3
• REVIEWER_MODEL = gpt-5.4 via Codex MCP, reasoning effort always xhigh
• REVIEWER_BACKEND = codex — Default: Codex MCP (xhigh). Override with — reviewer: oracle-pro for GPT-5.4 Pro via Oracle MCP. See shared-references/reviewer-routing.md.
• AUDIT_DOC: PROOF_AUDIT.md in project root (cumulative log)
• REPORT_TEX: proof_audit_report.tex (formal before/after PDF)
• STATE_FILE: PROOF_CHECK_STATE.json (for recovery)
• SKELETON_DOC: PROOF_SKELETON.md (micro-claim inventory)

Acceptance Gate (objective, replaces subjective scoring)