Proof Checker: Rigorous Mathematical Verification & Fixing

🔒 Do not wrap this skill in /loop, /schedule, or CronCreate. It is verdict-bearing — it judges proof validity across rounds, threading the reviewer's memory from Phase 1 → Phase 3 via codex-reply so the reviewer can check whether a fix actually closed the gap it flagged. An external timer re-enters from the top each tick, starting a fresh thread and losing that memory. Schedule the external wait that precedes it, not the verdict. See shared-references/external-cadence.md.

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-5.5 — Default model for the Codex backend, reasoning effort always xhigh. Manual backend uses whatever model the user chooses, but it must be a non-Claude model — the executor is Claude, so routing the proof review into any Claude product makes Claude judge Claude and voids the cross-model invariant (see shared-references/reviewer-routing.md).
• REVIEWER_BACKEND = codex — Default: Codex MCP (xhigh). Override with — reviewer: oracle-pro for Oracle MCP, or — reviewer: manual for Manual Review MCP. If manual-review MCP is unavailable, stop and print the install command; do not fall back to Codex. See shared-references/reviewer-routing.md.