Verify Proof

Verify Proof

Use the local proof verification service as the canonical verifier before accepting a solution. Do not use this skill for partial proofs, isolated subgoals, or branches that have not yet produced a full proof draft of the whole problem.

Input Contract

Read:

• target theorem statement
• assembled proof blueprint candidate from results/{problem_id}/blueprint.md as pure markdown text
• relevant prior failure reports and branch context

Procedure

1. Read the current results/{problem_id}/blueprint.md draft as pure text.
2. First check that blueprint.md contains a full proof draft of the entire target theorem rather than a partial proof, fragment, or exploratory notes. If it does not, do not call the verifier yet.
3. Call MCP tool verify_proof_service with:
   • statement: target informal statement
   • proof: the raw markdown text from blueprint.md
4. Read verification_report.summary, critical_errors, gaps, verdict, and repair_hints.
5. Return and persist exactly what the verification service returns. Do not rename keys, add keys, or change the JSON structure.
6. Treat the proof as failed if any of the following hold:
   • verdict is "wrong"
   • verification_report.critical_errors is non-empty
   • verification_report.gaps is non-empty
7. Only treat the proof as passed when none of the failure conditions above hold.
8. If the proof passes, rename results/{problem_id}/blueprint.md to results/{problem_id}/blueprint_verified.md.

Output Contract

Append to verification_reports:

{
  "verification_report": {
    "summary": "string",
    "critical_errors": [
      {"location": "", "issue": "detailed description of the issue"}
    ],
    "gaps": [
      {"location": "", "issue": "detailed description of the gap"}
    ]
  },
  "verdict": "string",
  "repair_hints": "string"
}

Persist the verification service response exactly as returned.

If verification fails, revise blueprint.md directly and append to failed_paths when a branch is invalidated.

MCP Tools

• verify_proof_service
• memory_append
• memory_search
• branch_update
• Codex built-in web search and search_arxiv_theorems when the verifier identifies a missing lemma or gap

Failure Logging

Always persist verification output, including successful checks.