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Verify candidate proofs with the local proof verification MCP service. Use only when a full candidate proof of the entire problem has been assembled in markdown, and before publishing the final verified blueprint.
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SOC 職業分類に基づく
Screen a decomposition plan by first trying to prove all of its subgoals directly, then identifying the key stuck points if the plan does not fully go through. Use when a decomposition plan is created.
Find relevant math results, constructions, examples, counterexamples, and background references for a statement. Use when you need context for a new problem, supporting references for constructing examples or counterexamples, or external results while proving subgoals.
Validate externally referenced theorems by querying arXiv theorem search first and Codex's built-in web search second. Use when a markdown proof cites statements from external papers.
Verify a markdown proof in the order it is written. Use when the task is to check local correctness, theorem applicability, and reasoning gaps statement by statement through a paper-style proof.
Launch one sub-agent per decomposition plan after direct screening has identified the key stuck points for each plan. Use when all current plans have been screened by direct proving, none fully solves the problem, and parallel recursive work is needed.
Construct candidate counterexamples to test a proposed conjecture, lemma, or intermediate claim by keeping the assumptions true while making the claimed conclusion fail. Use when you are stuck in reasoning and want to see where the assumptions take effect and gain intuition, when a proposed conjecture/claim feels fragile or unproved, or when you want to test whether the assumptions can hold while the claimed conclusion fails.
| name | verify-proof |
| description | Verify candidate proofs with the local proof verification MCP service. Use only when a full candidate proof of the entire problem has been assembled in markdown, and before publishing the final verified blueprint. |
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.
Read:
results/{problem_id}/blueprint.md as pure markdown textresults/{problem_id}/blueprint.md draft as pure text.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.verify_proof_service with:
statement: target informal statementproof: the raw markdown text from blueprint.mdverification_report.summary, critical_errors, gaps, verdict, and repair_hints.verdict is "wrong"verification_report.critical_errors is non-emptyverification_report.gaps is non-emptyresults/{problem_id}/blueprint.md to results/{problem_id}/blueprint_verified.md.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.
verify_proof_servicememory_appendmemory_searchbranch_updatesearch_arxiv_theorems when the verifier identifies a missing lemma or gapAlways persist verification output, including successful checks.