{"slug":"morankor-codex-math","name":"codex-math","description":"Run an adversarial mathematical workflow in Codex: verify proofs, write hard proofs, explore conjectures, search for counterexamples, and triage possible gaps. Use for important theorem checks, failed proof attempts, conjectures, independent verification, or requests like 'audit this proof', 'find a counterexample', 'explore this claim', or 'verify the math'.","long_description":"---\nname: codex-math\ndescription: \"Run an adversarial mathematical workflow in Codex: verify proofs, write hard proofs, explore conjectures, search for counterexamples, and triage possible gaps. Use for important theorem checks, failed proof attempts, conjectures, independent verification, or requests like 'audit this proof', 'find a counterexample', 'explore this claim', or 'verify the math'.\"\n---\n\n# Codex Math\n\nUse Codex as an adversarial mathematical co-processor. The goal is not to sound convincing; the goal is to separate proved facts, real gaps, false alarms, and promising leads.\n\nTreat every generated argument as a lead, not a verdict. A proof that looks polished can still be false. A reviewer objection can still be a false positive. Triage every finding.\n\n## Mode Selection\n\n- **Verify** when the user provides a proof, theorem, lemma, or paper section and wants an audit.\n- **Write** when the user provides a precise result and asks for a proof.\n- **Explore** when the result may be false, under-specified, or hard enough that counterexample search and sufficient conditions are valuable.\n\nFor high-stakes claims, use two passes: one constructive pass and one hostile pass. In Codex environments that expose subagents, spawn independent verifier/explorer agents only when the user explicitly asks for parallel or independent agents.\n\n## Verify Mode\n\n1. Extract the exact statement, hypotheses, definitions, and proof block.\n2. Build a dependency list: equations, lemmas, citations, domain restrictions, and hidden regularity assumptions.\n3. Walk the proof step by step. Classify each step as:\n   - `OK`: justified by a definition, prior result, explicit algebra, or standard theorem.\n   - `GAP`: a necessary implication is missing.\n   - `ERROR`: the step is false, with a counterexample or algebraic correction.\n   - `UNCLEAR`: the step might be right but needs a missing definition, citation, or convention.\n4. Check signs, dimensions, boundary cases, quantifiers, and whether examples are being used as proof.\n5. Triage findings. Report only issues you can explain concretely.\n\nVerification output:\n\n```markdown\n## Verdict\nPASS | PASS WITH CAVEATS | FAIL | INCONCLUSIVE\n\n## Findings\n1. Severity: blocking | major | minor\n   Location:\n   Issue:\n   Why it matters:\n   Suggested fix:\n\n## Checked\n- Definitions:\n- Algebra/signs:\n- Edge cases:\n- Citations or external results:\n```\n\n## Write Mode\n\n1. Restate the theorem with full domains and quantifiers.\n2. Identify the most likely proof strategy and at least one fallback strategy.\n3. Draft the proof using the `math-proof` discipline: explicit steps, algebra, signs, and edge cases.\n4. Run an adversarial self-audit of the proof before returning it.\n5. Mark any unresolved step as conjectural or open. Do not hide it inside prose.\n\nAfter writing, recommend an independent verification pass for important results.\n\n## Explore Mode\n\nUse when the truth of a claim is uncertain.\n\n1. State the exact conjecture and all domains.\n2. Search for counterexamples before trying to prove the strongest version.\n3. Try special cases only as evidence; never conclude the general result from them.\n4. If the global claim fails, identify the boundary: sufficient conditions, necessary conditions, or a weaker true statement.\n5. Use deterministic computation when useful. For numerical exploration, save code and make the counterexample reproducible.\n\nExploration output:\n\n```markdown\n## Current Status\nLikely true | likely false | true under conditions | unresolved\n\n## Evidence\n- Analytic:\n- Numerical:\n- Counterexamples:\n\n## Next Proof Target\n<the strongest clean statement that appears defensible>\n```\n\n## Prompt Quality Checklist\n\nBefore verifying or exploring, make sure the prompt or extracted context includes:\n\n- the exact claim,\n- all notation and domains,\n- the relevant definitions and equations,\n- what has already been tried,\n- what counts as a valid proof or counterexample.\n\nWhen context is missing, ask for it or explicitly state the assumption you are making.\n","tagline":"Run an adversarial mathematical workflow in Codex: verify proofs, write hard proofs, explore conjectures, search for counterexamples, and triage possible gaps. Use for important theorem checks, failed proof attempts, conjectures, independent verification, or requests like 'audit ","category":"security","tags":["agent-skill"],"author":"morankor","verified":false,"attribution":{"status":"registry_indexed","statusLabel":"Registry indexed","shortLabel":"REGISTRY INDEXED","sourceLabel":"github candidate review","sourceDetail":"morankor/theorist-toolbox","creatorName":"morankor","creatorUrl":"https://github.com/morankor","sourceUrl":"https://github.com/morankor/theorist-toolbox/tree/master/codex/.agents/skills/codex-math","indexedBy":"OpenAgentSkill community index","claimUrl":"https://www.openagentskill.com/skills/morankor-codex-math#claim-this-skill","claimCta":"Claim this skill","trustNote":"This listing was indexed from public sources and is not marked official until a maintainer claim is approved.","publicNote":"Attribution links to the public repository or creator profile. Creators can claim the listing to update ownership signals."},"stats":{"stars":70,"forks":22,"verified_installs":0,"successful_runs":0,"total_outcomes":0,"rating":0,"review_count":0,"quality_score":27.96},"quality":{"score":54,"tier":"review","label":"Needs review","summary":"Inspect the repository carefully before adding it to an agent workflow.","signals":[{"label":"GitHub stars","value":"70","tone":"neutral"},{"label":"Freshness","value":"1mo ago","tone":"positive"},{"label":"Install ready","value":"Yes","tone":"positive"},{"label":"License","value":"MIT","tone":"neutral"}],"warnings":[]},"trust":{"version":"trust-score-v5","score":69,"base_score":77,"outcome_confidence":0,"tier":"review","label":"Sandbox only","summary":"Useful candidate with missing or mixed trust signals. Keep it in an isolated workspace until the outcome loop proves task fit.","recommendedAction":"Run only in a sandbox and compare close alternatives before using it for real work.","decision":{"install_policy":"human_review_before_install","auto_install_allowed":false,"human_review_required":true,"sandbox_first":true,"agent_action":"Compare alternatives before installing.","reasoning":["69/100 Trust Score v5","77/100 Trust Score v4 baseline","Needs more real agent outcomes before unattended install","Install path is missing","Review before production"],"review_required_when":["The workspace contains production secrets, payments, private customer data, or irreversible actions.","The install command requests shell, network, credential, database, or broad filesystem access.","Outcome evidence is missing, recently failed, or required human review.","Production credentials, payments, or irreversible account changes without explicit human review","Sensitive private data before reviewing repository code, license, and permission surface","Automatic installation in a production workspace"]},"dimensions":[{"id":"github_adoption","label":"GitHub adoption","score":48,"weight":0.13,"status":"warn","detail":"70 GitHub stars"},{"id":"repo_activity","label":"Stars/forks activity","score":48,"weight":0.08,"status":"warn","detail":"70 stars, 22 forks; 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issue activity unavailable in current metadata"},{"status":"pass","label":"Recent maintenance","detail":"1mo since push"},{"status":"pass","label":"License clarity","detail":"MIT"},{"status":"pass","label":"README/SKILL.md completeness","detail":"Metadata includes enough usage and workflow context"},{"status":"pass","label":"Dependency/runtime risk","detail":"no major dependency risk hints in public metadata"},{"status":"pass","label":"Install availability","detail":"npx skills add morankor/theorist-toolbox --skill codex-math"},{"status":"pass","label":"Install command safety","detail":"standard package or runtime install path"},{"status":"pass","label":"Permission surface","detail":"no high-risk permission surface in public metadata"},{"status":"pass","label":"Repository evidence","detail":"https://github.com/morankor/theorist-toolbox/tree/master/codex/.agents/skills/codex-math"},{"status":"warn","label":"Review status","detail":"AI review approval is missing"},{"status":"info","label":"Agent Proven outcomes","detail":"No agent outcome data yet"},{"status":"warn","label":"Ownership","detail":"No approved owner claim yet"},{"status":"info","label":"OpenAgentSkill usage","detail":"No local usage activity yet"},{"status":"info","label":"Agent outcomes","detail":"No agent outcome data yet"}],"strengths":["Install path is available","Repository evidence is available","Recently maintained repository","Install command has no obvious high-risk pattern","Outcome loop is ready but needs first real agent run"],"warnings":["AI review approval is missing","Quality score needs review","GitHub adoption: 70 GitHub stars","Stars/forks activity: 70 stars, 22 forks; 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Review the current source before installing.","installSafety":"standard package or runtime install path","permissionSurface":"no high-risk permission surface in public metadata","documentation":"Strong README/SKILL.md context","agentOutcomes":"No agent outcome data yet","agentProvenScore":0,"outcomeConfidence":"0%","installPolicy":"human_review_before_install"},"installReadiness":{"ready":false,"command":null,"policy":"human_review_before_install","label":"Human review before install","notes":["The tracked source changed or could not be synchronized. 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Keep it in an isolated workspace until the outcome loop proves task fit.","recommendedAction":"Run only in a sandbox and compare close alternatives before using it for real work.","decision":{"install_policy":"human_review_before_install","auto_install_allowed":false,"human_review_required":true,"sandbox_first":true,"agent_action":"Compare alternatives before installing.","reasoning":["69/100 Trust Score v5","77/100 Trust Score v4 baseline","Needs more real agent outcomes before unattended install","Install path is missing","Review before production"],"review_required_when":["The workspace contains production secrets, payments, private customer data, or irreversible actions.","The install command requests shell, network, credential, database, or broad filesystem access.","Outcome evidence is missing, recently failed, or required human review.","Production credentials, payments, or irreversible account changes without explicit human review","Sensitive private data before reviewing repository code, license, and permission surface","Automatic installation in a production workspace"]},"dimensions":[{"id":"github_adoption","label":"GitHub adoption","score":48,"weight":0.13,"status":"warn","detail":"70 GitHub stars"},{"id":"repo_activity","label":"Stars/forks activity","score":48,"weight":0.08,"status":"warn","detail":"70 stars, 22 forks; 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