{
  "id": "2026-07-10-openai-cycle-double-cover",
  "slug": "openai-cycle-double-cover",
  "recordState": "queued",
  "canonicalUrl": "https://stateofproof.org/dockets/openai-cycle-double-cover",
  "url": "https://stateofproof.org/dockets/openai-cycle-double-cover",
  "field": "Graph theory",
  "claim": "Every finite bridgeless undirected graph has a cycle double cover",
  "notice": "Queued record · four gates mapped · no examination route has run",
  "summary": "The three-page manuscript claims the cycle double cover conjecture and ships with a public Lean artifact. Both sources are locked. The first gate is prose-to-Lean statement and definition correspondence; the repository has not been built or mathematically examined in this lab.",
  "scope": "The planned examination covers prose-to-Lean correspondence, a fresh pinned Lean replay, independent reconstruction and finite stress testing of Lemma 2.2, and the exact hypotheses of the cited graph reductions and flow inputs.",
  "evidencePacketUrl": null,
  "evidenceRelease": null,
  "publicMeaning": {
    "plainEnglish": "The manuscript claims that every finite bridgeless undirected graph can have its edges covered exactly twice by a collection of cycles. A Lean formalization is available, but neither its build nor its correspondence to the manuscript has been checked in this docket.",
    "ifHolds": "If the mathematical claim holds, it would establish the stated general graph-theory result. A successful formal check would matter only after confirming that its encoded definitions and theorem match the public claim.",
    "potentialConcerns": "Small differences in definitions—such as the treatment of loops, parallel edges, connectedness, bridges, and cycles—can change what a formal statement covers. The cited reductions and flow results also need their hypotheses checked.",
    "ifNot": "If the proof or its formal correspondence fails, the Lean artifact might still establish a narrower or different statement. It would not by itself settle the advertised theorem."
  },
  "sourcePreservation": {
    "state": "public-archive-found-not-hash-verified",
    "summary": "The manuscript and commit-pinned Lean artifact are separately identified. A public Wayback PDF snapshot was found, but it has not been hash-compared with the locked docket file.",
    "url": "https://web.archive.org/web/20260819160431/https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98d31/cdc_proof.pdf",
    "label": "Wayback PDF snapshot from 2026-08-19 (not hash-compared)",
    "sha256": null,
    "checkedAt": "2026-08-27",
    "lockedSource": {
      "url": "https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98d31/cdc_proof.pdf",
      "label": "Three-page OpenAI manuscript",
      "version": "PDF + Lean 577e9d9",
      "sha256": "b4797f5053d9067329b3dcfcbf913f8bb40d13467453b1300f6d78d08460fc13",
      "locked": "2026-08-26",
      "retrieved": "2026-08-26T20:09:53Z"
    },
    "formalArtifact": {
      "classification": "commit-pinned-artifact",
      "url": "https://github.com/openai/cdc-lean/archive/577e9d9ea326d520f80672ee69b830bf1d513df5.tar.gz",
      "label": "Lean archive at commit 577e9d9",
      "sha256": "1ba9fc60c7cdfd42ab6840d70983a07c101f290fcf5442cd3997c90fcad521ee"
    }
  },
  "authorContact": {
    "state": "no-contact-recorded",
    "summary": "No author outreach, correspondence, response, or author approval is recorded for this docket.",
    "lastUpdated": "2026-08-27",
    "responsePublished": false,
    "response": null,
    "contactUrl": "mailto:team@materialshift.com?subject=State%20of%20Proof",
    "note": "No author response is currently published; the record steward can receive a response or correction request."
  },
  "recordProvenance": {
    "maintainedBy": "Material Shift",
    "recordType": "queued intake record",
    "summary": "Claim map and route plan prepared by Material Shift from the recorded public sources; no mathematical finding or external review is recorded.",
    "lastUpdated": "2026-08-27",
    "docketId": "2026-07-10-openai-cycle-double-cover",
    "canonicalUrl": "https://stateofproof.org/dockets/openai-cycle-double-cover",
    "steward": "Material Shift",
    "lastMaterialChange": "2026-08-27",
    "sourceLock": {
      "sha256": "b4797f5053d9067329b3dcfcbf913f8bb40d13467453b1300f6d78d08460fc13",
      "locked": "2026-08-26",
      "retrieved": "2026-08-26T20:09:53Z"
    }
  },
  "routeProvenance": [
    {
      "route": "formal",
      "state": "queued",
      "lastUpdated": "2026-08-26",
      "methodAndProvenance": "Planned Material Shift route against the pinned public Lean archive; no build or formal replay is recorded.",
      "inputs": [
        "locked source",
        "published claim map"
      ],
      "performedBy": "Not yet run",
      "machineAssistance": "AI-assisted claim mapping and route preparation",
      "independentSpecialistReview": "None recorded",
      "artifact": null,
      "logPublished": false,
      "publicArtifactUrl": null,
      "note": "Planned: fresh Lean 4.31.0 replay, compiled-source scan, axiom closure, and hashed outputs."
    },
    {
      "route": "computational",
      "state": "queued",
      "lastUpdated": "2026-08-26",
      "methodAndProvenance": "Planned Material Shift route derived from the locked source and claim map; no run is recorded.",
      "inputs": [
        "locked source",
        "published claim map"
      ],
      "performedBy": "Not yet run",
      "machineAssistance": "AI-assisted claim mapping and route preparation",
      "independentSpecialistReview": "None recorded",
      "artifact": null,
      "logPublished": false,
      "publicArtifactUrl": null,
      "note": "Planned: independent finite property tests for cubic bridgeless multigraphs and admissible flows."
    },
    {
      "route": "literature",
      "state": "queued",
      "lastUpdated": "2026-08-26",
      "methodAndProvenance": "Planned source-comparison route; no literature conclusion is recorded.",
      "inputs": [
        "locked source",
        "published claim map"
      ],
      "performedBy": "Not yet run",
      "machineAssistance": "AI-assisted claim mapping and route preparation",
      "independentSpecialistReview": "None recorded",
      "artifact": null,
      "logPublished": false,
      "publicArtifactUrl": null,
      "note": "Planned: lock the primary graph-reduction and flow theorems and verify their exact hypotheses."
    },
    {
      "route": "expert",
      "state": "queued",
      "lastUpdated": "2026-08-26",
      "methodAndProvenance": "No specialist report, sign-off, or external review is recorded.",
      "inputs": [
        "locked source",
        "published claim map"
      ],
      "performedBy": "Not yet run",
      "machineAssistance": "AI-assisted claim mapping and route preparation",
      "independentSpecialistReview": "None recorded",
      "artifact": null,
      "logPublished": false,
      "publicArtifactUrl": null,
      "note": "Planned: graph-theorist review of the cycle-decomposition inference and scope correspondence."
    }
  ],
  "dependencies": [
    {
      "node": "G1",
      "label": "Paper-to-Lean statement and definition correspondence",
      "deps": "locked PDF · pinned commit",
      "status": "claim-mapped"
    },
    {
      "node": "G2",
      "label": "Fresh pinned Lean build and kernel replay",
      "deps": "G1",
      "status": "claim-mapped"
    },
    {
      "node": "G3",
      "label": "Independent reconstruction and finite stress tests for Lemma 2.2",
      "deps": "G1",
      "status": "claim-mapped"
    },
    {
      "node": "G4",
      "label": "Cited reductions and nowhere-zero-flow inputs",
      "deps": "primary source hypotheses",
      "status": "claim-mapped"
    }
  ],
  "findings": [
    "No Lean build, replay, or mathematical examination route has run in this lab.",
    "A successful formal build would support only the encoded endpoint; it would not by itself establish correspondence with the prose theorem."
  ],
  "openSteps": [
    {
      "field": "Graph theory and formal verification",
      "question": "Do the Lean definitions and endpoint match the manuscript's advertised theorem across loops, parallel edges, connectedness, bridgelessness, and cycle conventions?",
      "why": "Formal replay is meaningful only after the encoded statement is shown to match the public claim.",
      "evidence": [
        {
          "route": "formal",
          "note": "pinned source available; replay not started"
        }
      ],
      "scope": "examination not started",
      "docket": "2026-07-10-openai-cycle-double-cover"
    }
  ],
  "materialHistory": [
    {
      "date": "2026-08-27",
      "type": "record-provenance",
      "docket": "Record classified as queued; source preservation, route provenance, and author-contact state published"
    },
    {
      "date": "2026-08-26",
      "type": "new-docket",
      "docket": "Manuscript and Lean commit locked; four examination gates mapped; no gate run"
    }
  ],
  "stewardship": "Selected and maintained by Material Shift as protocol research. No external sponsor or author involvement is recorded for this case."
}