{
  "id": "2026-08-01-openai-nonsofic-group",
  "slug": "openai-nonsofic-group",
  "recordState": "queued",
  "canonicalUrl": "https://stateofproof.org/dockets/openai-nonsofic-group",
  "url": "https://stateofproof.org/dockets/openai-nonsofic-group",
  "field": "Group theory",
  "claim": "The unit group of the binary Leavitt algebra L_F₂(1,2) is not sofic",
  "notice": "Queued record · four gates mapped · no examination route has run",
  "summary": "Chapter 3 of OpenAI's updated Ten Advances manuscript claims that the binary Leavitt algebra's unit group is not sofic. The pinned Lean commit predates a substantive prose revision by four days. Paper-to-Lean and version correspondence is therefore the first gate; no build or mathematical examination has run.",
  "scope": "The planned examination covers original-to-revised source lineage, paper-to-Lean correspondence, a fresh pinned formal replay, the exact hypotheses of cited theorems, and an independent specialist reconstruction of the revised proof.",
  "evidencePacketUrl": null,
  "evidenceRelease": null,
  "publicMeaning": {
    "plainEnglish": "The manuscript claims that the group of invertible elements of a particular algebra cannot be approximated by finite models in the sense captured by soficity. The prose was revised after the linked Lean artifact was created, and no formal or mathematical examination has yet run here.",
    "ifHolds": "If the claim holds, it would provide a group that does not have the stated finite-approximation property. That is a mathematical consequence about the defined group, not a conclusion about downstream uses of the algebra.",
    "potentialConcerns": "The first issue is whether the earlier Lean artifact actually matches the revised manuscript's definitions and endpoint. The proof also depends on specialized claims about expanders, group approximations, and the algebra's unit group.",
    "ifNot": "If the revised argument does not hold, the earlier formal artifact may still be relevant to a different statement, but it would not establish the revised public claim without a demonstrated correspondence."
  },
  "sourcePreservation": {
    "state": "archival-reference-found-not-hash-verified",
    "summary": "The manuscript and commit-pinned Lean artifact are separately identified. A dated Wayback reference was found, but availability is intermittent and its bytes have not been hash-compared with the locked docket file.",
    "url": "https://web.archive.org/web/20260807062522/https://cdn.openai.com/pdf/ten-proofs-oai.pdf",
    "label": "Wayback archival reference from 2026-08-07 (availability intermittent; not hash-compared)",
    "sha256": null,
    "checkedAt": "2026-08-27",
    "lockedSource": {
      "url": "https://cdn.openai.com/pdf/ten-proofs-oai.pdf",
      "label": "Updated Ten Advances manuscript",
      "version": "updated 2026-08-06",
      "sha256": "ebc561ab5c53dbd240e17a8fdb6fffeb648591eca85dbfc7466f563638f8c566",
      "locked": "2026-08-26",
      "retrieved": "2026-08-26T20:09:54Z"
    },
    "formalArtifact": {
      "classification": "commit-pinned-artifact",
      "url": "https://github.com/openai/ten-proofs/archive/94bc0feb6a9ff12c7d31d6de640a725c9d43d2b6.tar.gz",
      "label": "Lean archive at commit 94bc0fe",
      "sha256": "540a31b0459bd693ca4f199206c8d8c18865808116fe4d70b0450dcca45f8dbd"
    }
  },
  "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": "2026-08-01-openai-nonsofic-group",
    "canonicalUrl": "https://stateofproof.org/dockets/openai-nonsofic-group",
    "steward": "Material Shift",
    "lastMaterialChange": "2026-08-27",
    "sourceLock": {
      "sha256": "ebc561ab5c53dbd240e17a8fdb6fffeb648591eca85dbfc7466f563638f8c566",
      "locked": "2026-08-26",
      "retrieved": "2026-08-26T20:09:54Z"
    }
  },
  "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: build and kernel-check the pinned Lean target, then keep its result separate from prose correspondence."
    },
    {
      "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: exact-hypothesis table for every load-bearing cited theorem."
    },
    {
      "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: independent group-theory reconstruction of the August 6 proof route."
    }
  ],
  "dependencies": [
    {
      "node": "G1",
      "label": "Paper-to-Lean and August 2/August 6 version correspondence",
      "deps": "original PDF · revised PDF · pinned commit",
      "status": "claim-mapped"
    },
    {
      "node": "G2",
      "label": "Fresh pinned formal replay and axiom closure",
      "deps": "G1",
      "status": "claim-mapped"
    },
    {
      "node": "G3",
      "label": "Cited-theorem hypothesis table",
      "deps": "primary literature",
      "status": "claim-mapped"
    },
    {
      "node": "G4",
      "label": "Independent examination of the revised expander and Leavitt-algebra route",
      "deps": "G1 · G3",
      "status": "claim-mapped"
    }
  ],
  "findings": [
    "No Lean build, replay, or mathematical examination route has run in this lab.",
    "The August 2 Lean commit predates the substantive August 6 manuscript revision, so repository proximity cannot establish correspondence."
  ],
  "openSteps": [
    {
      "field": "Group theory and formal verification",
      "question": "Which exact Lean endpoints, witnesses, and definitions correspond to the revised paper's unit-group claim?",
      "why": "The formal artifact predates the revised proof and may encode a materially different route or endpoint.",
      "evidence": [
        {
          "route": "formal",
          "note": "versioned sources are locked; correspondence examination not started"
        }
      ],
      "scope": "examination not started",
      "docket": "2026-08-01-openai-nonsofic-group"
    }
  ],
  "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": "Updated and original manuscripts plus Lean commit locked; four gates mapped; no gate run"
    },
    {
      "date": "2026-08-06",
      "type": "source-updated",
      "docket": "OpenAI published a substantive Chapter 3 revision; the August 2 Lean commit predates it"
    }
  ],
  "stewardship": "Selected and maintained by Material Shift as protocol research. No external sponsor or author involvement is recorded for this case."
}