{
  "id": "2026-08-23-alpoge-s6",
  "slug": "alpoge-s6",
  "recordState": "active",
  "canonicalUrl": "https://stateofproof.org/dockets/alpoge-s6",
  "url": "https://stateofproof.org/dockets/alpoge-s6",
  "field": "Complex geometry",
  "claim": "A completed (3,4,∞) modular family gives a compact complex threefold diffeomorphic to S⁶",
  "notice": "Examination underway · two scoped local replays published · headline claim remains unresolved",
  "summary": "The 108-page manuscript claims that a completed (3,4,∞) family of complex two-tori produces a compact complex threefold diffeomorphic to S⁶. Exact finite identities and a stipulated local torsion mechanism have been reproduced locally. Analytic quotient and gluing, relative meridian signs, integral homology, and the headline theorem remain unresolved.",
  "scope": "This first pass covers the page-2 monodromy identities, the conditional arithmetic of Theorem 7.17, a candidate local Kähler-differential torsion channel, and the smallest unresolved geometric and topological gates. It is not a whole-paper validation.",
  "evidencePacketUrl": "https://stateofproof.org/artifacts/alpoge-s6/README.md",
  "evidenceRelease": {
    "provider": "GitHub immutable releases",
    "label": "Immutable release",
    "url": "https://github.com/fremont-materialshift/state-of-proof-records/releases/tag/alpoge-s6-replay-v1.1.0"
  },
  "publicMeaning": {
    "plainEnglish": "The manuscript proposes a way to build a compact three-dimensional complex space whose underlying smooth shape is the six-sphere, S⁶. Some finite calculations have been reproduced, but the construction's key geometric and topological steps have not been independently settled.",
    "ifHolds": "If the full argument holds, it would show that S⁶ carries the claimed complex structure. That consequence depends on the global construction and topology, not on the reproduced local calculations alone.",
    "potentialConcerns": "The unresolved issues include how local pieces are joined, the signs in a crucial topological calculation, and whether the quotient construction works globally. These are load-bearing specialist questions in complex geometry and topology.",
    "ifNot": "If a key step fails, the reproduced matrix identities or local model calculations may still be correct, but they would not establish the claimed complex structure on S⁶."
  },
  "sourcePreservation": {
    "state": "public-archive-found-not-hash-verified",
    "summary": "The public record preserves the canonical URL, retrieval timestamp, byte length, and SHA-256 of the manuscript and cited source. It does not redistribute their source bytes.",
    "url": "https://web.archive.org/web/20260825015231/https://alpo.ge/s6.pdf",
    "label": "Wayback snapshot from 2026-08-25 (not hash-compared)",
    "sha256": null,
    "checkedAt": "2026-08-27",
    "lockedSource": {
      "url": "https://alpo.ge/s6.pdf",
      "label": "108-page source manuscript",
      "version": "retrieved 2026-08-24",
      "sha256": "283bba102dd1d5dc346af81b28145bdaaea6654398d5032e76e97bafb9a858f2",
      "locked": "2026-08-24",
      "retrieved": "2026-08-24T14:30:22Z"
    },
    "formalArtifact": null
  },
  "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": "scoped local replay record",
    "summary": "This docket and its public replay artifacts were prepared by Material Shift from the recorded sources. They are not author-supplied materials, independent verification, peer review, or an external referee report.",
    "lastUpdated": "2026-08-27",
    "docketId": "2026-08-23-alpoge-s6",
    "canonicalUrl": "https://stateofproof.org/dockets/alpoge-s6",
    "steward": "Material Shift",
    "lastMaterialChange": "2026-08-28",
    "sourceLock": {
      "sha256": "283bba102dd1d5dc346af81b28145bdaaea6654398d5032e76e97bafb9a858f2",
      "locked": "2026-08-24",
      "retrieved": "2026-08-24T14:30:22Z"
    }
  },
  "routeProvenance": [
    {
      "route": "computational",
      "state": "completed-local",
      "lastUpdated": "2026-08-28",
      "methodAndProvenance": "Material Shift local replay of manually transcribed finite inputs. It is not an independent verification of the manuscript.",
      "inputs": [
        "locked manuscript SHA-256 283bba…858f2",
        "manual transcription finite-skeleton-v1.json"
      ],
      "performedBy": "Material Shift research workflow",
      "machineAssistance": "AI-assisted analysis and public-record preparation",
      "independentSpecialistReview": "None recorded",
      "artifact": {
        "url": "/artifacts/alpoge-s6/replay-manifest.json",
        "label": "Public replay manifest · finite-skeleton route",
        "sha256": "4aa9216343b689857fdf10584d7fd323c0d46f7ad5468114a17df602f5993511"
      },
      "logPublished": true,
      "publicArtifactUrl": "/artifacts/alpoge-s6/replay-manifest.json",
      "note": "Exact rational and integer replay reproduced the encoded page-2 identities and the conditional Smith arithmetic. The geometry that supplies those inputs was not established."
    },
    {
      "route": "symbolic",
      "state": "completed-local",
      "lastUpdated": "2026-08-28",
      "methodAndProvenance": "Material Shift local custom checker for a stipulated double-crossing model. No independent CAS replay or source-to-model derivation is claimed.",
      "inputs": [
        "locked manuscript and cited-source hashes",
        "stipulated kahler-local-model-v1.json"
      ],
      "performedBy": "Material Shift research workflow",
      "machineAssistance": "AI-assisted analysis and public-record preparation",
      "independentSpecialistReview": "None recorded",
      "artifact": {
        "url": "/artifacts/alpoge-s6/replay-manifest.json",
        "label": "Public replay manifest · local-model route",
        "sha256": "4aa9216343b689857fdf10584d7fd323c0d46f7ad5468114a17df602f5993511"
      },
      "logPublished": true,
      "publicArtifactUrl": "/artifacts/alpoge-s6/replay-manifest.json",
      "note": "A custom exact local-module certificate reproduced a candidate torsion differential inside the stipulated model. Model applicability and the global implication remain open."
    },
    {
      "route": "literature",
      "state": "queued",
      "lastUpdated": "2026-08-24",
      "methodAndProvenance": "A source comparison is recorded as a planned review surface only; no independent literature conclusion is published in this docket.",
      "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": "The printed CDP20 reduction and the manuscript's proposed local mechanism define the comparison surface; specialist source-to-model review is still required."
    },
    {
      "route": "expert",
      "state": "queued",
      "lastUpdated": "2026-08-24",
      "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": "Required next: independent complex-geometric and topological review of the sign, gluing, and integral-topology gates."
    }
  ],
  "dependencies": [
    {
      "node": "S6-C1",
      "label": "Page-2 monodromy identities and exact finite skeleton",
      "deps": "locked matrices",
      "status": "reproduced-in-scope"
    },
    {
      "node": "S6-C2",
      "label": "Candidate local torsion mechanism in the stipulated double-crossing model",
      "deps": "source-to-model applicability",
      "status": "reproduced-in-scope"
    },
    {
      "node": "S6-C3",
      "label": "Relative meridian signs and zero residual toric translation",
      "deps": "local quotient maps",
      "status": "open-dependency"
    },
    {
      "node": "S6-C4",
      "label": "Analytic quotient, freeness, gluing, and collar compatibility",
      "deps": "Theorems 4.5 and 6.2",
      "status": "human-review-required"
    },
    {
      "node": "S6-C5",
      "label": "Integral homology, simple connectivity, and six-manifold recognition",
      "deps": "S6-C3 · S6-C4",
      "status": "human-review-required"
    }
  ],
  "findings": [
    "All encoded page-2 matrix identities and the conditional Theorem 7.17 integer/Smith arithmetic were reproduced locally.",
    "A nonzero local torsion differential was reproduced inside the stipulated double-crossing model; this does not show that the model follows from the manuscript's global hypotheses.",
    "Changing one relative sign changes the candidate fundamental-group parameter from |p|=1 to |p|=7, so the meridian-sign gate is load-bearing.",
    "The headline S⁶ complex-structure claim remains human-review-required. Nothing in this docket is a validation, proof, certification, or referee report."
  ],
  "openSteps": [
    {
      "field": "Complex geometry and topology",
      "question": "Do the two local quotient maps induce the same meridian exponent sign, and does the toric zero-section give μ=0?",
      "why": "The already-passing Smith calculation decides simple connectivity only after these geometric inputs are fixed.",
      "evidence": [
        {
          "route": "computational",
          "note": "both sign branches and their group arithmetic are already encoded"
        }
      ],
      "scope": "specialist geometric trace",
      "docket": "2026-08-23-alpoge-s6"
    },
    {
      "field": "Complex geometry",
      "question": "Do the analytic quotient and gluing steps establish a compact complex threefold with the claimed compatibility?",
      "why": "Finite identities cannot supply freeness, proper discontinuity, convergence, or global gluing.",
      "evidence": [
        {
          "route": "expert",
          "note": "Theorems 4.5 and 6.2 identified as the review surface"
        }
      ],
      "scope": "specialist proof review",
      "docket": "2026-08-23-alpoge-s6"
    }
  ],
  "materialHistory": [
    {
      "date": "2026-08-28",
      "type": "immutable-release",
      "docket": "Replay packet anchored in a GitHub immutable release with a separately downloadable SHA-256 checksum"
    },
    {
      "date": "2026-08-28",
      "type": "privacy-hardening",
      "docket": "Exact interpreter patch, operating system, and architecture removed from the public run metadata"
    },
    {
      "date": "2026-08-27",
      "type": "evidence-packet-published",
      "docket": "Scoped local replay packet published with checkers, declared inputs, captured outputs, hashes, and limitations"
    },
    {
      "date": "2026-08-27",
      "type": "record-provenance",
      "docket": "Record state, source preservation, route provenance, and author-contact state published"
    },
    {
      "date": "2026-08-24",
      "type": "check-reproduced",
      "docket": "Finite matrix identities and conditional Smith arithmetic reproduced locally"
    },
    {
      "date": "2026-08-24",
      "type": "open-step",
      "docket": "Relative meridian signs recorded as the highest-risk next gate"
    },
    {
      "date": "2026-08-24",
      "type": "new-docket",
      "docket": "108-page source locked and five load-bearing gates mapped"
    }
  ],
  "stewardship": "Selected and maintained by Material Shift as protocol research. No external sponsor or author involvement is recorded for this case."
}