{
  "id": "2025-10-27-nesterov-point-convergence",
  "slug": "nesterov-point-convergence",
  "recordState": "queued",
  "canonicalUrl": "https://stateofproof.org/dockets/nesterov-point-convergence",
  "url": "https://stateofproof.org/dockets/nesterov-point-convergence",
  "field": "Optimization",
  "claim": "The stated Nesterov accelerated-gradient iterates converge to a minimizer for every L-smooth convex objective with a minimizer",
  "notice": "Queued record · four gates mapped · no examination route has run",
  "summary": "The locked v2 manuscript claims point convergence of the Nesterov iterates, not merely convergence of objective values. Four load-bearing gates are mapped from the recurrence and energy inequality through the unique-cluster-point argument. No gate has run.",
  "scope": "The examination target is Theorem 3.5 in arXiv v2 under its stated finite-dimensional assumptions. The withdrawn v1 side claim, infinite-dimensional extensions, FISTA, OGM, and other damping regimes are outside this docket.",
  "evidencePacketUrl": null,
  "evidenceRelease": null,
  "publicMeaning": {
    "plainEnglish": "The manuscript studies a specified accelerated optimization method and claims that its sequence of proposed answers converges to an actual minimizer. This is stronger than showing only that the objective values approach the best possible value.",
    "ifHolds": "If the argument holds under its stated assumptions, it would establish point convergence for that particular method and parameter schedule in the specified finite-dimensional setting. It would not automatically extend to other accelerated methods or settings.",
    "potentialConcerns": "The conclusion rests on an exact recurrence, an energy inequality, boundedness, and a final argument that rules out multiple limiting points. No part of that chain has yet been examined in this docket.",
    "ifNot": "If a step fails, weaker conclusions may still be possible, but this manuscript would not have established convergence of the iterates themselves under the stated conditions."
  },
  "sourcePreservation": {
    "state": "version-pinned-primary-source",
    "summary": "The source is pinned to arXiv v2. No separate public Wayback snapshot was found in the read-only availability check.",
    "url": "https://arxiv.org/pdf/2510.23513v2",
    "label": "Versioned arXiv v2 source",
    "sha256": "31dafeda57a8b0f933fbadefe20d32543ca36ea176292dfaf240d179f3b273f0",
    "checkedAt": "2026-08-27",
    "lockedSource": {
      "url": "https://arxiv.org/pdf/2510.23513v2",
      "label": "arXiv 2510.23513v2",
      "version": "arXiv v2",
      "sha256": "31dafeda57a8b0f933fbadefe20d32543ca36ea176292dfaf240d179f3b273f0",
      "locked": "2026-08-26",
      "retrieved": "2026-08-26T20:09:53Z"
    },
    "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": "queued intake record",
    "summary": "Claim map and route plan prepared by Material Shift from the recorded source; no mathematical finding or external review is recorded.",
    "lastUpdated": "2026-08-27",
    "docketId": "2025-10-27-nesterov-point-convergence",
    "canonicalUrl": "https://stateofproof.org/dockets/nesterov-point-convergence",
    "steward": "Material Shift",
    "lastMaterialChange": "2026-08-27",
    "sourceLock": {
      "sha256": "31dafeda57a8b0f933fbadefe20d32543ca36ea176292dfaf240d179f3b273f0",
      "locked": "2026-08-26",
      "retrieved": "2026-08-26T20:09:53Z"
    }
  },
  "routeProvenance": [
    {
      "route": "computational",
      "state": "queued",
      "lastUpdated": "2026-08-26",
      "methodAndProvenance": "Planned Material Shift route derived from the locked v2 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: exact recurrence replay and independent algebraic derivation of the energy inequality."
    },
    {
      "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: source comparison for the cited scalar convergence lemma."
    },
    {
      "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: finite-dimensional convex-analysis review of the cluster-point and common-limit steps."
    }
  ],
  "dependencies": [
    {
      "node": "G1",
      "label": "Recurrence equivalence and discrete energy inequality",
      "deps": "locked v2 assumptions",
      "status": "claim-mapped"
    },
    {
      "node": "G2",
      "label": "Boundedness of the auxiliary and NAG sequences",
      "deps": "G1",
      "status": "claim-mapped"
    },
    {
      "node": "G3",
      "label": "Scalar convergence bridge and all tₖ hypotheses",
      "deps": "G2",
      "status": "claim-mapped"
    },
    {
      "node": "G4",
      "label": "Unique cluster point and common xₖ,yₖ limit",
      "deps": "G3",
      "status": "claim-mapped"
    }
  ],
  "findings": [
    "No examination route has run and no mathematical finding has been issued.",
    "Version 2, not version 1 or an invented version 3, is the locked examination target."
  ],
  "openSteps": [
    {
      "field": "Convex optimization",
      "question": "Does the stated recurrence yield the one-step energy inequality under exactly the manuscript's tₖ condition?",
      "why": "Every later boundedness and convergence step depends on this first algebraic gate.",
      "evidence": [
        {
          "route": "computational",
          "note": "planned independent algebraic replay"
        }
      ],
      "scope": "examination not started",
      "docket": "2025-10-27-nesterov-point-convergence"
    }
  ],
  "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": "arXiv v2 locked and four examination gates mapped; no gate run"
    },
    {
      "date": "2026-01-19",
      "type": "source-updated",
      "docket": "v2 published; the withdrawn v1 r∈[1,3) route retained as lineage only"
    }
  ],
  "stewardship": "Selected and maintained by Material Shift as protocol research. No external sponsor or author involvement is recorded for this case."
}