{
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  "source": "vibemath",
  "problem_id": "vibemathed:nesterov-point-convergence",
  "title": "Point Convergence of Nesterov's Accelerated Gradient Method",
  "canonical_statement": "Nesterov's accelerated gradient method (1983) is a cornerstone of optimization, yet whether its iterates themselves converge to a minimizer, rather than just the function values, stayed open for over forty years. Jang and Ryu resolve it in the affirmative. Ryu first announced the continuous-time result on X; Bot, Fadili and Nguyen's concurrent human proof of the critical-regime case (answering a decade-old conjecture of Attouch and co-authors) explicitly credits that AI-assisted announcement as what it discretizes.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "resolved",
  "solution_events": [
    {
      "id": "vibemathed:nesterov-point-convergence:event",
      "problem_id": "vibemathed:nesterov-point-convergence",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2025-10-27T00:00:00.000Z",
      "title": "arXiv",
      "summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:nesterov-point-convergence:attempt"
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      "id": "vibemathed:nesterov-point-convergence:attempt",
      "problem_id": "vibemathed:nesterov-point-convergence",
      "model": "GPT-5 Pro",
      "provider": "OpenAI",
      "attempted_at": "2025-10-27T00:00:00.000Z",
      "human_collaborators": [
        "Uijeong Jang",
        "Ernest K. Ryu"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The discovery was heavily assisted by ChatGPT (GPT-5 Pro), and the paper documents how: the process was highly interactive, with roughly 80% of generated arguments incorrect but several ideas novel enough to pursue; the working prompt supplied the continuous-time proof in LaTeX and asked for a discrete-time analogue. The authors note that after the result was found, GPT-5 Pro could reproduce a correct proof from a single well-formulated prompt.",
      "failed_routes": [],
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          "license": null
        },
        {
          "label": "Bot-Fadili-Nguyen: concurrent human proof of the critical regime, crediting Ryu's announcement",
          "url": "https://arxiv.org/abs/2510.22715",
          "kind": "independent",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2510.23513",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Point Convergence of Nesterov's Accelerated Gradient Method",
          "url": "https://vibemathed.com/problem/nesterov-point-convergence",
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      "solution_event_id": "vibemathed:nesterov-point-convergence:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "A v2 preprint submitted for journal review; the result triggered immediate follow-up work (Bot-Fadili-Nguyen, and inexact-FISTA extensions) but no formal review has appeared.",
      "sources": [
        {
          "label": "VibeMathed: Point Convergence of Nesterov's Accelerated Gradient Method",
          "url": "https://vibemathed.com/problem/nesterov-point-convergence",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2510.23513",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
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  ],
  "sources": [
    {
      "label": "arXiv",
      "url": "https://arxiv.org/abs/2510.23513",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Point Convergence of Nesterov's Accelerated Gradient Method",
      "url": "https://vibemathed.com/problem/nesterov-point-convergence",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
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  "recommended_exposure": "result_only",
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      "generated_at": "2026-09-13T16:28:40.178Z"
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  "uncertainties": [
    "VibeMath has not independently verified the mathematical claim.",
    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
    "VibeMath has not independently audited the mathematical statement, proof, or novelty claim."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}