{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:hall-ho-heat-flow-conjecture",
  "title": "The Hall-Ho Heat Flow Conjecture for Random Matrices",
  "canonical_statement": "Hall and Ho conjectured how the zeros of the heat-flow-evolved characteristic polynomial of a random matrix behave in the large-$n$ limit. General cases are proved; in particular, for a complex Ginibre matrix the empirical measure of those zeros converges almost surely to the semicircle law.",
  "plain_summary": "VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "partial",
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      "type": "proved",
      "status": "partial",
      "occurred_at": "2026-07-27T00:00:00.000Z",
      "title": "arXiv",
      "summary": "Proves general cases of the conjecture rather than every case.",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
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      "method_family_ids": [
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      "problem_id": "vibemathed:hall-ho-heat-flow-conjecture",
      "model": "ChatGPT Pro 5.5, ChatGPT 5.6 Sol Ultra",
      "provider": "OpenAI",
      "attempted_at": "2026-07-27T00:00:00.000Z",
      "human_collaborators": [
        "Theodoros Assiotis"
      ],
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      "prompt_public": null,
      "outcome": "An unusually direct disclosure: \"In the course of the research presented here I have been using AI tools extensively, most significantly ChatGPT Pro 5.5 and ChatGPT 5.6 Sol Ultra for ideation, technical help, editing and checking the proofs and general editing and proofreading of the manuscript, at the level of a co-author. All mistakes are my own responsibility.\" The phrase \"at the level of a co-author\" is the author's own.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2608.05185",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Hall-Ho Heat Flow Conjecture for Random Matrices",
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          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
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      "solution_event_id": "vibemathed:hall-ho-heat-flow-conjecture:event",
      "level": "unreviewed",
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      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "A preprint, with no independent review.",
      "sources": [
        {
          "label": "VibeMathed: The Hall-Ho Heat Flow Conjecture for Random Matrices",
          "url": "https://vibemathed.com/problem/hall-ho-heat-flow-conjecture",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
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          "label": "arXiv",
          "url": "https://arxiv.org/abs/2608.05185",
          "kind": "primary-mathematical-source",
          "license": null
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      "label": "arXiv",
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      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Hall-Ho Heat Flow Conjecture for Random Matrices",
      "url": "https://vibemathed.com/problem/hall-ho-heat-flow-conjecture",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "expand",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:hall-ho-heat-flow-conjecture:signal:recent_partial_result",
      "problem_id": "vibemathed:hall-ho-heat-flow-conjecture",
      "kind": "recent_partial_result",
      "reason": "A source-reported partial result may support bounded expansion.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "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"
}