{
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  "source": "vibemath",
  "problem_id": "vibemathed:curvature-smoothing-flame-speed",
  "title": "Monotone Slowdown of Turbulent Flame Speed under Curvature",
  "canonical_statement": "Curvature is expected to smooth flame-front wrinkles and so reduce turbulent flame speed, and in two-dimensional shear flows this was proved. In three dimensions it fails: there is a smooth periodic shear flow for which introducing Markstein curvature diffusivity increases the effective flame speed predicted by the level-set G-equation.",
  "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:curvature-smoothing-flame-speed:event",
      "problem_id": "vibemathed:curvature-smoothing-flame-speed",
      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-07-28T00:00:00.000Z",
      "title": "arXiv:2607.25185 - Turbulent Flame Speed Can Increase under Curvature Smoothing",
      "summary": "within the curvature G-equation model, in three dimensions",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:curvature-smoothing-flame-speed:attempt"
      ],
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      ],
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      "id": "vibemathed:curvature-smoothing-flame-speed:attempt",
      "problem_id": "vibemathed:curvature-smoothing-flame-speed",
      "model": "ChatGPT 5.5 Plus",
      "provider": "OpenAI",
      "attempted_at": "2026-07-28T00:00:00.000Z",
      "human_collaborators": [
        "Hung V. Tran",
        "Jack Xin",
        "Yifeng Yu"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The paper devotes a section titled Exploratory Journey Leading to the Proof to this, and says the model played a significant role in developing the proof. Asked directly about monotonicity, several models including this one took the natural route of differentiating the cell problem and applying a maximum principle, which did not work. Once the authors switched to searching for an example with positive derivative, ChatGPT 5.5 Plus suggested the main formal steps leading to the construction: it helped identify promising ansatzes, organize the linearized calculation, and formulate the orbit-average mechanism showing how a positive value could arise. The authors verified, refined and made the ideas rigorous.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
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          "label": "arXiv:2607.25185 - Turbulent Flame Speed Can Increase under Curvature Smoothing",
          "url": "https://arxiv.org/abs/2607.25185",
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          "license": null
        },
        {
          "label": "VibeMathed: Monotone Slowdown of Turbulent Flame Speed under Curvature",
          "url": "https://vibemathed.com/problem/curvature-smoothing-flame-speed",
          "kind": "source-assertion",
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      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "arXiv preprint; not yet peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: Monotone Slowdown of Turbulent Flame Speed under Curvature",
          "url": "https://vibemathed.com/problem/curvature-smoothing-flame-speed",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
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          "label": "arXiv:2607.25185 - Turbulent Flame Speed Can Increase under Curvature Smoothing",
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  "sources": [
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      "label": "arXiv:2607.25185 - Turbulent Flame Speed Can Increase under Curvature Smoothing",
      "url": "https://arxiv.org/abs/2607.25185",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Monotone Slowdown of Turbulent Flame Speed under Curvature",
      "url": "https://vibemathed.com/problem/curvature-smoothing-flame-speed",
      "kind": "source-assertion",
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    {
      "id": "vibemathed:curvature-smoothing-flame-speed:signal:watch_only",
      "problem_id": "vibemathed:curvature-smoothing-flame-speed",
      "kind": "watch_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"
}