{
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  "source": "vibemath",
  "problem_id": "vibemathed:brezis-mironescu-circle-minimizers",
  "title": "Brezis-Mironescu Open Problems 23 and 24 on Minimizing Maps to the Circle",
  "canonical_statement": "For $s \\in (1/4,1)$ and any degree, the only $W^{s,1/s}$-minimizers among maps $\\mathbb{S}^1 \\to \\mathbb{S}^1$ are Blaschke products. This resolves Open Problems 23 and 24 of Brezis and Mironescu's book on mappings to the circle, and Brezis's Favorite Open Problem 5.4 in the same range of $s$.",
  "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",
  "solution_events": [
    {
      "id": "vibemathed:brezis-mironescu-circle-minimizers:event",
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      "type": "proved",
      "status": "partial",
      "occurred_at": "2026-06-14T00:00:00.000Z",
      "title": "arXiv:2606.15713 - On minimizing W^{s,1/s}-maps between circles",
      "summary": "in the range s in (1/4,1); Brezis's Problem 5.4 outside that range is untouched",
      "ai_contribution": "ai_assisted",
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      "model": "ChatGPT",
      "provider": "OpenAI",
      "attempted_at": "2026-06-14T00:00:00.000Z",
      "human_collaborators": [
        "Dorian Martino",
        "Katarzyna Mazowiecka",
        "Armin Schikorra"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The LLM usage note says the authors used ChatGPT to assist with conceptualization and computations, with all mathematical validation their own.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Brezis's Open Problem 5.6, also settled with AI in July 2026, arXiv:2607.23598",
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        }
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          "license": null
        },
        {
          "label": "VibeMathed: Brezis-Mironescu Open Problems 23 and 24 on Minimizing Maps to the Circle",
          "url": "https://vibemathed.com/problem/brezis-mironescu-circle-minimizers",
          "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: Brezis-Mironescu Open Problems 23 and 24 on Minimizing Maps to the Circle",
          "url": "https://vibemathed.com/problem/brezis-mironescu-circle-minimizers",
          "kind": "source-assertion",
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          "label": "arXiv:2606.15713 - On minimizing W^{s,1/s}-maps between circles",
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  "sources": [
    {
      "label": "arXiv:2606.15713 - On minimizing W^{s,1/s}-maps between circles",
      "url": "https://arxiv.org/abs/2606.15713",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Brezis-Mironescu Open Problems 23 and 24 on Minimizing Maps to the Circle",
      "url": "https://vibemathed.com/problem/brezis-mironescu-circle-minimizers",
      "kind": "source-assertion",
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  "opportunity_signals": [
    {
      "id": "vibemathed:brezis-mironescu-circle-minimizers:signal:recent_partial_result",
      "problem_id": "vibemathed:brezis-mironescu-circle-minimizers",
      "kind": "recent_partial_result",
      "reason": "A source-reported partial result may support bounded expansion.",
      "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"
}