{
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  "problem_id": "vibemathed:multiway-cut-rounding-records",
  "title": "Improved Approximation Ratios for Multiway Cut",
  "canonical_statement": "New upper and lower bounds on the approximation ratio achievable for Multiway Cut via large mixtures of new and old rounding schemes for the CKR relaxation, advancing the ratio ladder that has run since Călinescu-Karloff-Rabani (1998).",
  "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": "2026-03-30T00:00:00.000Z",
      "title": "arXiv",
      "summary": "Record bounds on the ratio; the exact approximability of Multiway Cut remains open.",
      "ai_contribution": "ai_assisted",
      "attempt_ids": [
        "vibemathed:multiway-cut-rounding-records:attempt"
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      "provider": "OpenAI",
      "attempted_at": "2026-03-30T00:00:00.000Z",
      "human_collaborators": [
        "Joshua Brakensiek",
        "Neng Huang",
        "Aaron Potechin",
        "Uri Zwick"
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      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "\"We acknowledge help from ChatGPT while writing the code for discovering new rounding schemes and while preparing some of the plots. We emphasize that we did not use ChatGPT or any other LLM model while writing our verification code.\"",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2603.28700",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Improved Approximation Ratios for Multiway Cut",
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      "sources": [
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          "label": "VibeMathed: Improved Approximation Ratios for Multiway Cut",
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          "kind": "source-assertion",
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          "label": "arXiv",
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          "kind": "primary-mathematical-source",
          "license": null
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    {
      "label": "arXiv",
      "url": "https://arxiv.org/abs/2603.28700",
      "kind": "primary-mathematical-source",
      "license": null
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    {
      "label": "VibeMathed: Improved Approximation Ratios for Multiway Cut",
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      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
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    {
      "id": "vibemathed:multiway-cut-rounding-records:signal:recent_partial_result",
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      "kind": "recent_partial_result",
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      "generated_at": "2026-09-13T16:28:40.178Z"
    }
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    "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"
}