{
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  "problem_id": "vibemathed:multivariate-independence-polynomial-bounds",
  "title": "Lower Bounds for Multivariate Independence Polynomials",
  "canonical_statement": "The multivariate independence polynomial is the partition function of the hard-core model with per-vertex fugacities. The paper proves a lower bound extending to the multivariate setting a result Tao proved in the univariate case, and settles a conjectured generalization for a multiaffine version of the semiproper colouring partition function with two proper colours.",
  "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",
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      "occurred_at": "2026-08-05T00:00:00.000Z",
      "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:multivariate-independence-polynomial-bounds:attempt"
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      "model": "Aletheia (Gemini Deep Think), Harmonic Aristotle",
      "provider": "Google DeepMind, Harmonic",
      "attempted_at": "2026-08-05T00:00:00.000Z",
      "human_collaborators": [
        "Joonkyung Lee",
        "Jaehyeon Seo"
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      "prompt_public": null,
      "outcome": "\"The key steps in both proofs were obtained, at least in part, by using Aletheia, a mathematics research agent built upon Gemini Deep Think at Google DeepMind.\" The paper marks where the agent contributed, publishes raw prompts and outputs in a repository, and calls the work a benchmark demonstrating that current models can in part assist with mathematical research. Theorem 1.4 was separately formalized in Lean 4 with Harmonic Aristotle.",
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          "label": "arXiv",
          "url": "https://arxiv.org/abs/2602.02450",
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        {
          "label": "VibeMathed: Lower Bounds for Multivariate Independence Polynomials",
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      "note": "Theorem 1.4 is formalized in Lean 4 using Harmonic Aristotle, with the files public; the rest of the paper is not formalized, and nobody independent has audited the informal-to-formal correspondence.",
      "sources": [
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      "license": null
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      "label": "VibeMathed: Lower Bounds for Multivariate Independence Polynomials",
      "url": "https://vibemathed.com/problem/multivariate-independence-polynomial-bounds",
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    "VibeMath has not independently verified the mathematical claim.",
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  "generated_at": "2026-09-13T16:28:40.178Z"
}