{
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  "source": "vibemath",
  "problem_id": "vibemathed:dimer-constant-cubic-lattice",
  "title": "The Dimer Constant of the Cubic Lattice",
  "canonical_statement": "The dimer constant of $\\mathbb{Z}^3$, the exponential growth rate of perfect matchings of the cubic lattice, has no closed form and is pinned only by bounds. The upper bound improves from Lundow's $0.457547$, standing since 2001, to $0.452130$, via diagonal transfer layers and an inequality of Csikvari relating the spectral radius of the transfer matrix to the constant.",
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      "status": "partial",
      "occurred_at": "2026-07-30T00:00:00.000Z",
      "title": "arXiv:2607.28810 - A new upper bound on the dimer constant of Z^3",
      "summary": "a record upper bound; the exact constant remains unknown",
      "ai_contribution": "ai_co_developed",
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      "provider": "OpenAI",
      "attempted_at": "2026-07-30T00:00:00.000Z",
      "human_collaborators": [
        "Qidong He"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The acknowledgement attributes the paper's two key ingredients to the model: the diagonal transfer layers, which replace the symmetry argument special to the rectangular torus, and the connection with Csikvari's inequality.",
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    {
      "label": "VibeMathed: The Dimer Constant of the Cubic Lattice",
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    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
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  "generated_at": "2026-09-13T16:28:40.178Z"
}