Problem detail · source-aware
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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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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.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Single-author arXiv preprint; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
a record upper bound; the exact constant remains unknown
Source-reported tools: computation.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.