Lower Bounds for Multivariate Independence Polynomials
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.
Context
Extends a result of Tao to the multivariate hard-core model, a documented question at the combinatorics and statistical physics boundary, specialist in reach.
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"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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machine: partially checkedscope Lean formalization of the core argument; statement correspondence not independently audited
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.
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