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.
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proof attempt · #1
Joonkyung Lee and Jaehyeon Seo, using Aletheia (Gemini Deep Think), Harmonic AristotleThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
"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.
Machine-checked by Lean on #1 · not a person
lean: partially checkedLeanscope 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.
Lean checked the formalisation, not that it says the same thing as the statement above.
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