Lower Bounds for Multivariate Independence Polynomials
resolvedconfidence 70%
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Precise 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.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement
fidelity, correctness, priority, or novelty.
What AI did
Aletheia (Gemini Deep Think), Harmonic Aristotle
"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.
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.
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.