VibeMathedMath problems solved by AI

Gaussian Mass Maximality of the Integer Lattice

Regev and Stephens-Davidowitz conjectured that Zn\mathbb{Z}^n maximizes the Gaussian mass ΘL(t)=∑x∈Le−t∥x∥2\Theta_L(t) = \sum_{x \in L} e^{-t\|x\|^2} over stable lattices for every t>0t > 0. The sharp inequality holds for every integral unimodular lattice of rank n≤32n \le 32, with equality only at Zn\mathbb{Z}^n.

Result
Proved(see note)
Status
Partial result
AI contribution
AI-assisted
Method
Argument
Field
Geometry of numbers
Posed by
Oded Regev, Noah Stephens-Davidowitz
Year posed
2017
Years open
9y
Solved
2026-05-31
Model
GPT-5.5 Pro, Claude Opus 4.7
Vendor
OpenAI / Anthropic
Collaborators
Scott Duke Kominers
Verification
Unreviewed
Publication
Preprint
Significance
25 / 100
Disclosed cost
—
Wikipedia
No dedicated article

What was actually shown

integral unimodular lattices of rank at most 32; the general conjecture is open

What the AI did

The disclosure says the models were used for computations, analysis and synthesis in preparing the article, without separating which of the three, so the lowest tier applies.

Verification

Single-author arXiv preprint; not yet peer-reviewed.

Source

arXiv:2606.01347 - A Sharp Reverse Minkowski Inequality for the Gaussian Mass of Integral Unimodular Lattices

Discussion