This page collects mathematical notes whose main proof arguments were generated using AI systems. My collaborators (where applicable) and I make these notes available because their mathematical content may be useful, but we do not consider our contributions to their development sufficient to claim authorship. I maintain this collection as curator rather than author.
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An elementary extension of the Rogers–Zong translative covering estimate, using additive combinatorics and lattice discretization. Recovers Gorodzha's illumination bound and gives an upper bound with exponential base 3 for the covering index of arbitrary convex bodies.
A further exponential improvement, with a claimed base below 1.166374, using a common self-dual cone, Gaussian transport, and matrix constraints on Hermite moments. Includes a Python program for the numerical certificates.
Read the note (PDF) LaTeX source (.tex) Numerical certificate (.py)
An elementary improvement of the classical exponential upper bound for Borsuk's partition number.