Hyperbolic surfaces with large systoles in every large genus

Limit-infimum constant improved to one

Model / AI: GPT-5.6 Sol

Yifei Cai reports that GPT-5.6 Sol developed the first complete proof within Cai's constant-twist pants-decomposition framework. The note constructs surfaces with systole at least log g minus 12 log log g, improving the previously stated asymptotic lower-bound constant from 2/9 to 1.

Source read 2026-09-08. Read the abstract, theorem and AI-use declaration in arXiv v1. The proof was not independently checked.

• Paper — Paper