Proves that the standard sine map on the two-dimensional torus has positive metric entropy with respect to area for every sufficiently large positive parameter. This establishes Sinai's positive-parameter-measure conjecture for the original family, with the stronger conclusion of a full parameter tail. (Lean)
Manuscript
Positive Metric Entropy for the Standard Map at Large Parameters
September 23, 2026 · source · cite as \cite{OAI:Positive-Metric-Entropy-for-the-Standard-Map-at-Large-Parameters-September-23-2026}
We prove that the standard sine map of the two-dimensional torus has positive metric entropy with respect to normalized area for every sufficiently large positive parameter. This gives a full parameter tail, and hence answers Sinai's positive-parameter-measure conjecture affirmatively.
Result 146 · Dynamical systems and ergodic theory. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md