{"id":"openai-math/Positive-Metric-Entropy-for-the-Standard-Map-at-Large-Parameters","pdf":"https://github.com/openai/math/blob/main/preprints/Positive-Metric-Entropy-for-the-Standard-Map-at-Large-Parameters-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Positive-Metric-Entropy-for-the-Standard-Map-at-Large-Parameters-September-23-2026","tags":["dynamical-systems","ergodic-theory","hamiltonian-systems"],"score":0,"title":"Positive Metric Entropy for the Standard Map at Large Parameters","domain":"Dynamical systems and ergodic theory","family":"146","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DS","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-23","reactions":{},"discussion":[{"url":"https://www.quantumcalculus.org/positive-entropy-for-standard-map-by-open-ai/#:~:text=The%20September%208%20event%20in%20mathematics","kind":"web","site":"quantumcalculus.org","text":"The September 8 event in mathematics was the solution to a millenium problem. Even more brutal (for me at least) is the October 6 announcement of the solution of hundreds of open mathematics problem s. It is a slaughter house! One of them is the solution of a problem I had been working on for more…","added":"2026-11-03","title":"Positive entropy for Standard Map by Open AI - Quantum Calculus","author":"Oliver Knill"}],"formalized":false,"family_title":"Positive metric entropy for the standard map"}