{"id":"openai-math/Uniform-marked-polygon-estimates-and-sharp-finite-bridge-moments","pdf":"https://github.com/openai/math/blob/main/preprints/Uniform-marked-polygon-estimates-and-sharp-finite-bridge-moments-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Uniform-marked-polygon-estimates-and-sharp-finite-bridge-moments-September-26-2026","tags":["statistical-mechanics","random-polygons","honeycomb-lattice","probability"],"score":0,"title":"Uniform marked-polygon estimates and sharp finite bridge moments","domain":"Probability and statistical mechanics","family":"237","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove a uniform bound for critical honeycomb polygons through two axial marks on a periodic staircase. The bound retains an explicit power of the ratio between the period and the marked separation. We also prove sharp finite strip estimates: bridge mass of order h −1/4 , first-length mass at most $`Ch^{13/12}`$, and mass at least $`ch^{-1/4}`$ on bridges with length at least $`ch^{4/3}`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-26","reactions":{},"formalized":false,"family_title":"The three-quarter exponent for honeycomb self-avoiding walk"}