{"id":"openai-math/Marked-polygon-correlations-and-one-arc-bounds","pdf":"https://github.com/openai/math/blob/main/preprints/Marked-polygon-correlations-and-one-arc-bounds-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Marked-polygon-correlations-and-one-arc-bounds-September-26-2026","tags":["percolation","honeycomb-lattice","polygons","probability"],"score":0,"title":"Marked polygon correlations and one-arc bounds","domain":"Probability and statistical mechanics","family":"237","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"At the critical honeycomb vertex activity, the squared-length mass of simple polygons of diameter at most H , counted modulo translations, is at most $`H^{2/3+o(1)}`$. We also prove a quantitative two-mark cylinder estimate and a polynomial one-arc bound uniform even for arbitrarily unequal marked intervals.","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"}