{"id":"openai-math/Cap-selected-amplitudes-and-triangle-chords-for-honeycomb-walks","pdf":"https://github.com/openai/math/blob/main/preprints/Cap-selected-amplitudes-and-triangle-chords-for-honeycomb-walks-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Cap-selected-amplitudes-and-triangle-chords-for-honeycomb-walks-September-26-2026","tags":["self-avoiding-walks","honeycomb-lattice","statistical-mechanics"],"score":0,"title":"Cap-selected amplitudes and triangle chords for honeycomb walks","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 fugacity, self-avoiding port-to-port chords in an equilateral lattice triangle of side R , summed over both boundary endpoints and restricted to diameter at least $`R/100`$, have partition sum comparable to R 3/4 and mean length $`R^{4/3+o(1)}`$. We also determine the amplitude selected by two vacuum caps on a cylinder of circumference N and prove that it grows as $`N^{1/6+o(1)}`$.","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"}