{"id":"openai-math/Critical-honeycomb-chords-with-prescribed-boundary-endpoints","pdf":"https://github.com/openai/math/blob/main/preprints/Critical-honeycomb-chords-with-prescribed-boundary-endpoints-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Critical-honeycomb-chords-with-prescribed-boundary-endpoints-September-26-2026","tags":["self-avoiding-walks","probability","lattice-models"],"score":0,"title":"Critical honeycomb chords with prescribed boundary endpoints","domain":"Probability and statistical mechanics","family":"237","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"Critical self-avoiding walks between prescribed, macroscopically separated boundary ports of a regular honeycomb hexagon have length $`R^{4/3+o(1)}`$ in probability, where R is the scale of the hexagon. We prove the corresponding statements for half-plane arches, parallel cuts and nonparallel pure cuts. The half-plane law also has mean length $`R^{4/3+o(1)}`$. A separate strip argument gives endpoint mean laws on one density-one set of heights and in an aligned, critically weighted mixture of all even heights in a macroscopic interval.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-26","reactions":{},"formalized":true,"family_title":"The three-quarter exponent for honeycomb self-avoiding walk"}