{"id":"openai-math/Cylinder-amplitudes-and-logarithmic-bridge-length-windows-on-the-honeycomb-lattice","pdf":"https://github.com/openai/math/blob/main/preprints/Cylinder-amplitudes-and-logarithmic-bridge-length-windows-on-the-honeycomb-lattice-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Cylinder-amplitudes-and-logarithmic-bridge-length-windows-on-the-honeycomb-lattice-September-26-2026","tags":["self-avoiding-walks","lattice-models","statistical-mechanics"],"score":0,"title":"Cylinder amplitudes and logarithmic bridge-length windows on the honeycomb lattice","domain":"Probability and statistical mechanics","family":"237","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove a logarithmic window of critical honeycomb bridge lengths: summed through height $`2h(\\log h)^{1/64}`$, bridges of lengths between $`h^{4/3}(\\log h)^{-1/8}`$ and $`2h^{4/3}(\\log h)^{1/2}`$ have mass at least $`h^{3/4}(\\log h)^{-C}`$.","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"}