{"id":"openai-math/Signed-cylinder-propagation-and-marked-polygons-on-the-honeycomb-lattice","pdf":"https://github.com/openai/math/blob/main/preprints/Signed-cylinder-propagation-and-marked-polygons-on-the-honeycomb-lattice-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Signed-cylinder-propagation-and-marked-polygons-on-the-honeycomb-lattice-September-26-2026","tags":["statistical-mechanics","percolation","honeycomb-lattice","critical-phenomena"],"score":0,"title":"Signed cylinder propagation and marked polygons 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":"At the critical activity and loop fugacity two, we prove a 1/6 partition exponent for disjoint honeycomb polygons separating opposite marks on a balanced infinite cylinder, and a 1/12 planar nesting exponent. For ordered first-exit chords in a regular hexagon of side R , with both boundary ports summed and diameter at least $`R/10`$, the finite critical partition is $`R^{3/4+o(1)}`$ and the normalized mean length is $`R^{4/3+o(1)}`$. A separate two-bond estimate on tilted cylinders with controlled site proportions bounds the length-square mass of planar polygons of diameter at most H ,…","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"}