{"id":"openai-math/Cylinder-loop-weights-and-planar-nesting","pdf":"https://github.com/openai/math/blob/main/preprints/Cylinder-loop-weights-and-planar-nesting-September-26-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Cylinder-loop-weights-and-planar-nesting-September-26-2026","tags":["lattice-models","polymers","statistical-mechanics"],"score":0,"title":"Cylinder loop weights and planar nesting","domain":"Probability and statistical mechanics","family":"237","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We determine the growth exponent, at every fixed positive loop fugacity, of the critical honeycomb partition function for disjoint polygons separating two prescribed markers on a balanced cylinder. At fugacity two the cylinder exponent is 1/6; the corresponding planar nesting exponent and middle-strip nesting exponent are 1/12.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-26","reactions":{},"discussion":[{"url":"https://arxiv.org/abs/2610.18089","date":"2026-10-13","kind":"web","site":"arXiv.org","text":"AI has become increasingly helpful in scientific discovery, yet human expert review remains essential for those problems without reliable automated evaluation, posing a fundamental challenge as candidate generation scales beyond available review capacity. This paper studies verification under…","added":"2026-10-24","title":"One-Sided Verification Under Limited Expert Review","author":"Fan Nie, Haotian Ye, Shurui Liu, Zihao Wang et al."}],"formalized":false,"family_title":"The three-quarter exponent for honeycomb self-avoiding walk"}