{"id":"openai-math/The-curve-scaling-limit-of-half-plane-double-dimers","pdf":"https://github.com/openai/math/blob/main/preprints/The-curve-scaling-limit-of-half-plane-double-dimers-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-curve-scaling-limit-of-half-plane-double-dimers-September-23-2026","tags":["probability","conformal-loop-ensemble","dimers","scaling-limits"],"score":0,"title":"The curve scaling limit of half-plane double dimers","domain":"Probability and statistical mechanics","family":"226","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove that the complete double-dimer loop ensemble for the Temperleyan square lattice in the upper half-plane converges to nested CLE 4 . The convergence holds along the full mesh limit and matches every macroscopic loop as an unparametrized curve. This resolves the half-plane Temperleyan form of the double-dimer CLE 4 scaling-limit conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"The double-dimer loop ensemble converges to CLE 4"}