{"id":"openai-math/An-Isolated-Particle-Pole-for-the-Two-Dimensional-O3-Spin-Field","pdf":"https://github.com/openai/math/blob/main/preprints/An-Isolated-Particle-Pole-for-the-Two-Dimensional-O3-Spin-Field-October-4-2026/o3-particle-pole.pdf","url":"https://github.com/openai/math/tree/main/preprints/An-Isolated-Particle-Pole-for-the-Two-Dimensional-O3-Spin-Field-October-4-2026","score":0,"title":"An Isolated Particle Pole for the Two-Dimensional O(3) Spin Field","domain":"Probability and statistical mechanics","family":"215","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We consider the continuum spin field constructed from the nearest-neighbor two-dimensional $`O(3)`$ model by the fixed prescription of the companion paper. We prove that its vector two-point spectral measure has a positive atom corresponding to the lowest mass, separated by a positive gap from all remaining mass support.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-04","reactions":{},"formalized":false,"family_title":"Canonical $`O(3)`$ continuum limit and exact $`O(4)`$ mass asymptotics"}