{"id":"openai-math/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model","pdf":"https://github.com/openai/math/blob/main/preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026/massive-continuum-o3.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-canonical-massive-continuum-limit-of-the-two-dimensional-O3-model-October-4-2026","score":0,"title":"The canonical massive continuum limit of the two-dimensional O(3) model","domain":"Probability and statistical mechanics","family":"215","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We construct a canonical interacting massive continuum limit of the two-dimensional nearest-neighbor $`O(3)`$ model with unit-length spins, no external field, and no topological term. Normalized by susceptibility and second-moment correlation length, the limit exists as the bare coupling tends to infinity through all positive real values, without selecting subsequences. The limiting fields satisfy the Osterwalder–Schrader axioms and have a nonzero connected four-point correlation on separated time supports. Their reconstructed theory has a unique vacuum, a nonzero vacuum complement, and a…","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"}