{"id":"openai-math/Sharp-mass-bounds-for-the-two-dimensional-O4-model","pdf":"https://github.com/openai/math/blob/main/preprints/Sharp-mass-bounds-for-the-two-dimensional-O4-model-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Sharp-mass-bounds-for-the-two-dimensional-O4-model-September-23-2026","score":0,"title":"Sharp mass bounds for the two-dimensional O(4) model","domain":"Probability and statistical mechanics","family":"215","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove sharp mass bounds for the two-dimensional nearest-neighbor $`O(4)`$ model. For all sufficiently large inverse couplings β , the full transfer gap, including rotation-invariant local-observable sectors, is bounded above and below by positive multiples of $`\\sqrt\\beta e^{-\\pi\\beta}`$. We also prove that the model has a unique periodic local limit and a positive full gap at every finite β > 0, resolving the all-temperature lattice mass-generation conjecture for this periodic state. Under the stated cutoff scaling, the mass bounds are uniform in independently fixed physical units. A…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Canonical $`O(3)`$ continuum limit and exact $`O(4)`$ mass asymptotics"}