OpenAI · 215-02 · 2026-10-04 · Probability and statistical mechanics

An Isolated Particle Pole for the Two-Dimensional O(3) Spin Field

preprints/An-Isolated-Particle-Pole-for-the-Two-Dimensional-O3-Spin-Field-October-4-2026

Family 215. Massive continuum limits and exact mass asymptotics for planar $O (n)$ models.

The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.

Read against the standing problems

Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N

Constructs the canonical continuum limit of the two-dimensional nearest-neighbor $O (3)$ model: a non-Gaussian local relativistic theory with a unique vacuum and a positive mass gap. For the square-lattice $O (4)$ model, determines the exact leading asymptotic of the full transfer gap, $m_{lat} (β) \sim 32 e^{π /4 - 1/2} β e^{- π β}$ . The family also proves exponential spin-correlation decay for two-dimensional nearest-neighbor $O (n)$ models with $n \geq 3$ at every positive temperature.

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.

Preprint source and Lean scope

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A Lean scope note is stored for family 215, but it does not name this preprint. It names 215-05. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.