Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 215-04. Sharp mass bounds for the two-dimensional O(4) model
Manuscript map · lines 6305–6314
OpenAI@2026-10-07#rem:oai-p-215-04
Authors: OpenAI. Family 215.
Title: Sharp mass bounds for the two-dimensional O(4) model.
Abstract: 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 continuum spectral interpretation requires separate convergence hypotheses for the transfer semigroup and the block observables.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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