Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 236-01. The sharp factor-of-IID threshold for the free Ising model on regular trees
Manuscript map · lines 6925–6934
OpenAI@2026-10-07#rem:oai-p-236-01
Authors: OpenAI. Family 236.
Title: The sharp factor-of-IID threshold for the free Ising model on regular trees.
Abstract: For every integer d ≥ 3 and inverse temperature β ≥ 0, the free zero-field ferromagnetic Ising measure on the infinite d-regular tree is a factor of IID exactly when ${}tanh{}beta{}le(d-1){}{-1/2}$. We prove the positive implication, including equality, resolving the conjecture of Nam, Sly and Zhang; the strict converse is known. The spin factor can be chosen to commute with every tree automorphism on every label input.
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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