Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 229-01. The Reconstruction Threshold for the Ferromagnetic Four-State Potts Model
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OpenAI@2026-10-07#rem:oai-p-229-01
Authors: OpenAI. Family 229.
Title: The Reconstruction Threshold for the Ferromagnetic Four-State Potts Model.
Abstract: We establish the exact Kesten–Stigum reconstruction threshold for the ferromagnetic four-state Potts broadcast model on every regular d-ary tree with d ≥ 2 and every Poisson Galton–Watson tree of mean d > 0. Reconstruction occurs exactly when $d{}lambda{}2{}gt 1$; we prove nonreconstruction at and below the threshold, including equality. In the Poisson model the whole tree is observed and the reconstruction advantage is averaged without conditioning on survival. The proof uses reproducible exact-arithmetic verification of polynomial inequalities.
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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