Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 229-02. A Capacity Criterion for Four-State Potts Reconstruction on Trees
Manuscript map · lines 6785–6794
OpenAI@2026-10-07#rem:oai-p-229-02
Authors: OpenAI. Family 229.
Title: A Capacity Criterion for Four-State Potts Reconstruction on Trees.
Abstract: For the ferromagnetic four-state broadcast model with $0{}lt {}lambda{}lt 1$, we prove that reconstruction on a bounded-degree deterministic rooted tree occurs exactly when its L3 capacity with edge resistances ${}lambda{}{-2|e|}$ is positive. This gives an exact criterion without regularity or growth-rate assumptions on the tree, including at the exponential critical boundary.
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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