Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 214-01. Nonuniqueness of percolation on nonamenable quasi-transitive graphs
Manuscript map · lines 6265–6274
OpenAI@2026-10-07#rem:oai-p-214-01
Authors: OpenAI. Family 214.
Title: Nonuniqueness of percolation on nonamenable quasi-transitive graphs.
Abstract: We prove the bond-percolation nonuniqueness conjecture of Benjamini and Schramm: every infinite connected, locally finite, nonamenable quasi-transitive graph has a nonempty interval of parameters for which Bernoulli bond percolation almost surely has infinitely many infinite clusters. We also prove Hutchcroft's stronger operator-threshold conjecture, establishing $p_c{}lt p_{2{}to2}{}le p_u$.
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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