Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 213-01. Critical bond and site percolation on the cubic lattice
Manuscript map · lines 6245–6254
OpenAI@2026-10-07#rem:oai-p-213-01
Authors: OpenAI. Family 213.
Title: Critical bond and site percolation on the cubic lattice.
Abstract: We prove that nearest-neighbor Bernoulli bond and site percolation on ℤ3 have no infinite cluster at their respective critical parameters. The proof combines a finite connection inequality for independent hyperedges with a finite-scale extension estimate and an adaptive exploration.
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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