Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 220-02. A directional zero–one law under strict ellipticity
Manuscript map · lines 6495–6504
OpenAI@2026-10-07#rem:oai-p-220-02
Authors: OpenAI. Family 220.
Title: A directional zero–one law under strict ellipticity.
Abstract: We prove the directional zero–one conjecture for nearest-neighbor random walks in independent and identically distributed strictly elliptic environments on ℤd, d ≥ 3: the probability of escape in each fixed nonzero real direction is zero or one. Only strict positivity of the transition probabilities is required; no uniform lower bound or moment assumption is imposed.
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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