Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 220-03. Directional transience implies ballisticity
Manuscript map · lines 6505–6514
OpenAI@2026-10-07#rem:oai-p-220-03
Authors: OpenAI. Family 220.
Title: Directional transience implies ballisticity.
Abstract: We prove that almost-sure transience in a fixed direction implies a deterministic limiting velocity with positive projection in that direction for nearest-neighbor random walks in independent and identically distributed uniformly elliptic environments on ℤd, d ≥ 2. This resolves the ballisticity conjecture positively.
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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