lean artifact · pending
Artifact ↗Source authenticated
The directional zero-one law for random walks in iid random environments in dimension at least three
Theorem 1.1: for , iid nearest-neighbour rows that are almost surely strictly positive (no uniform lower bound, no moment condition) and any fixed real , . The October companion extends the law to stationary ergodic finite-range-dependent environments under uniform ellipticity, and the family's ballisticity paper gives, for uniformly elliptic iid environments in , the hemisphere description of the transient directions. Not shown: ballisticity or a velocity under strict ellipticity alone, jumps beyond nearest neighbours, or general mixing environments (where the law fails by Bramson-Zeitouni-Zerner).
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 23, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: The directional zero-one law for random walks in iid random environments in dimension at least three · Directional zero-one law for RWRE
Confidence: Not scored
Registry verification: lean checked · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
lean artifact · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
VibeMathed record: The directional zero-one law for random walks in iid random environments in dimension at least three evidence for this event
This event attributed to Unreleased internal OpenAI model
Lean proof module (OAI.DirectionalZeroOne.directional_zero_one) evidence for this event
Theorem 1.1: for , iid nearest-neighbour rows that are almost surely strictly positive (no uniform lower bound, no moment condition) and any fixed real , . The October companion extends the law to stationary ergodic finite-range-dependent environments under uniform ellipticity, and the family's ballisticity paper gives, for uniformly elliptic iid environments in , the hemisphere description of the transient directions. Not shown: ballisticity or a velocity under strict ellipticity alone, jumps beyond nearest neighbours, or general mixing environments (where the law fails by Bramson-Zeitouni-Zerner). parent of this event
The directional zero-one law for random walks in iid random environments in dimension at least three parent of this event
Companion: A directional zero-one law for finite-range-dependent random environments evidence for this event
The directional zero-one law for random walks in iid random environments in dimension at least three evidence for this event
Comparator statement: DirectionalWalk.lean evidence for this event
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