No bigeodesics in planar first-passage percolation under a minimum-of-four second-moment condition
Theorem 1.1: if the edge-weight law on has no atoms and the minimum of four independent copies has finite second moment, then almost surely there is no bigeodesic, all paths excluded simultaneously on one probability-one event, with no assumption of differentiability, strict convexity or curvature of the limit shape. The law may be singular continuous, have bounded support or infinite mean. It does not cover laws failing the moment condition, higher dimensions, or directed models.
Exact FrontierDelta
Scope and record
Occurred: Sep 24, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. 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: No bigeodesics in planar first-passage percolation under a minimum-of-four second-moment condition · No bigeodesics in planar FPP
Confidence: Not scored
Registry verification: unreviewed · announcement · partial
Attribution
VibeMathed
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Unreleased internal OpenAI model
model · ai model contributor · OpenAI
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This event attributed to Unreleased internal OpenAI model
No bigeodesics in planar first-passage percolation under a minimum-of-four second-moment condition parent of this event
Strict convexity and differentiability of the planar first-passage limit shape for exponential weights evidence for this event
Companion: No bigeodesics in planar first-passage percolation evidence for this event
Theorem 1.1: if the edge-weight law on has no atoms and the minimum of four independent copies has finite second moment, then almost surely there is no bigeodesic, all paths excluded simultaneously on one probability-one event, with no assumption of differentiability, strict convexity or curvature of the limit shape. The law may be singular continuous, have bounded support or infinite mean. It does not cover laws failing the moment condition, higher dimensions, or directed models. parent of this event
VibeMathed record: No bigeodesics in planar first-passage percolation under a minimum-of-four second-moment condition evidence for this event
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