Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 212-02. Strict convexity and differentiability of the planar exponential first-passage limit shape
Manuscript map · lines 6235–6244
OpenAI@2026-10-07#rem:oai-p-212-02
Authors: OpenAI. Family 212.
Title: Strict convexity and differentiability of the planar exponential first-passage limit shape.
Abstract: We prove that the limit shape of undirected nearest-neighbor first-passage percolation on ℤ2 with independent exponential edge weights is strictly convex and has a C1 boundary. This resolves the strict convexity and differentiability conjectures for the planar exponential model. More generally, we prove differentiability of the time-constant norm for every Gamma edge-weight law with positive shape and rate.
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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