Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 224-02. A Pivotal Amplitude for Voronoi Percolation from Cardy's Formula
Manuscript map · lines 6635–6644
OpenAI@2026-10-07#rem:oai-p-224-02
Authors: OpenAI. Family 224.
Title: A Pivotal Amplitude for Voronoi Percolation from Cardy's Formula.
Abstract: Taking Cardy's conformal crossing formula for critical planar Poisson–Voronoi percolation in every bounded Jordan quadrilateral as an input, we prove that the expected number of color-pivotal cells for a unit-square crossing is asymptotic to a positive constant times ${}varepsilon {}{-3/4}$, where the point intensity is ${}varepsilon {}{-2}$. No rate of convergence in Cardy's formula is required.
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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