# Voronoi critical crossing calibration

Family 224: Critical and quenched near-critical universality for Poisson–Voronoi percolation. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Percolation researchers can compare annealed crossing probabilities and quenched threshold laws using each model's own pivotal normalization.

## Applicability and commercial boundary

Expected pivotal counts and environment averaging are not interchangeable with single-sample finite risk estimates. No explicit finite-size accuracy follows from convergence alone.

## Initial business decision

Research infrastructure. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Measure pivotal normalization cost and identify a finite-size comparison with uncertainty estimates.

## Evidence scope

The catalog statement was individually reviewed. This record does not imply a manuscript proof review or formal-scope comparison. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[From critical crossings to quenched near-critical universality in Voronoi percolation](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/From-critical-crossings-to-quenched-near-critical-universality-in-Voronoi-percolation-October-5-2026/critical-crossings-quenched-near-critical-universality-voronoi-percolation.pdf).