OpenAI · 224-01 · 2026-10-05 · Probability and statistical mechanics
From critical crossings to quenched near-critical universality in Voronoi percolation
preprints/From-critical-crossings-to-quenched-near-critical-universality-in-Voronoi-percolation-October-5-2026
Family 224. Critical and near-critical universality for Voronoi percolation.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves Cardy's formula for annealed critical Poisson–Voronoi crossing probabilities in every bounded Jordan quadrilateral. With each model normalized by its own expected unit-square pivotal count, the conditional joint near-critical crossing-threshold laws for rational polygonal quads converge in environment probability to the triangular-lattice reference law. This establishes quenched near-critical universality for crossing thresholds.
Taking Cardy's crossing formula for critical Poisson–Voronoi percolation as an input, we prove a universal joint limit for the near-critical crossing thresholds of rational polygonal quadrilaterals under the monotone coupling. Conditional on the Poisson tessellation, the threshold law converges in probability over tessellations to the same law as on the triangular lattice. Each model is normalized by its own expected number of color-pivotal sites for a unit-square crossing.
Preprint source and Lean scope
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