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OpenAI reports a conditional quenched near-critical Voronoi limit

Individual problem

Assuming the scalar, annealed Cardy crossing formula for fair-colored critical Poisson–Voronoi percolation on every bounded Jordan quadrilateral, the jointly coupled near-critical crossing thresholds of rational polygonal quadrilaterals, normalized by each model’s expected number of unit-square color-pivotal sites, have conditional laws that converge in probability over Voronoi tessellations to the triangular-lattice limit.

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OpenAI reports a conditional quenched near-critical Voronoi limit

  • Mathematics

Assuming the scalar, annealed Cardy crossing formula for fair-colored critical Poisson–Voronoi percolation on every bounded Jordan quadrilateral, the jointly coupled near-critical crossing thresholds of rational polygonal quadrilaterals, normalized by each model’s expected number of unit-square color-pivotal sites, have conditional laws that converge in probability over Voronoi tessellations to the triangular-lattice limit.

AI involvementAI-led
ImportanceNotable
Technical verificationReported
Human understandingFew

Understanding the problem

Read the background

Assuming the scalar, annealed Cardy crossing formula for fair-colored critical Poisson–Voronoi percolation on every bounded Jordan quadrilateral, the jointly coupled near-critical crossing thresholds of rational polygonal quadrilaterals, normalized by each model’s expected number of unit-square color-pivotal sites, have conditional laws that converge in probability over Voronoi tessellations to the triangular-lattice limit.

Why it matters

If correct under its stated critical input, transfers near-critical crossing universality from the triangular lattice to typical Poisson–Voronoi geometries.

What counts as progress

Does scalar critical Cardy convergence imply a quenched joint near-critical crossing-threshold limit for Voronoi percolation?

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