OpenAI reports a conditional quenched near-critical Voronoi limit

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.

Sources for this record

What was already known

The triangular-lattice near-critical scaling limit and critical Poisson–Voronoi box-crossing and quenched concentration estimates were known. A scalar critical crossing formula alone did not identify the joint conditional threshold process under one monotone coupling.

AI involvement AI-led

OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.

OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.

Importance Notable

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

Limitations

The theorem explicitly assumes the scalar critical Voronoi Cardy formula, supplied in a companion manuscript; this record does not claim an unconditional result. Each model uses its own deterministic mean-pivotal normalization, and the Poisson convergence is in probability over geometries. No completed independent check was documented.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.

Correction and publication history

2026-10-18 · publication

Primary manuscript, attribution, prior-work, and precise Lean-scope or conditional-input review for non-notifying local inclusion.

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