# Percolation criticality research simulator

Family 213: Critical percolation on every quasi-transitive graph. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Network researchers can illustrate the absence of infinite clusters at criticality in the specified infinite quasi-transitive graph class.

## Applicability and commercial boundary

An infinite cluster event is different from a finite network reliability objective; the statement does not supply finite size thresholds, critical values or error bars.

## Initial business decision

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

## Next verification action

Choose a finite approximation with a separately justified scaling study.

## 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

[Critical bond and site percolation on the cubic lattice](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Critical-bond-and-site-percolation-on-the-cubic-lattice-September-24-2026/paper.pdf).