# Random-cluster interface reference library

Family 223: Random-cluster interfaces: critical, disordered, thermal, and natural-time scaling. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Random-geometry researchers can compare interface and loop observables to the stated SLE/CLE limits across q regimes.

## Applicability and commercial boundary

Boundary regularity, marked approximations and parameter range matter. Unparametrized or scaling-limit geometry is not a finite image segmentation guarantee.

## Initial business decision

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

## Next verification action

Record exact domain and parameter normalizations with a bounded simulation example.

## 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

[Square-lattice FK interfaces and nested loops for 1 <= q < 4](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Square-lattice-FK-interfaces-and-nested-loops-for-1-leq-q-lt-4-September-23-2026/paper.pdf).