# Laughlin model disorder robustness audit

Family 269: Uniform Laughlin gap and stability under bounded scalar disorder. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Quantum Hall researchers can organize perturbation studies around the round-sphere V1 model at filling one third and its claimed uniform scalar-disorder threshold.

## Applicability and commercial boundary

The specific interaction, geometry and projected one-body scalar disorder do not describe every physical sample. Effective thresholds, finite size and Landau-level mixing need separate treatment.

## Initial business decision

Conditional research. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Extract explicit threshold dependence and compare with one finite exact model.

## 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

[Uniform Stability of the Spherical Laughlin Gap](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf).