# SLE fractal-measure normalization reference

Family 230: Exact Hausdorff gauges for SLE. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Random-curve researchers can track the correct Hausdorff gauge and positive finite measure statement for SLE traces.

## Applicability and commercial boundary

The gauge is asymptotic and the curve law is specific. It is not an automatic length estimator for arbitrary coastlines, paths or digital shapes.

## Initial business decision

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

## Next verification action

Inspect numerical gauge estimators and their finite-resolution behavior.

## 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

[An exact Hausdorff gauge for SLE](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-exact-Hausdorff-gauge-for-SLE-September-25-2026/An-exact-Hausdorff-gauge-for-SLE-September-25-2026.pdf).