# Directional filtering scale contract

Family 083: Hilbert transforms along Lipschitz directions. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Image-filter researchers could relate Lipschitz direction-field variation to the permitted short integration scale.

## Applicability and commercial boundary

A reciprocal-Lipschitz short scale and continuum L2 bound do not guarantee a finite directional filter has desired visual quality or numerical stability.

## Initial business decision

Research or conditional engineering only until an effective implementation and a recurring buyer problem are identified. No commercial demand or profitability is established. Where a direct product bridge is weak, the legitimate use is a research reference or evidence adapter, rather than a new standalone company.

## Next verification action

Extract constants and compare a discrete filter only under a separately justified approximation.

## Evidence scope

The catalog statement was individually reviewed. The manuscript proof and selected formal statement have not yet been compared in depth for this family. No independent proof verification was run. Pinned source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[A uniform Hilbert transform estimate for Lipschitz directions](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-uniform-Hilbert-transform-estimate-for-Lipschitz-directions-September-25-2026/main.pdf).