Scale-space maximal filter regularity audit

Family 085: Endpoint Sobolev regularity of centered disk averages. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Image-analysis researchers can study whether a centered-disk maximal operator respects a specified total gradient budget.

Applicability and commercial boundary

The theorem concerns real W1,1 functions and an unspecified absolute constant, with local W1,1 membership. Pixel disks, image boundaries and finite filters require separate analysis.

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

Inspect the constant and test a continuum-compatible fixture with a finite-discretization study.

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.

An Endpoint Gradient Bound for the Centered Disk Maximal Operator.