Curved-surface Fourier extension reference

Family 077: Fourier restriction for positively curved surfaces. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Wave-analysis researchers can document when diagonal extension bounds apply to smooth positively curved surfaces in three dimensions.

Applicability and commercial boundary

The strict p>3 range, curvature and continuum operator matter. No efficient transform or boundary reconstruction follows directly.

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

Identify an explicit surface and separately justified discretization error.

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.

Elliptic capacity propagation and Fourier restriction to the sphere.