Multilinear singular-integral reference suite

Family 082: Annular variation and dyadic absolute bounds for the triangular Hilbert transform. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Harmonic-analysis researchers can distinguish maximal truncation, variation and convergence conclusions for the triangular Hilbert transform.

Applicability and commercial boundary

Specific complex L3 inputs, output exponents and r>2 variation do not establish arbitrary nonlinear signal filters or practical computation.

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 a smooth compact-input numerical example with a trusted truncation comparison.

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.

Annular variation of the triangular Hilbert transform at the symmetric point.