# Binary waveform constraint feasibility audit

Family 179: The circulant Hadamard and Barker-sequence conjectures. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Radar researchers can rule out universal binary Barker-sequence targets beyond the stated finite length set and distinguish them from high-merit-factor designs.

## Applicability and commercial boundary

Aperiodic peak-correlation magnitude at most one, integrated merit factor and circulant orthogonality are different objectives. The result supplies no replacement sequence design algorithm.

## 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

Combine exact correlation fixtures with family 076 while keeping all three objectives distinct.

## 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).

[The circulant Hadamard conjecture](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-circulant-Hadamard-conjecture-September-23-2026/paper.pdf).