# Binary waveform spectrum and correlation contract audit

Family 076: Real ultraflat Littlewood polynomials and unbounded binary merit factors. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Radar and communication R&D teams could benchmark binary sign sequences against new flatness targets and separate spectral flatness from autocorrelation objectives.

## Applicability and commercial boundary

The selected formal statements are existential upper-maximum and finite-Lp flatness results, with no effective convergence rate or signing algorithm. They do not cover the latest uniform two-sided flatness headline.

## 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 construction effectiveness and implement exact finite correlation diagnostics before any improved-waveform claim.

## Evidence scope

The catalog statement was individually reviewed. Main-paper abstracts and available selected formal scopes were additionally inspected; explicit effectiveness passages were inspected for 076, 143 and 178. No independent proof verification was run. Pinned source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Ultraflat real Littlewood polynomials](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Ultraflat-real-Littlewood-polynomials-October-5-2026/ultraflat-real-littlewood-polynomials.pdf).