# Boolean Fourier degree limitation reference

Family 192: Boolean functions violate the square-root degree bound by arbitrary factors. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Learning-theory researchers can test the proposed square-root degree correlation bound against explicit counterexamples.

## Applicability and commercial boundary

Signed aggregate first-order Fourier correlation is not prediction accuracy, feature importance or a general neural-network complexity bound.

## 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 finite explicit Boolean function and compare exact Fourier coefficients.

## 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).

[Unbounded Violations of the Square-Root Degree Bound](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026/Unbounded-Violations-of-the-Square-Root-Degree-Bound-September-26-2026.pdf).