# Ordered matrix pattern-sampling limitation audit

Family 190: Polynomial removal fails for ordered binary matrices. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Data-quality researchers can flag overclaims that a few sampled ordered binary patterns guarantee low edit distance to pattern-free data.

## Applicability and commercial boundary

The specific 66-by-66 pattern and worst-case counterexamples do not invalidate all statistical checks. Both zeros and ones and row/column order are essential.

## 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 adversarial fixture and identify a real checker relying on the disproved polynomial relation.

## 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).

[Polynomial removal fails for ordered binary matrices](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Polynomial-removal-fails-for-ordered-binary-matrices-September-25-2026/paper.pdf).