# Graph null-model motif counterexample audit

Family 161: Counterexamples to Sidorenko’s conjecture and the forcing conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Network researchers can test whether an asserted motif-density comparison or quasirandomness certificate incorrectly relies on a universal conjecture.

## Applicability and commercial boundary

The counterexample uses a specific 35-vertex bipartite pattern and graphon law; it does not refute all motif-based diagnostics.

## 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 the graphon/pattern data and design a controlled false-certificate fixture.

## 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).

[A counterexample to Sidorenko's conjecture](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-counterexample-to-Sidorenkos-conjecture-September-23-2026/paper.pdf).