# Hypergraph cover relaxation limitation audit

Family 162: Counterexamples to Ryser’s covering conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Resource-cover modeling teams can flag the specified Ryser or monochromatic tree-cover conjectural guarantee.

## Applicability and commercial boundary

Intersecting partite hypergraphs and large-prime constructions are special. A counterexample does not supply a better cover algorithm or invalidate proven restricted bounds.

## 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 instance and compare actual integral/fractional cover behavior.

## 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).

[Balanced counterexamples to Ryser's conjecture at prime orders](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Balanced-Counterexamples-to-Rysers-Conjecture-at-Prime-Orders-September-27-2026/paper.pdf).