Polynomial removal fails for ordered binary matrices

What OpenAI claims

Disproves polynomial ordered binary matrix removal with one fixed 66×66 zero–one pattern. Matrices can require many binary-entry changes to become pattern-free while their copy density is smaller than every proposed polynomial bound in that distance. Copies preserve row and column orders and match both zeros and ones. (Lean)

Paper

1. Polynomial removal fails for ordered binary matrices

   25 September 2026 · Preprint, not peer reviewed · PDF

   We construct a fixed 66×66 binary matrix for which ordered matrix removal has no polynomial bound. This disproves the polynomial ordered binary matrix-removal conjecture. Ordered copies preserve the separate row and column orders and match both zeros and ones; removal permits changing entries in either direction.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.