Disproves polynomial ordered binary matrix removal with one fixed 66\times66 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)
Manuscript
Polynomial removal fails for ordered binary matrices
September 25, 2026 · source · Lean formalization available · cite as \cite{OAI:Polynomial-removal-fails-for-ordered-binary-matrices-September-25-2026}
We construct a fixed 66\times66 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.
Result 190 · Combinatorics. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md