Preprint in the OpenAI Math release

Polynomial removal fails for ordered binary matrices

OpenAI

Abstract

We construct a fixed $66 \times 66$ 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.

open until 1 Jan 2028

est. 50% chance this result is independently verified by the end of 2027.

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