Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 190. Polynomial removal fails for ordered binary matrices
Family claims › Combinatorics · lines 1303–1308
OpenAI@2026-10-07#rem:oai-190
Disproves polynomial ordered binary matrix removal with one fixed 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.
The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- remark: Remark: Family 155. A counterexample to periodic tiling in dimension three
- remark: Remark: Family 156. Borsuk's conjecture fails in dimension nine
- remark: Remark: Family 157. Counterexamples to the Hadwiger and Colin de Verdi conjectures
- remark: Remark: Family 158. The Euclidean plane cannot be colored with five colors
- remark: Remark: Family 159. Erd (o)s's reciprocal-sum conjecture and quasipolynomial Szemerédi bounds
- remark: Remark: Family 160. Superexponential van der Waerden numbers
- remark: Remark: Family 161. Counterexamples to Sidorenko's conjecture and the forcing conjecture
- remark: Remark: Family 162. Counterexamples to Ryser's covering and Gyárfás's tree-cover conjectures