What was already known
Alon, Fischer, and Newman raised the ordered-matrix testing question, and Alon and Ben-Eliezer formulated the polynomial removal question for forbidden binary patterns.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Disproves the polynomial ordered binary matrix-removal conjecture with a fixed pattern.
Limitations
Rows and columns are ordered separately; copies match zeros and ones, and the normalized edit distance allows changing entries in either direction.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note identifies this selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- One explicit 66×66 binary pattern has no polynomial ordered matrix-removal bound: for every c,C>0 there are binary matrices far from avoiding it but with fewer than c ε^C n^132 induced ordered copies.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision