Let ω be the smallest real number, such that any two n x n matrices over the complex numbers can be multiplied in O(n^{ω+ε}) field operations, for all ε>0.

We know that ω≥2. OpenAI's latest result, if true, implies that ω≤2.25.

Each option will independently resolve YES once any result here is proved true and has community consensus on its validity. A stronger bound also establishes all weaker listed bounds. Similarly, I will resolve an option as NO if there is an accepted proof of a lower bound ruling it out.

This applies to proofs made publicly available before January 1, 2028. Community consensus may be reached afterward. I expect to resolve the remaining options in early 2028, but may delay resolution if a qualifying proof is still undergoing substantive expert assessment. Options whose claims are not established under these criteria will resolve NO.