The matrix multiplication exponent: is omega at most 9/4?

Theorem 1.1: for every $\varepsilon>0$ two complex $n\times n$ matrices can be multiplied with $O_\varepsilon(n^{9/4+\varepsilon})$ arithmetic operations, so $\omega\le9/4$ over $\mathbb C$. The companions prove $\alpha>0.465$ over every field of characteristic zero, $\omega(1,0.709,1)<2.092$, $\omega<2.258$ over all fields outside one uncomputed finite set of positive characteristics, and $\omega<2.371054886006746$ over every field. Not shown: anything about $\omega=2$, bit complexity, or a practical crossover size; the 9/4 proof gives no competitive finite matrix size and its transfer to positive characteristic is not claimed.

Theorem 1.1: for every $\varepsilon>0$ two complex $n\times n$ matrices can be multiplied with $O_\varepsilon(n^{9/4+\varepsilon})$ arithmetic operations, so $\omega\le9/4$ over $\mathbb C$. The companions prove $\alpha>0.465$ over every field of characteristic zero, $\omega(1,0.709,1)<2.092$, $\omega<2.258$ over all fields outside one uncomputed finite set of positive characteristics, and $\omega<2.371054886006746$ over every field. Not shown: anything about $\omega=2$, bit complexity, or a practical crossover size; the 9/4 proof gives no competitive finite matrix size and its transfer to positive characteristic is not claimed.