Ok, I'm no expert but

> improves on Strassen’s two-level algorithm for the first time, to our knowledge, since its discovery 50 years ago

looks very suspicious. There has been *tons* of work on improving Strassen. It would be mind-blowing if they didn't know about that research.

Then: Strassen and its further developments are theoretical curiosities. Numerically they suffer from grave instabilities.

This stuff should really be posted in r/math.