Auto Research: Integer multiplication below n log n

Is there any good writeup yet of intuitively where the speedup comes from? E.g. with fast fourier transform you can see that there's a lot of symmetry & recomputation in the Vandermonde matrix, so that's where the speed up comes from.

Some more context

https://nitter.click/RohanArun/status/2109336015814959200?s=...

(Replace top-level with healthy instances or x.com as needed)