Hate to break it to you but often not even the reviewers actually read the paper.
Seems like doing the sorting, recursion, and alignment would have a nontrivial performance penalty, but it’s still a pretty interesting idea.
probably it would improve the paper to remove the russian-peasant-multiplication references entirely, or reduce them to a throwaway aside in one place
in part this is because you surely won't be the last person careless enough to make this obvious error
but also it's because russian-peasant multiplication is a totally normal way for hardware multipliers to work, and the main content of the paper is totally decoupled from whether the final multiplication at the end of all the reductions are done with russian-peasant multiplication or (as would probably be a better idea) something like a dadda multiplier or a booth multiplier
There is no new math discovered as far as I understand. It's basically "we know how to do multiplication with a lot of additions".
If this was effective rather than just "simulate multiplication with a lot of additions" it would have been super interesting for parallelization of multiplications and communication bounds.