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Indeed, this article is a really really nice read! Without knowing much about this topic, the first 10-15 pages give a really nice hand-holding whiteboard-style exposition of some of the ideas. Unfortunately, the conclusion:

Carlos Scheidegger@cscheid.net

This is a very good article on the o(n log n) multiplication algorithm claim: web.maths.unsw.edu.au/~davidharvey...

yes, exactly what I was thinking! This is the math we need for the future. In fact I probably learned more from this than from a formal human-written proof of the main result.

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