It's perfect in the sense that its running time is O(n log n), and there is evidence that this is the fastest running time possible (at least up to a constant factor).
I would say most mathematical conjectures are stronger than most scientific theories. What I mean is that the conjectures are easily falsifiable (i.e., counter examples, if found, can easily be verified) and have been shown to be true for an enormous number of of cases. So unproven mathematical conjectures are not just "wild hypotheses."
According to the article, it rests on a plausible conjecture. I need to read further.
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According to the abstract of the paper referred to in the article (https://arxiv.org/abs/1902.10935) it rests on a "central conjecture in the area of network coding". Make of that what you will.
Ah but that's not what this game is about. It's about what you can prove. And conjectures are by definition things you can't prove yet. So the longer they stand and the more paths they block the more frustrating it gets.
>In this work, we prove that if a central conjecture in the area of network coding is true, then any constant degree boolean circuit for multiplication must have size Ω(nlgn), thus almost completely settling the complexity of multiplication circuits
So, given an unproven assumption and also given that we are constrained to doing multiplication on a boolean circuit, this may be "perfect" in a sense.
