Or Zamir

Another one bites the dust: the k-Clique conjecture is dead, for good! @pinkfloydie and I show that for all k>k0 we can find (and count) k-cliques in n^((w/3-c)k) time, where k0,c>0 are consts independent of both k and the matrix mult exp w, even if w=2!
orz.am/kclq

Blum-Luby-Rubinfeld showed that matrix multiplication is as hard on a random input as it is in the WC. I give the first unconditional such reduction for matrix inversion; and conditional (on our trapdoor matrices) reductions for singularity, rank, and det.
arxiv.org/abs/2611.03058

What do I think makes more plausible fine-grained hardness conjectures? Problems for which we know absolutely no useful structural mechanism, and can hope there isn't any.
When we had non-trivial factoring algorithms, a poly quantum (or classical) one shouldn't be shocking.
(1/2)

So what changes? Most works on exp-time algos are now obsolete (incl. some of my own), and much elegance in fine-grained complexity is lost. Many intermediate conjs still hold (eg, OV), but the slickness of "we have a central assumption that sounds like a strong NP!=P" is buried

To slightly calm down the external discourse: Breaking ETH does not directly imply anything about P vs NP, nor that every NP problem has a better algorithm; in fact, even for SAT (rather than k-SAT for a constant k) we still don't know if (2-eps)^n time is possible!