Another very normal day, lol
APSP and 3SUM hypotheses are refuted: arxiv.org/abs/2610.067...
KLS conjecture is proved:
arxiv.org/abs/2610.014...
arxiv.org
Truly Subquadratic 3SUM and Truly Subcubic APSP via Triangles in Sparse Lopsided Graphs
We give the first polynomial improvements over the textbook algorithms for $3$SUM and All-Pairs Shortest Paths (APSP): we show how to deterministically solve $3$SUM on $n$ integers of polynomial size ...