We prove an $\Omega((\log n/\log\log n)^2)$ unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in $n$-node directed acyclic graphs under edge insertions. This improves the $\widetilde{\Omega}(\log^{3/2} n)$ lower bound of Larsen and Yu [SICOMP 2025], and matches the ... more >>>

In a recent breakthrough, Chattopadhyay, Hatami, Lee, Lovett, Tal, and Viola (ECCC'26) established exponential correlation bounds for polynomials over $\mathbf{F}_2$ and, as a consequence, obtained a major improvement in PRG constructions for low-degree polynomials over the binary field. In particular, they obtained seed length $\widetilde{O}(d^2\log^2 n)$ for fooling degree-$d$ polynomials ... more >>>

The strong Koml\'os conjecture asserts that every ordered family of Euclidean-unit vectors admits a signing whose signed prefixes have uniformly bounded \(\ell_\infty\)-norm. We disprove this conjecture by constructing explicit finite families with unbounded fixed-order prefix discrepancy. At level \(k\), our integer matrix has \(d_k=2^{2^k-1}\) rows and exactly \(s_k=2^k\) nonzero \(\pm1\) ... more >>>