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 >>>

We construct explicit non-malleable affine extractors for every constant entropy rate, with linear output length and exponentially small error, against any fixed number of affine tamperings without fixed points. For every fixed $00$.

Our extractors derandomize the lossless lifting of Efremenko and Itsykson (STOC 2026). For every fixed $0<\xi<1$, this ... more >>>