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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 >>>
Beginning with the work of Dinur, Lin, and Vidick (FOCS, 2024), tensor codes with constant product expansion have been foundational to recent advances in quantum locally testable codes (qLTCs) based on cubical complexes. Informally, product expansion says that any low-weight parity check of the tensor code can be written as ... more >>>
