We give a unified hidden-derivative framework for list decoding and mutual correlated agreement of ordinary Reed--Solomon codes over prime fields, on arbitrary prescribed evaluation sets. For every fixed slack $\gamma>0$, every sufficiently large block length $n$, every prime $q\ge n$, and every dimension $1\le k\le(1-\gamma)n$, a deterministic algorithm finds all ... more >>>

Guo and Wang gave a deterministic polynomial-time black-box identity test for $\Sigma^{[3]}\Pi\Sigma\Pi^{[\delta]}$ circuits over fields of arbitrary characteristic, for constant $\delta$, assuming that one product gate is squarefree. This note communicates an observation suggested by a large language model: the squarefreeness assumption can be removed by combining the normalization argument ... more >>>

Kane and Williams proved average-case wire lower bounds at the $n^{5/2}/\mathrm{polylog}, n$ scale for an explicit function against depth-two linear-threshold circuits. We prove an almost-everywhere near-cubic wire lower bound for a language in $\mathrm{E}^{\mathrm{NP}}$. For every fixed $c>0$, there is one language $F_c$ and positive constants $b_{S,c}$ and $b_{T,c}$ such ... more >>>