This page collects papers generated with AI (not all prompted by the owner of this page) that are not planned for submission for publication. As such, the content here is less verified and polished than of a published paper, though the author is fairly confident about the correctness of each document. Each entry includes an abstract describing the main results, applications, and a very high-level sketch of the proof.
Abstract. For seminorms N1,...,Nm on Rn, this paper proves that their sum has a uniform (1 ± ε)-sparsifier supported on O(dε−2 log(1/ε)) reweighted summands, where d is the dimension after quotienting by the common kernel. Consequently, sums of normalized symmetric submodular functions admit sparsifiers with the same effective-dimension bound, and every weighted hypergraph on n vertices has a cut sparsifier with O((n − κ)ε−2 log(1/ε)) hyperedges, where κ is the number of connected components of its positive-weight 2-section. At a high level, the proof represents seminorms by compact centrally symmetric convex support sets, extends the Reis–Rothvoss coefficient-space argument from sums of segments to arbitrary Minkowski sums using convexity of volume under Minkowski erosion, and applies partial coloring to eliminate a constant fraction of the summands at each step.