1) V1 For all t,r≥2, are there K_t(r)-free t-uniform n-vertex hypergraphs with at least n^(t-r^(1-t)-o(1)) edges?
open, filed Tue Aug 25 2026 08:37:31 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Whole proof attacks tested random deletion, random algebraic tensors, finite-field incidence hypergraphs, norm forms, tensor products, and asymmetric-to-balanced reduction. Refutation attacks tested hypergraph KST upper counting, supersaturation, entropy, and exponent consistency with t=2 Zarankiewicz cases. Critics checked t-uniformity, disjoint classes, all transversals, labeled vertices, non-induced containment, quantifier order in t/r/ε/n, and expansion of the o(1) exponent.
Scope. Labeled finite t-uniform hypergraphs; K_t(r) has t pairwise-disjoint classes of size r and all transversal edges; the o(1) exponent is expanded as every ε>0 and an eventual n^(target-ε) lower bound.