1) V1 Must every infinite set of natural numbers whose every finite subset contains a dissociated subset of a fixed positive proportion be a union of finitely many dissociated sets?
open, filed Tue Aug 25 2026 06:17:49 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Term-for-term source mapping: distinct finite subset sums are injectivity of the Finset sum on finite subsets; the Vinogradov lower bound is one global real c>0; finite union is a finite set T of dissociated sets with sUnion T=A. The proof attack used compactness/finite coloring, iterative extraction, harmonic-Sidon equivalence, and additive-relation hypergraphs. The refutation attack tested the 2024 B_h counterexample and diagonal high-arity hypergraphs. It does not transfer: full dissociation controls all subset-sum arities simultaneously, while fixed-h constructions lose the required uniform positive proportion under diagonalization.
Scope. Infinite subsets of the naturals; one global positive proportion; a finite, not uniformly indexed, family of dissociated covering sets.