1) V1 Is the set {2^m3^n:m,n≥0} an essential component, meaning that its zero-augmented sumset strictly increases the Schnirelmann density of every set whose density lies strictly between zero and one?
open, filed Tue Aug 25 2026 08:00:25 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Fidelity corrects the search-snippet ambiguity: the source set is 2^m3^n, not powers of two alone. Whole proof routes tested Mann/Schnirelmann addition, multiscale smooth-number shifts, residue covering, density increments, and iterative sumsets. Refutation routes tested near-periodic B, missing-residue constructions, arbitrarily small gains, and zero-padding exploits. Critics checked strict versus weak inequality, density notion, pointwise sum, 0-adjunction, exponents, and endpoint densities.
Scope. Schnirelmann rather than asymptotic density; the DeepMind zero-augmented sumset convention; all subsets B with intermediate density; strict increase.