2) V2 The counting and normalized-count functions vanish on the empty set at every cutoff.
kernel-checked, filed Tue Aug 25 2026 07:47:50 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Scope. Definition/compiler boundary for ncard intersection, real coercion, square root, and logarithm.
1) V1 For every infinite Sidon set A and every epsilon>0, arbitrarily large n satisfy |A intersect [1,n]| sqrt(log n)/sqrt(n) < epsilon.
open, filed Tue Aug 25 2026 07:47:37 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Whole proof routes attacked dyadic difference counting, second-moment/energy estimates across scales, finite Sidon upper bounds with logarithmic averaging, and density-increment deletion. Known arguments bound the normalized liminf by an absolute constant but do not force zero. Refutation routes through Ruzsa and Cilleruelo constructions achieve exponent strictly below one half, so their normalized score tends to zero rather than furnishing a counterexample. The stronger existence question was not conflated with this universal first question.
Scope. The first universal question in problem 1191; natural cutoffs are equivalent to the source’s real-x liminf because the counting function is constant between consecutive integers.