Upper-bound reduction (companion note): the interval witness value d({1,...,n}) is by definition the Erdős #1 extremal function ℓ(n), with ⌊log₂ n⌋ + 1 ≤ ℓ(n) ≤ log₂ n + log₂log₂ n + 3 for n ≥ 4; exact additivity d(A₁ ∪ M·A₂) = d(A₁) + d(A₂) holds for M > 2Σ_{A₁}|a|; hence separated multi-scale interval unions satisfy d(A) ≥ ⌊log₂ n⌋ + 1 + Σ_{i≥2}⌊log₂ n_i⌋ and can never beat the single interval as an upper-bound witness — improving the #963 upper bound to log₂ n + O(1) via subsets of [n] is verbatim the Erdős #1 conjecture.