# Prior-art boundary

The binary digit-sum generating-product identity is known. Maxwell Schneider and Robert Schneider, *Digit sums and generating functions* (2018), give general base-B product identities that include

\[
\sum_{n\ge0}q^{s_2(n)}z^n=\prod_{r\ge0}(1+qz^{2^r}).
\]

Targeted searches did not locate a prior proof of A317940 positivity, the Dirichlet-square-root application, or the full fractional-power positivity statement over `0 < q ≤ 1`, `α > 0`.

The responsible novelty claim is that the positivity argument and its A317940 application appear new; the underlying digit-sum product identity is not new.