Binary normality of a localized logarithm value

Yes. Every finite binary word occurs with its expected limiting frequency, overlapping occurrences counted. The one-prime members of this family were already known to be normal: $\alpha_{b,p}=\sum_{k\ge1}p^{-k}b^{-p^{k}}$ is Stoneham's constant, proved normal under primitive-root hypotheses by Stoneham in 1973 and unconditionally for coprime parameters by Bailey and Crandall in 2002. The new content is the mixed-prime support, where all the indices $2^{a}3^{c}$ contribute at once and the argument turns on the largest power of three in the truncation denominator surviving addition. The paper states that it has not located an earlier published conjecture about $\xi$, so this settles no previously posed question. The Lean development covers qualitative normality of this constant only; the paper's quantitative discrepancy bound and its extension to larger finite sets of primes are outside the formalisation.

Yes. Every finite binary word occurs with its expected limiting frequency, overlapping occurrences counted. The one-prime members of this family were already known to be normal: $\alpha_{b,p}=\sum_{k\ge1}p^{-k}b^{-p^{k}}$ is Stoneham's constant, proved normal under primitive-root hypotheses by Stoneham in 1973 and unconditionally for coprime parameters by Bailey and Crandall in 2002. The new content is the mixed-prime support, where all the indices $2^{a}3^{c}$ contribute at once and the argument turns on the largest power of three in the truncation denominator surviving addition. The paper states that it has not located an earlier published conjecture about $\xi$, so this settles no previously posed question. The Lean development covers qualitative normality of this constant only; the paper's quantitative discrepancy bound and its extension to larger finite sets of primes are outside the formalisation.