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Claim. K. Benli, C. Dartyge, C. Dombrowsky, P. Pollack and L. Thompson, On the digits of the sum of proper divisors, arXiv:2607.18981 (v1, 21 July 2026), Theorem 1.4: "Fix $g\geq2$, $\gamma\in(0,1)$, and a nonempty set $\mathcal{D}\subsetneq\{0,1,\ldots,g-1\}$. For all sufficiently large $x$, the number of $n\leq x$ for which $s(n)$ has all of its digits in base $g$ restricted to digits in $\mathcal{D}$ is $O(x\exp(-(\log\log x)^\gamma))$" (result page). The paper cites the earlier Theorem 1.8 of Benli, Cesana, Dartyge, Dombrowsky and Thompson for $g\ge3$ and proves the case $g=2$, omitted there, by a separate elementary argument in its Appendix A. It keeps the general assertion as its Conjecture 1.3 and says that it remains open.

Covers. The base-$2$ missing-digit targets, which the earlier theorem omits; with it, the missing-digit targets in every base $g\ge2$. The general assertion stays open.

Depends on. The 2023 missing-digit theorem for $g\ge3$.

Acceptance. Claimed: an arXiv preprint, with no refereed publication or curator credit on record.