Other-bases conjecture for non-half residue stopping sets

Fix an even modulus $n\geq2$, a subset $S\subset\{0,\dots,n-1\}$ of residue classes, and the associated discrete stick-fragmentation process with stopping set determined by $S$. Let $X$ denote a final stick length and let $B$ be a base. Other Bases conjecture. The final collection of stick lengths does not converge to strong Benford behavior for any base $B$ if $|S|\neq n/2$. Specifically, if $|S|>n/2$, the limiting distribution depends on the mantissa of $L$ in base $B$, and the density of

$$\log_B(X/L)\pmod 1$$

is skewed towards $1$. The conjecture is supported by the theorem establishing non-uniformity for sufficiently large bases, while the all-bases assertion and a precise description of the limiting distribution remain open.