2 problems

Generic means conjecture. For a generic set of points $x_1,\ldots,x_n$ in $\bar{X}$, $\bar{\bar{X}}$, $\bar{Z}$, or $\bar{\bar{Z}}$, means exist and are unique.

Surjectivity conjecture. Every almost surely positive density $g$ on $[0,1]$ is the pdQ transformation of a density function, and hence uniquely represents a location-scale family.