Comeagerness of algebraically independent metrics

Determine whether metrics with algebraically independent distances are comeager on every strongly zero-dimensional metrizable space, beyond the established case of strongly zero-dimensional -compact spaces.

Background

The paper studies compatible metrics for which the distances assigned to every finite collection of distinct two-point subsets are algebraically independent over the rationals. It proves that, on strongly zero-dimensional -compact spaces, these metrics form a dense $G_\delta$ subset of $Met(X)$, and hence are comeager.

The broader question concerns arbitrary strongly zero-dimensional metrizable spaces. The result in the paper settles only the -compact case, so the general comeagerness problem remains unresolved in the stated passage.