Conjecture on decidable properties of the space of marked groups

Let $\mathcal{G}$ be the space of marked groups and let $\Lambda_{WP}$ denote the word-problem representation. A property of $\mathcal{G}_{WP}$ is $\Lambda_{WP}$-decidable when its characteristic decision problem is decidable relative to $\Lambda_{WP}$; a subset is clopen when it is both open and closed.

Decidability–clopenness conjecture. Every $\Lambda_{WP}$-decidable property of $\mathcal{G}_{WP}$ is clopen.

The conjecture asks whether the topological classification of natural properties captures their decidability status. The converse, that clopen properties are decidable, is known in the compact bounded-generator case but fails in $\mathcal{G}$; the forward implication remains open.