Non-semi-decidability of isolated groups from finite presentations

Let $\Lambda_{FP}$ denote the representation by finite presentations, and let an isolated group mean a group represented by an isolated marked-group point. A property is $\Lambda_{FP}$-semi-decidable when it can be semidecided from finite-presentation input.

Finite-presentation isolated-groups conjecture. The set of isolated groups is not $\Lambda_{FP}$-semi-decidable.

The paper presents this as an open analogue of the corresponding word-problem conjecture: even with finite-presentation descriptions, it remains unknown whether isolated groups can be partially recognized.