Residually finite non-effectively-residually-finite Pi group

Construct or rule out a finitely generated residually finite Pi-group that is not effectively residually finite.

Background

Effective residual finiteness requires an algorithm producing finite quotients separating nontrivial words. The problem asks whether ordinary residual finiteness can occur without this effective uniformity.

References

Is there a f.g., residually finite $\Pi$-group that is not effectively r.f.?

— Open Problems in Mathematical Logic  (2608.26628 - Barmpalias et al., 27 Aug 2026) in 2025 Section 6, subsection Profinite groups, item (b)