Kirby Problem 5.16 for noncommutative semifree DGAs

The problem asks whether algorithms can decide stable tame isomorphism, quasi-isomorphism, or derived Morita equivalence for semifree noncommutative DGAs; it is part of Kirby Problem $5.16$. The claimed result addresses the noncommutative half, not the graded-commutative analogue.

May 2026 undecidability theorem

The preprint claims undecidability of all three equivalence problems, and also of tame isomorphism, over any nontrivial unital Turing-computable commutative ring $R$. Its reductions use triviality problems for finitely presented associative algebras and groups; for the constructed pairs, stable tame isomorphism $\Rightarrow$ quasi-isomorphism $\Rightarrow$ derived Morita equivalence, with each equivalent to triviality of the underlying presentation. The claim is not independently verified.

Current status (as of May 2026): the noncommutative cases are claimed undecidable, but are not yet independently corroborated; the graded-commutative cases remain open.