What was already known
Kirby Problem 5.16 asked whether the relevant equivalences for semifree DG algebras are decidable. The noncommutative and graded-commutative cases were separate.
AI involvement
Aletheia produced essentially autonomous solutions to two posed undecidability questions. Manolescu and Rozenblyum checked and streamlined the reductions and supplied the cross-application to all three notions.
The authors describe Aletheia as producing two solutions essentially autonomously after being posed the questions; they explicitly separate their later cross-application observation.
Importance
Resolves the noncommutative half of the named decidability problem.
Limitations
The graded-commutative half remains open. Manolescu and Rozenblyum made the further observation that the two model reductions apply across all three equivalence notions; they report checking both proofs without a separate audit record.
Technical verification
The two named human authors expressly report that they checked the model-produced proofs of the reductions. Their observation extends each checked reduction across all three equivalence notions.
Formal checking
human checking of the model-produced proofs; source-reported.
- Checker
- Ciprian Manolescu and Nick Rozenblyum
- Scope
- The two undecidability reductions underlying Theorem 1 for semifree noncommutative DGAs
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the two reductions to known undecidable triviality problems and identify how the equivalence notions connect; no central unexplained step is reported.
Correction and publication history
Resolves the noncommutative half of the named decidability problem.
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