Kirby Problem 5.16 for Noncommutative Semifree DGAs
For semifree noncommutative differential graded algebras over a nontrivial computable unital commutative ring, are stable tame isomorphism, quasi-isomorphism, or derived Morita equivalence algorithmically decidable? All three are undecidable.
- Result
- Disproved(see note)
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Decision problems in topology
- Posed by
- —
- Year posed
- —
- Years open
- —
- Solved
- 2026-04-28
- Model
- Aletheia (Gemini Deep Think)
- Vendor
- Google DeepMind
- Collaborators
- —
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
resolves the noncommutative half of the Kirby-list problem
What the AI did
Two essentially autonomous solutions were produced by the Aletheia research agent iterating generate-verify-revise on Gemini Deep Think.
Verification
Human-checked public proofs with released transcripts. Not yet peer-reviewed.
Source
arXiv:2605.08122 - Undecidability problems for semifree DG algebras