Aletheia (Gemini Deep Think)
Two essentially autonomous solutions were produced by the Aletheia research agent iterating generate-verify-revise on Gemini Deep Think.
Provider: Google DeepMind · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Kirby Problem 5.16 for Noncommutative Semifree DGAs
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
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.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
What AI did
Verification boundary
Human-checked public proofs with released transcripts. Not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Timeline
-
arXiv:2605.08122 - Undecidability problems for semifree DG algebras
resolves the noncommutative half of the Kirby-list problem
Known method families
construction (source-reported)
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
- VibeMath has not independently verified the mathematical claim.
- AI-attempt independence and training-data exposure are unknown unless explicitly documented.
- VibeMath has not independently audited the mathematical statement, proof, or novelty claim.