Belinskaya's Theorem for Measure-Preserving Flows
Two free ergodic measure-preserving flows whose full groups are isomorphic as abstract groups are conjugate up to a scalar time change. This proves the flow analogue of Belinskaya's theorem, answering a question posed by François Le Maître and the author.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Ergodic Theory, Orbit Equivalence
- Posed by
- François Le Maître and Konstantin Slutsky
- Year posed
- 2021
- Years open
- 5y
- Solved
- 2026-07-16
- Model
- GPT-5 + Claude Opus 4
- Vendor
- OpenAI; Anthropic
- Collaborators
- Konstantin Slutsky
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The paper states the criterion the proof turns on and its application were discovered autonomously by a two-agent AI system running GPT-5 and Claude Opus 4 in a research loop; Codex was used separately for proofreading and stylistic editing.
Verification
No independent review. The paper attributes the key criterion to an autonomous agent loop rather than to prompted assistance. Preprint, not refereed.
Sources
- PaperarXiv
- Problem recordLe Maitre & Slutsky 2021, Questions 10.10 & 10.17: Problem statement