Belinskaya's Theorem for Measure-Preserving Flows

Precise statement

Two free ergodic measure-preserving flows whose $\mathrm{L}^1$ 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.

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

GPT-5 + Claude Opus 4

The paper states that 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.

Provider: unknown · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

No independent review. The paper attributes the key criterion to an autonomous agent loop rather than to prompted assistance. Preprint, not refereed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-07-16

   arXiv

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

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.