Stable Phase Retrieval for Spans of Independent Random Variables
After normalization, stable phase retrieval holds over the -spans of independent real-valued centered random variables exactly when all but possibly one coordinate satisfies a uniform two-sided bound. This confirms the characterization conjectured by Calderbank, Daubechies, Freeman and Freeman.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Functional Analysis, Phase Retrieval
- Posed by
- Calderbank, Daubechies, Freeman and Freeman
- Year posed
- 2023
- Years open
- 3y
- Solved
- 2026-07-07
- Model
- GPT-5 + Claude Opus 4
- Vendor
- OpenAI; Anthropic
- Collaborators
- Pedro Abdalla, Jaume de Dios Pont, João P. G. Ramos, Mitchell A. Taylor
- Verification
- Lean-checked, statement unaudited
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
Under a heading on the usage of large language models, the authors say the models played a significant role in the development of the work, describing arguments proposed by the authors and then found by GPT-5, with Claude Opus 4 also used.
Verification
No independent review. The disclosure describes a back-and-forth in which the model supplied arguments the authors had proposed in outline. Preprint, not refereed. Lean formalization available, not audited by a third party yet.
Sources
- PaperarXiv
- Lean proofGitHub repo of the proof
- Problem recordCalderbank et al 2023: Conjecture statement