Strichartz's Question on Fourier Frames for the Cantor Measure
Does the middle-third Cantor measure admit a Fourier frame, that is, a countable set of exponentials giving two-sided frame bounds on its space? No. The Cantor measure with base admits no Fourier frame for any odd integer , which answers Strichartz's question for the middle-third case.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Harmonic analysis
- Posed by
- Robert S. Strichartz
- Year posed
- 2000
- Years open
- 26y
- Solved
- 2026-07-09
- Model
- GPT-5.5, GPT-5.5 in Codex
- Vendor
- OpenAI
- Collaborators
- Jaume de Dios Pont, Lukas Liehr, Mitchell A. Taylor
- Verification
- Lean-verified
- Publication
- Preprint
- Significance
- 25 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The paper devotes a section to it. The authors were trying to build a frame, not to rule one out. With GPT-5.5 they analyzed why their translated ternary digit set candidates fail to give scale-uniform frame bounds, and it is that failed construction which suggested the obstruction the final proof turns on. The model also simplified the key normalized polynomial into a more concise equivalent form. GPT-5.5 in Codex then wrote the Lean formalization, and the authors state that the proof files were generated by language models while they curated and checked the statement.
Verification
Lean 4 formalization of the main theorem at the linked repository. Showcase.lean carries a self-contained statement the authors curated and reviewed for human readability; the proof files themselves were LLM-generated, and the trust rests on Mathlib's definitions. We have not recompiled it. arXiv preprint, not yet peer-reviewed.
Sources
arXiv:2607.08656 - Cantor measures with odd base do not admit Fourier frames