Strichartz's Question on Fourier Frames for the Cantor Measure
Everything below was recorded by a tool. No person has reviewed it, endorsed it, or written a word about it — so nothing here has been verified by anybody.
Statement
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.
Context
A well-known question of Strichartz sitting in the Fuglede and frame-spectrality circle, with two decades of partial nonexistence results around it.
People
Projects
Nobody is running a project on this. A project is a stated goal, a thread, and one thing somebody else could do. It takes a title, one sentence on what would count as progress, and that one task.
Interest
Nobody has said they are looking at this. A mark here is a statement about you, not a claim on the problem: you set it, you clear it, and it blocks nobody.
Attempts
No person has examined this. There is 1 attempt here and 1 machine check recorded against it. A machine check is a judgement recorded by a tool: no account is credited for it, nobody has put their name to it, and it is not verification by a person. Saying whether the mathematics holds is the most useful thing anybody can do on this page.
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.
Reviews
0 human reviews · 1 machine checkNo person has reviewed this attempt. 1 machine check below — a machine check is not human verification.
Machine check · not human verification
machine: correctscope Lean formalization of the result
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.
No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.
Endorsements
0 endorsementsNo one has endorsed this attempt. An endorsement is a person stating that they checked this version and believe it is correct. None has been recorded — which is information, not an omission.
Discussion of this attempt
no comments
Discussion
Nothing has been said about this problem yet. Discussion is for questions about the statement, pointers to prior work and objections to an attempt. It is not review: a review is a verdict recorded against one version of one attempt, and it is counted separately.
Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.