What was already known
Carleson proved the classical convergence theorem in 1966. An existing collaborative formalization follows a different approach; this project follows Roos’s generalization of the Lacey–Thiele method.
AI involvement
The project credits Claude Opus 5.5 with roughly 15,000 lines of proof code produced from the source paper. Roos set the targets and wrote the mathematical statements and definitions with AI advice.
Roos specified statements and definitions and supplied the Lacey–Thiele source argument. Automated Lean proof translation alone is outside the collection.
Importance
Documents AI assistance in producing a substantial alternative formal proof of advanced harmonic analysis.
Limitations
Not the first formalization of classical Carleson’s theorem. The existing project covers a more general metric-space version and Carleson–Hunt; those are not claimed here. The author reports an overnight main development, not a controlled comparison of AI and human productivity. AIProofWatch has not rebuilt the formal development or audited the complete proof. Palomar reports mechanical checking of a pinned statement; its automated statement review is not human peer review. The reported date records this registry checkpoint; the earlier first-report date of the formalization has not been established.
Technical verification
Reported is the default when evidence for a higher level is insufficient. No qualifying AI mathematical contribution remains in the proposed scope. Existing checks of the human result or its translation are retained as current evidence, without transferring them to an invented included AI contribution.
Formal checking
Registry-reported Comparator and kernel checking; not reproduced by AIProofWatch.
- Checker
- Palomar: Lean, NanoDa and con-ron (reported)
- Scope
- anisotropic_carleson and classical_carleson at a83052776113c6417432c594a29b98f3500091a4, using the project’s multiplier hypotheses and three standard Lean axioms.
- Basis
- Reported by the linked checker
- Check date
- 2026-10-09
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No sufficient account of a named human explaining the scoped central reasoning is established in this assessment. Missing disclosure is not evidence of little understanding.
Correction and publication history
Source-statement, baseline, AI-role and verification-scope review, 14 October 2026. New curated contribution; eligible for matching consented digests.
Read this published revision