What was already known
Irrationality was known for ζ₂(3) and ζ₂(5). Lai proved that at least one of ζ₂(7), ζ₂(9), ζ₂(11), ζ₂(13) is irrational. The same maintainer’s earlier formal results narrowed the alternative to three and then two values.
AI involvement
The maintainer explicitly states that AI agents produced both the mathematics and Lean code under human direction. The human directed and published the project; no task-only autonomy is documented.
The maintainer explicitly credits Claude agents with the mathematical construction, informal proof and Lean formalization under human direction. The human directed and registered the work.
Importance
Identifies a specific irrational 2-adic zeta value where prior established work proved only that at least one member of a short list was irrational.
Limitations
The Lean statement uses a Volkenborn-normalized value. Its identification with the Kubota–Leopoldt value is cited from Lai, Sprang and Zudilin and is not formalized; the identification changes only by a nonzero rational factor. The project reports no human expert mathematical review. An unrefereed earlier draft by C. D. Long claims a broader result including ζ₂(7); this project reports an apparent gap in its large-prime argument, so exclusive priority is unresolved. Earlier pair and triple alternatives by the same maintainer are logical consequences of this selected result.
Technical verification
The source reports a complete Lean proof, kernel-checked finite certificates and Comparator matching for the exact Volkenborn-defined value. The separate identification of this definition with the Kubota–Leopoldt 2-adic zeta value comes from a cited theorem and is not formalized; Formal attaches only to the defined value, with that scope stated.
Formal checking
Source-reported Lean kernel and comparator checks of the hypothesis-free Volkenborn-defined irrationality theorem.
- Checker
- Lean 4 kernel and Comparator as run by maintainer and Palomar registry
- Scope
- Existence of the Volkenborn limits and irrationality of the project-defined zeta2(7); excludes formal verification of its identification with the Kubota–Leopoldt normalization
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The source says the mathematics has not been reviewed by a human expert and gives no documented human explanation of the new linear-form construction. Few is the evidence default; it does not assert that experts are unable to understand it.
Correction and publication history
Primary-source review of exact formal definition, prior alternatives, AI authorship, full Lean check scope and competing draft.
Read this published revision