What was already known
Dubickas asked whether √3 belongs to Z. The m=2 and m≥9 cases were known; several intermediate square roots were unresolved.
AI involvement
Stephan’s project disclosure credits Claude Fable 5 with the discovery and Fable 5 and Opus 5 with formalization. Stephan chose the problem, directed the work, revised the prose and checked statement alignment.
The attributed first-person account assigns the mathematical discovery to the agent, while Stephan directed and reviewed; the manuscript independently confirms substantial Claude Code collaboration.
Importance
Answers Dubickas’s √3 question and completes the integer square-root classification.
Limitations
The Lean statements cover the √3 witness and classification. The paper’s separate divisibility and transcendental-witness results are outside this assessment.
Technical verification
The named √3 and classification statements have Lean 4 proofs. The repository describes comparator statement matching and standard-axiom checks, and Palomar reports a machine check at a cited commit. The paper’s unformalized §4.1 thickness calculation and §8 are outside the assessed theorems.
Independent checking
kernel type checking and comparator comparison of public challenge statements and permitted axioms
- Checker
- Lean 4 kernel and leanprover/comparator, as reported by Stephan and Palomar
- Scope
- SZ.sqrtThree_mem_MahlerZ and SZ.sqrt_natCast_mem_S_iff, matching Theorems A and B
- Basis
- Reported by the linked checker
Human understanding
Stephan’s exposition explains the two-scale reduction to base-m Cantor digits and the covering induction, and his attributed account says he directed and reviewed the result.
Correction and publication history
The √3 construction and integer square-root classification are assessed together.
Read this published revision