What was already known
Stoneham and Bailey–Crandall proved normality of individual constants under the stated coprimality conditions. Bailey and Borwein asked whether the sum is normal in the common defining base; their theorem about a sum being nonnormal in a different base does not answer this question.
AI involvement
VibeMathed records the submitter’s account that ChatGPT-6 Astra chose and proved the question and produced the Lean formalization. The unbylined primary repository does not independently separate model and human work.
VibeMathed records the submitter’s account that ChatGPT-6 Astra chose and proved the question and produced the Lean formalization. The unbylined primary repository does not independently separate model and human work. The AI-led assessment rests on that submitter attribution; absence of a human byline alone does not prove autonomy.
Importance
Answers Bailey and Borwein’s two-sum normality question in its full stated parameter range.
Limitations
VibeMathed records the submitter’s attribution of problem selection, proof and formalization to AI. The unbylined primary repository supplies the theorem and Lean proof but does not independently separate AI from human work.
Technical verification
The pinned Lean 4 solution proves the standalone Mathlib-only challenge statement; the repository reports a complete build, guarded axiom audit and successful CI, while VibeMathed reviewed the match to the 2012 question. This is a source-reported check of the exact selected theorem; AIProofWatch did not rerun the build.
Formal checking
The pinned Lean 4 solution proves the standalone Mathlib-only challenge statement; the repository reports a complete build, guarded axiom audit and successful CI, while VibeMathed reviewed the match to the 2012 question.
- Checker
- Lean 4 / mathlib, source-reported CI; VibeMathed statement review
- Scope
- For integers b,c,d≥2 with gcd(b,c)=gcd(b,d)=1, the sum of the two Stoneham constants α(b,c)+α(b,d) is normal in base b, including when c=d or the two parameters share prime factors.
- Basis
- Reported by the linked checker
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. The reviewed sources do not name a person who explains the central proof. Few is the default from missing documentation, not a finding that a person cannot understand it.
Correction and publication history
Primary paper, formal statement, prior work and submitter attribution reviewed for non-notifying local inclusion.
Read this published revision