What was already known
Stoneham and Bailey–Crandall proved normality for one-prime families. This value combines indices 2^a3^c across two prime directions; its authors did not identify an earlier published conjecture about this particular constant.
AI involvement
VibeMathed records the submitter’s account that ChatGPT-6 Astra selected and proved the normality claim and made the Lean proof. The primary repository independently calls it an AI-assisted mathematical project but does not specify who supplied the central proof.
VibeMathed records the submitter’s account that ChatGPT-6 Astra selected and proved the normality claim and made the Lean proof. The primary repository independently calls it an AI-assisted mathematical project but does not specify who supplied the central proof. The AI-led assessment rests on that submitter attribution; absence of a human byline alone does not prove autonomy.
Importance
Establishes normality for a distinct mixed-prime localized-logarithm value.
Limitations
The Lean development checks qualitative binary normality only, not the paper’s discrepancy bound or broader finite-prime extensions. VibeMathed records a submitter claim of central AI proof work; the unbylined repository describes an AI-assisted project without allocating the central mathematical steps.
Technical verification
The pinned Mathlib-only challenge states the double sum and all binary word frequencies directly, and the solution proves it. The repository reports guarded axiom audits and successful pinned CI; VibeMathed reviewed the statement match. This is a source-reported check of the exact selected theorem; AIProofWatch did not rerun the build.
Formal checking
The pinned Mathlib-only challenge states the double sum and all binary word frequencies directly, and the solution proves it. The repository reports guarded axiom audits and successful pinned CI; VibeMathed reviewed the statement match.
- Checker
- Lean 4 / mathlib, source-reported CI; VibeMathed statement review
- Scope
- The constant ξ=Σ_{a,c≥0}1/(2^a3^c·2^{2^a3^c}) is normal in base two: every finite binary word has its expected limiting frequency when overlapping occurrences are counted.
- 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