What was already known
Copeland and Erdős proved decimal normality. Belshaw and Borwein posed the stronger fluctuation question; Catt, Coons and Velich left prime concatenation unresolved under the law-of-the-iterated-logarithm definition.
AI involvement
VibeMathed records the submitter’s account that ChatGPT-6 Astra chose the question, developed the proof and wrote Lean. The unbylined primary paper does not independently allocate the human and AI work.
VibeMathed records the submitter’s account that ChatGPT-6 Astra chose the question, developed the proof and wrote the Lean formalization. The primary paper has no byline and does not independently document the division of mathematical work. The AI-led label rests on the submitter attribution, not on the absence of a human byline.
Importance
Answers a named question about the fluctuation of digits in a classical normal constant.
Limitations
Lean proves the conclusion from an explicit Ingham1937Input short-interval prime-count asymptotic. Ingham’s established analytic theorem is not formalized. The result addresses base 10, not strong normality in unrelated bases; outside expert review remains limited.
Technical verification
The public Actions run succeeded for the pinned Lean revision. Lean checks the exact digit and discrepancy deduction from an explicit `Ingham1937Input` hypothesis. Ingham’s classical short-interval theorem is cited but not formalized here; the unconditional claim therefore has a documented formal-check boundary. VibeMathed reports reading the short paper, but identifies no named human checker of the entire argument. AIProofWatch did not rerun the build.
Formal checking
The pinned public Actions run succeeded at this commit. The completed Lean theorem proves failure of simple and full base-10 strong normality from explicit Ingham1937Input; the external analytic theorem is not formalized.
- Checker
- Lean 4 kernel, as reported by the project
- Scope
- The decimal Copeland–Erdős constant is not simply strongly normal in base 10 and hence not strongly normal, assuming Ingham’s published short-interval asymptotic.
- 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. No named person is documented explaining the central argument. Editorial reading or a separate AI review does not establish human understanding. Few is the default from missing evidence, not a finding that people cannot explain it.
Correction and publication history
Pinned primary claim, prior baseline, AI attribution and checking scope reviewed for local inclusion without notification.
Read this published revision