What was already known
Classical zero-free regions permitted an exceptional real zero arbitrarily close to 1 as q varies. No uniform gap of this form was established in the cited baseline.
AI involvement
OpenAI credits its internal model with the manuscript and Lean artifacts. It identifies an exceptional workflow for the zero-free work but does not specify the amount of human direction.
The release credits its internal model with producing the mathematical manuscripts and proof artifacts; the exceptional workflow for zero-free work leaves autonomy undocumented.
Importance
This removes the exceptional Landau–Siegel-zero possibility for the stated real characters.
Limitations
The result excludes zeros near 1; it does not assert that no real zeros occur elsewhere in (0,1). The related 7/8 and 11/12 zero-free half-plane claims have different scope.
Technical verification
The cited Lean theorem states the uniform real-zero gap, and the cited scope note explicitly matches primitive nonprincipal real characters, q >= 3 and both parities to that statement. The repository provides a Comparator target. This is source-reported machine formalization; this review did not compile or replay it, and the quasi-Riemann applications are outside this check.
Independent checking
Formal theorem exists_absolute_real_zero_gap, with a separate Comparator statement and written scope comparison
- Checker
- Lean 4 formal development in the OpenAI release
- Scope
- Exists an absolute positive c giving 1 - beta >= c/log q for every real zero of each primitive nonprincipal real Dirichlet character with q >= 3
- Basis
- Reported by the linked checker
Human understanding
No named human explanation of the central proof is documented for this family. Few is the evidence default, not a finding that people cannot understand it.
Correction and publication history
If correct, this removes the exceptional Landau–Siegel-zero possibility for the stated real characters.
Read this published revision