What was already known
Dubickas ruled out confinement in closed intervals of length 1/3 at base 3/2. Earlier results also treated other particular windows and unions.
AI involvement
Ralf Stephan chose the targets and reviewed statements. He credits Claude Fable 5 with the mathematics and Claude Opus 4.8 with the Lean formalization.
The source explicitly credits Claude Fable 5 with the mathematical discovery and Claude Opus 4.8 with the formal proof under Stephan's direction.
Importance
The certified single interval is longer than the classical 1/3 threshold.
Limitations
This is a result for one positioned window, not every interval of length 3/8; it does not solve Mahler’s length-1/2 problem.
Technical verification
The 3/8 window is a named compared statement. The cited source reports Comparator checking its statement and Lean kernel evaluation of the exact integer certificate from raw data, with standard axioms only. This batch did not reproduce the check.
Formal checking
statement comparison and kernel reduction of Cert.ok on exact integer certificate data
- Checker
- Palomar Comparator and Lean kernel
- Scope
- Z32.ZSet_three_two_sixth_3_8, emptiness of the stated 3/2 confinement set
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Stephan checked statements, but the source assigns mathematical discovery and paper drafting to AI and records no named human explanation of the central certificate construction. Few is the missing-evidence default, not a claim that Stephan cannot understand it.
Correction and publication history
The certified single interval is longer than the classical 1/3 threshold.
Read this published revision