What was already known
An earlier certificate corpus reached a single-window length about 0.40722, and Dubickas printed a 31/81 exclusion. The new interval has length 3/7≈0.42857; Dubickas’s 2006 nearest-integer constant is slightly stronger than 2/7.
AI involvement
Stephan chose the target and checked statements; the disclosure credits Claude Fable 5 with the discovery and draft and Claude Opus 5 with the Lean formalization.
The source explicitly assigns mathematical discovery to Claude Fable 5 and formal proof work to Claude Opus 5 under Stephan's direction.
Importance
Extends the certified single-window exclusion for powers of 3/2.
Limitations
This does not resolve Mahler’s length-1/2 problem. The paper’s certificate-format and escape-time results are separate claims.
Technical verification
The four Theorem E forms are among the 14 compared declarations. The cited source reports Lean kernel evaluation of the raw exact integer certificate, Comparator statement matching and exported-proof replay. This review did not rerun the checker; search-only larger records are outside the assessed claim.
Formal checking
Challenge2/Solution2 comparison and kernel reduction of certTwoSeven.ok from raw integer data
- Checker
- Palomar Comparator and Lean kernel
- Scope
- Theorem E's closed [2/7,5/7] exclusion, eventual escape and infinitely-often nearest-integer forms for every nonzero real ξ
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Stephan checked statements and authored the paper, but credits the mathematical discovery and drafting to AI; no named human explanation of the rank-stratified certificate mechanism is documented. Few is the missing-evidence default.
Correction and publication history
Extends the certified single-window exclusion for powers of 3/2.
Read this published revision