What was already known
Kauers and Zeilberger conjectured both growth rates and gave coarse numerical estimates. The proposed proof imports cone-walk estimates and adapts them to Markov-modulated walks through a corrector ladder.
AI involvement
Claude developed the local-limit and asymptotic argument. Padhi selected the challenge, ran computations, applied controls and corrected model errors.
Claude generated the local-limit and asymptotic argument under Padhi’s problem selection and validation.
Importance
Reports solutions of Kauers–Zeilberger Conjectures 2a and 2b.
Limitations
Exact enumeration and symbolic checks cover selected initial terms and intermediate identities. The transported local-limit argument lacks a documented complete proof check, and the displayed decimal constants are extrapolations without certified error bounds.
Technical verification
Exact enumeration reproduces published initial terms and independent extrapolations support constants; symbolic algebra checks some covariance and corrector identities. The transported local-limit theorem and full asymptotic proof have no documented completed rigorous review.
Independent checking
Source-reported symbolic algebra checks of exact intermediate identities
- Checker
- Jaideep Sai Padhi, paper author, executing model-written code
- Scope
- Selected transfer-matrix covariance and odd-run corrector identities in Section 9
- Basis
- Reported by the linked checker
Human understanding
The paper explains the formal argument, but it credits Claude with the mathematics and does not identify a human who independently explains the Markov-additive corrector ladder; Few is the evidence default.
Correction and publication history
First report of the two tableau asymptotics.
Read this published revision