A Bessel-Factorization Proof of Mathar's Recurrence for Type-ace Lattice Walks
A recurrence proof with exact Ore-operator verification
A candidate proof of Mathar's conjectured recurrence for the Type-ace lattice-walk sequence OEIS A302186. Exact verification covers coefficients through n=100 and the Ore-operator identity.
- Identifier
- MF-PRISM-MATH-2026-09
- Series
- Mathematics
- Edition
- Version 1.1
- Length
- 9 pages
What is this paper trying to establish?
Can Mathar’s conjectured recurrence for Type-ace lattice walks be derived from a Bessel factorization?
The central idea.
A candidate proof of Mathar's conjectured recurrence for the Type-ace lattice-walk sequence OEIS A302186. Exact verification covers coefficients through n=100 and the Ore-operator identity.
Candidate proof released for independent specialist and publication-priority review.
This manuscript presents a candidate resolution. Publication is not verification: independent specialist review remains necessary before the result should be treated as established.
What changes if the method holds?
A proof would replace a conjectured numerical pattern with a structural explanation tied to special functions and operator factorization.
Where scrutiny should concentrate.
The paper identifies the following points as the highest-value targets for independent review.
- 01The Bessel-factorization derivation.
- 02The Ore-operator identity and recurrence transfer.
- 03The distinction between exact finite verification and the general proof, including priority review.
An open, inspectable research artifact.
The public record links the manuscript to its release, source package, review materials, and persistent identifier. Status travels with the paper; a reserved DOI is not presented as a published Zenodo record.
- Document
- Preprint
- Review status
- Open for independent review
- Published
- 2026-07-18
- DOI status
- Published · 10.5281/zenodo.21434724
- Canonical record
- MF-PRISM-MATH-2026-09