重复端点 Canon 排列：锥中游走与谱几何
Repeated-Endpoint Canon Permutations: Cone Walks and Spectral Geometry
研究概述
解析性的锥中游走伴篇，涉及概率、调和与谱几何。论文的完整形式化验证仍在进行。
原始公开问题
Laudone 问题 5.12：重复端点的 canon 排列
Robert Laudone: Pattern avoidance in canon permutations — Question 5.12: enumeration in the intermediate repeated-endpoint range, addressed by a reversible multichain encoding and an effective recurrence.
原文摘要（英文）
This preprint solves the intermediate repeated-endpoint enumeration for canon permutations by a multichain recurrence and cone-walk model. It proves upper-boundary non-D-finiteness and exact asymptotics, and develops the associated harmonic-kernel and higher-dimensional spectral geometry. The foundational framework and results first appeared in the original unified preprint (10.5281/zenodo.22088094); this article is the focused analytic component of the subsequent reorganization. The companion combinatorial article is 10.5281/zenodo.22091632. A Lean 4 formalization of the principal results is in progress.
数学审核
内部定稿（Paper Close）表示该工作在公开前已完成整理和内部审核，并以工作论文形式发布。请将它作为普通学术预印本来阅读和讨论；后续检查或讨论仍可能带来更正。它不表示已经完成完整形式化或经过外部同行评审。
审核标准