树的堆叠数
The stacking number of a tree
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中文总结 AI 辅助
本文证明有限树的堆叠数等于 Csernák 和 Soukup 猜想的距离-度估计量，并通过递归刻画、零分数障碍和加权抵消论证给出证明，且已在 Lean 4 中形式化验证。
中文摘要 AI 辅助
图的堆叠数是最小的整数 t >= 2，使得任意 t 个鹅卵石的配置都可以通过鹅卵石移动变换为支撑在单个顶点上的配置。我们证明，对于每个至少有两个顶点的有限树 T，该数等于 Csernák 和 Soukup 猜想的基于根的距离-度估计量。证明使用了在指定顶点处可堆叠性的精确递归刻画、一个显式的零分数障碍，以及针对任意不可堆叠配置的加权抵消论证。完整定理已在 Lean 4 中形式化；形式化结果也已通过 Palomar 机械验证，并公开注册为 PALOMAR-2026-09-25-000010。
英文摘要
The stacking number of a graph is the least integer t >= 2 such that every configuration of t pebbles can be transformed by pebbling moves into a configuration supported on one vertex. We prove that, for every finite tree T with at least two vertices, this number equals the rooted distance-and-degree estimator conjectured by Csernák and Soukup. The proof uses an exact recursive characterization of stackability at a prescribed vertex, an explicit zero-score obstruction, and a weighted cancellation argument for arbitrary nonstackable configurations. The complete theorem is formalized in Lean 4; the formal result has also passed Palomar mechanical verification and is publicly registered as PALOMAR-2026-09-25-000010.
