25 条边长臂蜘蛛树的零可旋转性

K25-ALL-ACTUAL-VERTEX-ZERO-ROTATABILITY 已提供证明

对于每个整数 n ≥ 2、每个整数 m ≥ 0，以及 S(25^n,1^m) 中每个实际存在的顶点 v，都存在该图的一个优美标号 f，使得 f(v)=0。标号可以随 v 而不同。

形式化验证

已在声明范围内完成形式化验证

审查状态

内部核查

证据

Independent mathematical/graph QA report SHA-256 315907b9cb57d5449de00172b2d1d3b4df80aa3013813303a843c405b4563771; author formal freeze report SHA-256 cdd8ce2cb2a393fc6d4ec4734f6f68ae59cb4c47f1b46e7794080fd768523c01; copied-source Lean replay report SHA-256 07bf8eb86738caae8701b34fd1bef5683544a3650c2125f606ca4ae5feb9b5a6; bounded priority comparison report SHA-256 80d1ea284b6cc9fdb0b4bad0b680b9b678859d41d653678b531346ede3211b2d.

范围

For every n ≥ 2 and m ≥ 0, every actual named vertex of S(25^n,1^m): its center, each depth 1 through 25 on every named arm, and each of its m original center leaves when present. A possibly different graceful labeling is supplied for each selected vertex. The graph has 25n+m edges; vertex labels are 0..25n+m and edge weights are 1..25n+m.

假设

S(25^n,1^m) is the finite spider with n named arms of exactly 25 edges each and m original unit leaves attached to the center. A graceful labeling is a bijection from vertices to 0 through |E| and induces a bijection from edges to 1 through |E| by absolute endpoint differences. Every selected vertex is handled separately.

工具链

Lean 4.34.0; 27 fixed-k25 modules freshly compiled with -DwarningAsError=true in author freeze and separate copied-source replay; theorem GracefulBoundary.K25Full.all_vertices; internal mathematical/graph QA. Standard Lean kernel verification.

审查者

Internal mathematical/graph QA and separate copied-source Lean replay only; no external or peer review is claimed.