AI 中文总结
本研究通过持续同调与双模型拓扑管道分析阿兹特克帝国多层网络，揭示其朝贡层结构脆弱性、特诺奇蒂特兰中心的关键作用、特拉斯卡拉区域的结构空洞，提出“空洞占据树”这一新帝国崩溃模式。
AI 中文摘要
我们将持续同调与双模型拓扑管道应用于阿兹特克帝国的多层网络（三王同盟，公元1427年—1521年），该网络由朝贡记录与38个节点（特诺奇蒂特兰中心、36个纳贡省份及特拉斯卡拉飞地）、208条边的地理邻接关系构建而成。我们报告四项主要结果：（i）朝贡（控制）层为纯提取树（贝蒂数β₁=0，所有时期的同调群秩H=0.000），其结构脆弱性高于采用相同管道分析的罗马、拜占庭或汉朝行政数据集中任何已记录的构型；（ii）移除特诺奇蒂特兰中心这一单节点会使巨分量从1.000降至0.630，同时消除30个冗余环，相对于随机扰动的结构不对称比＞4:1；（iii）特拉斯卡拉-普埃布拉区域与帝国地理点云的主导β₁类重合（持续长度=22.09km，其余区域均＜3km），该结构空洞在过滤中无论是否将特拉斯卡拉纳入建模均存在；（iv）逻辑回归证实，地理层的商业中心性（相关系数r=+0.462，p值=0.004）是早期同盟形成的主导预测因子，而朝贡负担无相关性（r=-0.033，p=0.845）。这四项结果定义了一种新的帝国崩溃模式——“空洞占据树”，即控制层零拓扑冗余与自治飞地占据的主导几何空洞共存，该构型此前在历史网络拓扑数据分析（TDA）中未被记录。
英文摘要
We apply persistent homology and a dual-model topological pipeline to a multilayer network of the Aztec Empire (Triple Alliance, 1427--1521 CE), constructed from tribute records and geographic adjacency among 38 nodes (Tenochtitlan-Centro, 36 tribute-paying provinces, and the Tlaxcala enclave) and 208 edges. We report four main results: (i) The tribute (control) layer is a pure extraction tree ($\bettione = 0$, $H = 0.000$ at all epochs): structurally more fragile than any documented configuration in the Roman, Byzantine, or Han administrative datasets analyzed with the same pipeline. (ii) Single-node removal of Tenochtitlan-Centro collapses the giant component from 1.000 to 0.630 and eliminates 30 redundancy cycles simultaneously, a structural asymmetry ratio of $>4$:1 relative to random perturbation. (iii) The Tlaxcala--Puebla region coincides with the dominant $\bettione$ class of the imperial geographic point cloud (persistence $= 22.09$~km, versus $< 3$~km for all others), a structural void that exists identically whether Tlaxcala is modeled as absent or present in the filtration. (iv) A logistic regression confirms that commercial centrality in the geographic layer ($r = +0.462$, $p = 0.004$) is the dominant predictor of early alliance formation, while tribute burden is uncorrelated ($r = -0.033$, $p = 0.845$). These four results define a new imperial collapse mode, the \emph{void-occupied tree}, in which zero topological redundancy in the control layer coincides with a dominant geometric void occupied by an autonomous enclave---a configuration not previously documented in historical network TDA.
Comments10 pages, 4 figures
