A Dual Topological Pipeline for Imperial Network Analysis: Persistent Homology, Structural Fragility, and the Aztec Collapse

Abstract

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.