arXiv subjects

Jose de Jesus Bernal Alvarado

Publications and source records attributed to Jose de Jesus Bernal Alvarado.

3 recordsLinked to original sources

arXiv2026

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

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.

physics.soc-ph↗

arXiv2026

Structural Divergence of the Inca Imperial Network, 1400--1572~CE: Persistent Homology, Substitution Topology, and the Topological Signature of Decapitation Collapse

We apply persistent homology to a six-layer temporal network model of the Inca Empire (Tawantinsuyu), built from the Qhapaq Ñan road system ($6{,}546$ segments; $12{,}031$~km): 4,492 nodes (4,452 active; 40 isolated removed), $4{,}358$ edges, $57$ temporal snapshots (1400--1572~CE). The complete flag complex yields $β_1 = 32$ cycles ($26$ macro-continental, $6$ meso-regional) and $β_0 = 264$ components at the finest filtration, evaluated across six layers: infrastructure, Inca political control, Spanish alliance growth, Andean tribute commerce, and Spanish legal/effective administration. Five results. (i) Infrastructure entropy $H_{\mathrm{infra}}=1.486\pm0.0001$ stays constant throughout, indicating no detectable topological disruption of the Qhapaq Ñan at this resolution. (ii) Inca political entropy $H_{\mathrm{inca}}$ is stable through the Cajamarca capture (1532~CE), then collapses to zero by 1537~CE; the dominant break is at Vilcabamba ($F=120.7$), not Cajamarca ($F=11.5$). (iii) Four of six layers reach the critical regime at 1532~CE, while infrastructure stays marginally below threshold ($\mathrm{ICT}=0.495$); trade and political reach the highest values ($\mathrm{ICT}=0.976$, $0.968$), marking Cajamarca as a synchronised multi-layer phase transition. (iv) Spanish legal administration converges to the infrastructure topology by 1572~CE ($W_1=5\times10^{-6}\approx0$): Substitution Topology, infrastructure-preserving collapse via topology transfer. (v) Legal--effective divergence decays from $W_1=0.591$ (1532) to $0.002$ (1572), quantifying resolution of colonial legal fiction. Together, these results support a distinct collapse mode---Substitution Topology---differing from erosion-dominated Roman/Byzantine collapse, Han fragmentation, and Aztec military destruction.

physics.soc-ph↗

arXiv2026

Topological Signatures of Imperial Stress: Persistent Homology of the Eastern Mediterranean Trade Network, 0--400 CE

We apply persistent homology to the ORBIS Geospatial Network Model of the Roman World in order to quantify the structural resilience of the Eastern Mediterranean trade network between 0 and 400 ce. The network is represented as a weighted transport system whose edges correspond to road, maritime, and riverine routes, each carrying a base cost derived from the ORBIS cost model. To introduce historical dynamics into this static spatial infrastructure, we construct a differential friction model in which edge weights vary by decade and by transport mode according to documented historical perturbations, including epidemic mortality, civil war, military pressure, administrative reorganisation, and imperial reunification. For each decadal snapshot, we compute all-pairs shortest-path distances on the active sub-network and construct a Vietoris--Rips filtration using an adaptive threshold defined by the 90th percentile of finite pairwise distances. The resulting betti number ($β_1$) persistent entropy time series identifies three structurally distinct phases in the Eastern Mediterranean network. Phase~I, from 0 to 200 ce, is a stationary high-redundancy regime consistent with the commercial integration of the early imperial and Antonine periods. Phase~II, from 210 to 280ce, corresponds to recoverable stress during the Crisis of the Third Century: betti number ($β_1$) entropy declines during the crisis but returns to the Phase~I baseline following Aurelianic reunification. Phase~III, from 290 to 400 ce, is qualitatively different: cycle redundancy declines monotonically and does not recover. The main contribution of this study is to show that persistent homology detects a dimension of imperial stress that is not reducible to single economic, military, or political indicators.

physics.soc-ph↗