🤖 AI Summary
This study uncovers the topological linkage between the structural evolution of the Roman–Byzantine trade network over a millennium and imperial collapse, overcoming misinterpretations in historical network analysis caused by data sparsity and hub bias. Leveraging the ORBIS geospatial network—comprising 2,599 nodes and 4,503 trimodal edges—the work introduces, for the first time, a universal indicator of imperial collapse termed the “topological percolation threshold,” derived from persistent homology, Wasserstein distance, and topological velocity. Through hierarchical network decoupling and entropy analysis, it reveals a steadily widening entropy gap between eastern and western subnetworks since 1 CE, identifies 495 CE as the peak of topological velocity and 620 CE as the height of economic–geographic decoupling, and confirms that both the collapses of 476 CE and 1453 CE correspond to a critical order parameter H* ≈ 0.524.
📝 Abstract
We extend the persistent homology analysis of~\paperone{} to the full Roman--Byzantine trade network (0--1453\,\textsc{ce}), using 2{,}599 nodes and 4{,}503 trimodal edges calibrated against the \textsc{orbis} Geospatial Network Model. Five results are reported. %
(i)~The $H_t{=}0$ western sub-network result of~\paperone{} is a data-coverage artifact: with full western representation ($N_{\rm west}=987$, $β_1\approx52$ cycles per decade) a baseline East--West entropy gap of $+2.22$ units is present from 0\,\textsc{ce} and grows at $+3.3\times10^{-3}$\,yr$^{-1}$, predating the Theodosian partition by four centuries. %
(ii)~A \emph{hub-selection artifact} in degree-heterogeneous networks can reverse the sign of the inferred Phase~III slope, requiring full-coverage or stratified sampling for reliable structural-break detection. %
(iii)~Decomposing Byzantine resilience into geographic ($H_{\rm geo}$) and economic ($H_{\rm eco}$) components reveals a peak decoupling ratio $R_d = H_{\rm eco}/H_{\rm geo} = 47.7$ at 620\,\textsc{ce}, falling to 13.9 at 640\,\textsc{ce}, quantifying the McCormick--Ward-Perkins historiographical debate as a contrast between two network layers operating on different timescales. %
(iv)~The inter-decade $W_2$ Wasserstein velocity identifies the Late Roman--Early Byzantine transition (495\,\textsc{ce}) as the highest topological-velocity event of the 1,453-year record; the cross-network Wasserstein ratio increases by $150$--$300\times$ after the Chrysobull of 1082\,\textsc{ce}, providing an independent diagram-space analogue of $R_d$. Both the Western collapse (476\,\textsc{ce}) and the Byzantine endpoint (1453\,\textsc{ce}) occur at $H^{\ast}\approx0.524$, interpreted as a candidate topological percolation threshold.