Structural Divergence of the Roman--Byzantine Trade Network, 0--1453\,CE: Persistent Homology, Topological Velocity, and Criticality Indicators of Imperial Collapse

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 ($N_{\rm west}=987$, $\beta_1\approx52$ 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.