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,$\text{textsc}ce$), using 2{,}599 nodes and 4{,}503 trimodal edges calibrated against the $\text{textsc}orbis$ 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 ($N_{\mathrm{w}\mathrm{e}\mathrm{s}\mathrm{t}}=987$, ${\beta }_1\approx 52$ cycles per decade) a baseline East–West entropy gap of $+2.22$ units is present from 0,$\text{textsc}ce$ and grows at $+3.3\times {10}^{-3}$,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 ($H_{\mathrm{g}\mathrm{e}\mathrm{o}}$) and economic ($H_{\mathrm{e}\mathrm{c}\mathrm{o}}$) components reveals a peak decoupling ratio $R_d=H_{\mathrm{e}\mathrm{c}\mathrm{o}}\mathrm{/}{H}_{\mathrm{g}\mathrm{e}\mathrm{o}}=47.7$ at 620,$\text{textsc}ce$, falling to 13.9 at 640,$\text{textsc}ce$, 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,$\text{textsc}ce$) 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,$\text{textsc}ce$, providing an independent diagram-space analogue of $R_d$. Both the Western collapse (476,$\text{textsc}ce$) and the Byzantine endpoint (1453,$\text{textsc}ce$) occur at $H^{\ast }\approx 0.524$, interpreted as a candidate topological percolation threshold.