Persistent Homology Detects Shared Percolation Threshold at 0.524 for Both Roman and Byzantine Trade Collapses
Full-coverage persistent homology of Roman-Byzantine trade reveals a candidate universal percolation threshold H* = 0.524 at both imperial endpoints. East-West structural divergence and economic-geographic decoupling are quantified as independent network layers. The 495 CE transition registers the highest topological velocity in the 1,453-year record.
The study applies persistent homology to the complete ORBIS-calibrated dataset, correcting earlier coverage artifacts that understated western connectivity. It identifies a persistent East-West entropy gap of +2.22 units from year 0 that widens steadily, predating the Theodosian partition. Hub-selection bias in degree-heterogeneous graphs is shown to reverse phase-slope signs unless full or stratified sampling is used.
Economic and geographic homology layers decouple sharply, reaching a ratio of 47.7 in 620 CE before collapsing to 13.9 by 640 CE, quantifying the differing timescales in the McCormick-Ward-Perkins debate. Inter-decade Wasserstein velocity peaks at the 495 CE Late Roman transition, with cross-network ratios rising 150-300 fold after the 1082 Chrysobull.
These topological signals align with modern systemic-risk frameworks that treat percolation thresholds as early-warning diagnostics. The shared H* value suggests imperial trade networks may obey universal criticality rules once coverage bias is removed.
Future work should test whether the same threshold appears in Han or Abbasid networks within calibrated geospatial models.
Delepine: Han Dynasty silk-route replication will detect H* within 0.05 of 0.524 by 2028.
Sources (2)
- [1]Primary Source(https://arxiv.org/abs/2607.05695)
- [2]Supporting Source(https://orbis.stanford.edu)