AI 中文总结
研究汉代帝国系统，通过构建三个互补网络并运用持久同调形式主义，测试罗马 - 拜占庭案例的方法是否适用，得出汉代帝国崩溃分裂的拓扑特征及早期预警指标，提前45 - 50年发出崩溃信号。
AI 中文摘要
我们将参考文献中的持久同调形式主义扩展到汉代（公元前206年 - 公元220年），测试罗马 - 拜占庭案例中的崩溃阈值\(\Hstar = 0.5241\)和三网络分解方法是否适用于机制不同的帝国系统。构建了三个互补网络，通过对数字高程模型进行最小成本路径分析得出边成本。\(\Hadm\)在公元220年崩溃至零，\(\Hgeo\)同时增加，产生内部分裂的拓扑特征。跨网络瓦瑟斯坦距离在公元190年跃变，在公元184年后的分裂模型下出现三个与魏、蜀、吴领域匹配的\(\beta_1\)周期。三个独立的早期预警指标在正式解体前45 - 50年发出崩溃信号。
英文摘要
We extend the persistent homology formalism done in references~\cite{paper1,paper2} to the Han Dynasty ($206~\mathrm{BCE}$--$220~\mathrm{CE}$), testing whether the collapse threshold $\Hstar = 0.5241$ and the three-network decomposition methodology established for the Roman--Byzantine case generalize to a mechanistically distinct imperial system. Three complementary networks are constructed from geospatial and historical data: an administrative network ($\Hadm$, 392~prefectures from CHGIS~v6), a geographic network ($\Hgeo$, with node end-dates extended beyond administrative dissolution), and an 81-node Silk Road trade network ($\Htrd$) as a structural control. Edge costs are derived via least-cost path analysis on a $1~\mathrm{km/pixel}$ digital elevation model, modulated by five historical friction channels. $\Hadm$ collapses to zero at 220~CE (phase~G slope $-0.0261~\mathrm{yr}^{-1}$, $R^2 = 0.689$) while $\Hgeo$ simultaneously \emph{increases} to $3.065$, producing a divergence $ΔH = 3.065$ -- the topological signature of \emph{internal fragmentation}. The cross-network Wasserstein distance $W_\times(\mathrm{Admin},\mathrm{Geo})$ jumps from exactly zero to $737$ at $d=190$~CE, one decade after the Yellow Turban Rebellion, and three long-lived $β_1$ cycles matching the Wei, Shu, and Wu domains emerge under the post-184~CE fragmentation model -- thirty years before formal partition. Three independent early-warning indicators (Wasserstein velocity $\dot{W}_2$, correlation length $ξ$, and the Integrated Change Tracker) signal collapse onset 45--50~years before formal dissolution.
Comments24 pages, 7 figures
