公元1400-1572年印加帝国网络的结构分歧：持续同调、替换拓扑与斩首式崩溃的拓扑特征
Structural Divergence of the Inca Imperial Network, 1400--1572~CE: Persistent Homology, Substitution Topology, and the Topological Signature of Decapitation Collapse
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中文总结 AI 辅助
本研究运用持续同调分析印加帝国六层时间网络，发现其崩溃为基础设施保留的替换拓扑模式，区别于其他古代文明的崩溃模式，且量化了殖民法律虚构的消解。
中文摘要 AI 辅助
我们将持续同调应用于基于Qhapaq Ñan道路系统构建的印加帝国（Tawantinsuyu）六层时间网络模型，该系统包含6546个路段、12031千米、4492个节点（其中4452个活跃，40个孤立节点已移除）、4358条边、57个时间快照（公元1400-1572年）。完全旗复形在最细过滤度下产生β₁=32个环（26个泛大陆级、6个区域级）和β₀=264个分量，该评估涵盖基础设施、印加政治控制、西班牙同盟扩张、安第斯朝贡贸易、西班牙法律/有效行政共六层。研究得出五项结果：（i）基础设施熵H_infra=1.486±0.0001全程保持恒定，表明该分辨率下Qhapaq Ñan未发生可检测的拓扑破坏；（ii）印加政治熵H_inca在1532年卡哈马卡俘获事件中保持稳定，至1537年崩溃为零；主要断裂发生在维尔卡班巴（F=120.7），而非卡哈马卡（F=11.5）；（iii）六层中的四层在1532年达到临界状态，而基础设施仍略低于阈值（ICT=0.495）；贸易与政治层达到最高值（ICT=0.976、0.968），标志卡哈马卡为同步多层相变；（iv）西班牙法律行政层至1572年收敛于基础设施拓扑（W₁=5×10⁻⁶≈0）：即替换拓扑，指通过拓扑转移实现的基础设施保留式崩溃；（v）法律-有效行政分歧从1532年的W₁=0.591降至1572年的0.002，量化了殖民法律虚构的消解。综上，这些结果支持一种独特的崩溃模式——替换拓扑，其与以侵蚀为主的罗马/拜占庭崩溃、汉朝分裂、阿兹特克军事破坏均不同。
英文摘要
We apply persistent homology to a six-layer temporal network model of the Inca Empire (Tawantinsuyu), built from the Qhapaq Ñan road system ($6{,}546$ segments; $12{,}031$~km): 4,492 nodes (4,452 active; 40 isolated removed), $4{,}358$ edges, $57$ temporal snapshots (1400--1572~CE). The complete flag complex yields $β_1 = 32$ cycles ($26$ macro-continental, $6$ meso-regional) and $β_0 = 264$ components at the finest filtration, evaluated across six layers: infrastructure, Inca political control, Spanish alliance growth, Andean tribute commerce, and Spanish legal/effective administration. Five results. (i) Infrastructure entropy $H_{\mathrm{infra}}=1.486\pm0.0001$ stays constant throughout, indicating no detectable topological disruption of the Qhapaq Ñan at this resolution. (ii) Inca political entropy $H_{\mathrm{inca}}$ is stable through the Cajamarca capture (1532~CE), then collapses to zero by 1537~CE; the dominant break is at Vilcabamba ($F=120.7$), not Cajamarca ($F=11.5$). (iii) Four of six layers reach the critical regime at 1532~CE, while infrastructure stays marginally below threshold ($\mathrm{ICT}=0.495$); trade and political reach the highest values ($\mathrm{ICT}=0.976$, $0.968$), marking Cajamarca as a synchronised multi-layer phase transition. (iv) Spanish legal administration converges to the infrastructure topology by 1572~CE ($W_1=5\times10^{-6}\approx0$): Substitution Topology, infrastructure-preserving collapse via topology transfer. (v) Legal--effective divergence decays from $W_1=0.591$ (1532) to $0.002$ (1572), quantifying resolution of colonial legal fiction. Together, these results support a distinct collapse mode---Substitution Topology---differing from erosion-dominated Roman/Byzantine collapse, Han fragmentation, and Aztec military destruction.
