The Arc of Coherence: A Flux‑Geometric Theory of Civilizational Phase Transitions

Abstract

Historical dynamics has identified recurrent patterns in the rise and fall of states, yet existing models treat polities as black boxes, relying on macroscopic proxy variables without an explicit topological anatomy of internal structure. We construct a non‑equilibrium flux framework in which pre‑modern states are open dissipative systems governed by three axioms: flux normalization (K+D≡1), an intrinsic noise floor (δmin=1/κ2), and spontaneous symmetry breaking. From these axioms, embedded in the mean‑field universality class of hierarchical coordination lattices, we derive a global flux purity P and prove that the separatrix between order and disorder occurs at the universal mean‑field critical point Pc=0.5. The framework predicts a maximum stable administrative hierarchy of eleven levels (L11) from the spectral eigenstructure of hierarchical tree graphs and partitions dynastic evolution into five mathematically defined phases: nucleation, homeostasis, entropic accumulation, critical stalemate, and phase transition.Using proxy variables drawn from Chinese dynastic records (221 BCE–1911 CE) and Roman fiscal‑military data (27 BCE–476 CE), we calibrate the model via Bayesian operationalization. All framework parameters (κ, γeff, Pc) are calibrated on these two datasets alone. Chinese dynasties exhibit a mean cycle length of 247±38 years, consistent with the relaxation time τR=γeff−1ln⁡(P0/Pc) (R2=0.81). Rome's Third‑Century Crisis shows critical slowing down as P→Pc+, with recovery times diverging according to the mean‑field power‑law singularity τrecovery∝|P−Pc|−1/2.We then project the framework onto a third, independent civilization—the Abbasid Caliphate (750–1258 CE)—as a coarse‑resolution out‑of‑sample test, without parameter retuning. The Abbasid trajectory crosses Pc during the Anarchy at Samarra (861–870 CE) at P=0.51±0.05, consistent with the predicted critical threshold. The framework is further extended to asymmetric conquest regimes—Norman England (1066), Ottoman Anatolia (1453), and Qing China (1644)—as qualitative consistency checks, demonstrating that conquest dynasties follow the same relaxation dynamics but with higher initial purity and variable membrane‑coupling strategies. A unified typology is proposed to classify conquest regimes by coupling strategy and residual purity of the conquered civilization. Four algorithmic predictions for single‑core endogenous dynasties are specified, with three additional predictions for conquest regimes reserved for future empirical evaluation. A counterfactual simulation demonstrates the framework's operational power by estimating the delay in dynastic collapse under modified fiscal‑fidelity initial conditions.