Computational Macrohistory: Operational Framework — State Space, Variables, and Dynamic Equations

This document constitutes Document II of the Computational Macrohistory (CMH) series, providing the operational framework that translates the axiomatic foundations established in Document I into a concrete mathematical apparatus for empirical analysis. We define a 25-dimensional state space comprising demographic (D), economic (E), political (P), social (S), and psychological-collective (Ψ) variables, each with precise operationalization protocols and data source specifications. The document presents coupled dynamic equations governing system evolution, derives composite indices including the Systemic Stress Index (SSI) and Elite Pressure Index, and specifies probabilistic event functions for instability episodes and regime transitions. Complete mathematical derivations, reference parameter values with calibration sources, and variable specifications are provided in appendices. This framework bridges abstract axiomatic principles with empirical implementation, enabling quantitative historical analysis and probabilistic scenario modeling while maintaining explicit acknowledgment of epistemic limitations inherent to complex social systems.