代数表达体系——"生产型政治哲学"经济周期分析的数理基础

This appendix presents a formal algebraic framework as a methodological extension of the "Productive Political Philosophy" theoretical system, specifically developed for the long-term analysis of economic cycles. It transforms the static foundation of the Community Cohesion Model — a core analytical tool within this system — into a dynamic diagnostic instrument. The framework introduces a crisis coefficient (κ) defined as the ratio of productive capacity (T) to total consumption capacity (K), where the latter is decomposed into domestic (K_domestic) and globally acquired (K_global) components through the outward projection of relations of production (R). The core mechanism is formalized as a self-reinforcing feedback loop: rising κ drives the acquisition of K_global, which distorts R, and the distorted R subsequently erodes the productive foundation (T_E × E × η), leading to a further increase in κ. This algebraic framework captures the structural logic of the stagnation-crisis cycle and establishes a unified mathematical basis for analyzing the evolutionary endgame of capitalist business cycles. Algebraic formalization; Community Cohesion Model; crisis coefficient; productive capacity; consumption capacity; feedback loop; methodological extension; Productive Political Philosophy