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 (Kdomestic) and globally acquired (Kglobal) 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 Kglobal, which distorts R, and the distorted R subsequently erodes the productive foundation (TE × 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
鑫培 骆 (Sun,) studied this question.