Time-Constrained Capital Dynamics:A Quantitative Reconstruction of Value Transformation and Platform Extraction

Contemporary theories of platform capitalism—whether critical (Zuboff, 2019; Srnicek, 2017) or institutional (Acemoglu & Robinson, 2012)—describe extraction and power asymmetry but provide no testable threshold for when such extraction triggers systemic collapse. Classical dynamical models like Goodwin (1967) offer endogenous cycles but remain limited to two dimensions, leaving no room for network monopoly power as an independent state variable. This paper addresses both gaps by treating irreversible individual life duration (T) as the fundamental binding constraint of economic exchange. We derive a dimensionless critical threshold, Θ = ω·η·C / γ, and embed it within a three-dimensional dynamical system governed by the Network Anchoring Coefficient (C), Structural Extraction Rate (η), and Base-Layer Effort Provision (P). Supported through both ordinary differential equations and agent-based simulation, the framework indicates that when the composite extraction ratio exceeds unity (Θ > 1), the base layer undergoes a nonlinear structural collapse. The threshold thus formalizes a hard biological boundary on capital accumulation: when extraction exhausts recovery, collapse is not a market failure but an endogenous phase transition.