The Φ-Stack: A Formal Specification of Decay, Flow, and Proportional Allocation for a Post-Scarcity Civic Operating System

This paper presents the mathematical core of the Thermostat Commons, a cybernetic model for a post-scarcity society. We formalize the integration of the golden ratio (Φ ≈ 1.618, φ ≈ 0.618) as a foundational constant governing the system's key dynamics. The specification defines: 1) the Φ-Decay Function, a voucher depreciation curve ensuring flow over hoarding; 2) the Labour Margin Homeostat, targeting 61.8% utilization (38.2% surplus) for antifragile resilience; 3) the Structural Allocation Ratio (Φ:1) between necessity (Commons) and aspiration (Sterling) infrastructure; 4) a Φ-progressing Mastery Hierarchy. Together, these form a coherent Φ-Stack—a resonant social architecture where operational parameters are derived from a universal optimization constant, aligning human systems with natural patterns of balanced growth and decay.