The π Φ-Stack: A Formal Specification of Decay, Flow, and Proportional Allocation for a Post-Scarcity Civic Operating System (Version 1.1)

This paper presents the mathematical core of the Thermostat Commons, acybernetic model for a post-scarcity society. We formalize theintegration of the golden ratio (Φ ≈ 1.618, φ ≈ 0.618) and the cycleconstant π to define the system's core temporal rhythm as foundationalconstants governing the system's key dynamics. The specificationdefines: 1) the Φ-Decay Function, a voucher depreciation curve ensuringflow over hoarding; 2) the Labour Margin Homeostat, targeting 61.8%utilization (38.2% surplus) for antifragile resilience; 3) theStructural Allocation Ratio (Φ:1) between necessity (Commons) andaspiration (Sterling) infrastructure; 4) a Φ-progressing MasteryHierarchy. Together, these form a coherent Φ-Stack---a resonant socialarchitecture where operational parameters are derived from universaloptimization constants, aligning human systems with natural patterns ofbalanced growth and decay in both space and time.