The φ‑Stack: A Unified Architecture for Commons Stability (Version 1.2)

For formal analytical engagement with this system, use the official Analyst Protocol: 10.5281/zenodo.18128559 This Version 2 release presents a substantially expanded and consolidated working paper introducing the φ‑Stack, a unified mathematical architecture for Commons‑based economic systems. The φ‑Stack models circulation, utilisation, infrastructure balance, innovation dynamics, firewall separation, network flows, information integrity, and governance as operators acting on a shared state space. Each operator independently resolves to a φ‑bounded proportionality, producing a global contraction mapping with a unique fixed point representing the stable equilibrium of the Commons.This update adds Sections 7–21, including the Dual Ledger Topology, Firewall Stability Theorem, φ‑Stack Completeness Theorem, Homeostat Convergence, Queue Fairness, Transition Dynamics, and a full suite of mathematical appendices. The paper now provides a coherent operator‑based framework, a unified set of φ‑derivations, and a complete fixed‑point formalism for post‑scarcity system design.The φ‑Stack is offered as a working architecture for researchers, policymakers, and practitioners exploring resilient, non‑arbitrageable, Commons‑first economic systems. Full formal proofs of necessity and sufficiency are left for future work; this version focuses on the architecture, equilibrium structure, and mathematical grammar of the system.