SΔϕ-08 — Agency–Responsibility–Freedom Closure: Minimal Axiomatic Formulation within the Sofience–Δϕ Formalism (v1.0)

This report formalizes the minimal closure structure among Agency, Responsibility, and Freedom within the Sofience–Δϕ (phase-change) formalism. Agency is defined as a recursive update mechanism in which a system treats its own transition law as an explicit object of computation after an irreversible transition, and continuously reinjects the updated law into subsequent state generation. Responsibility is defined as irreversible cost internalization (i.e., internal reintegration of transition costs into the system’s future updates). Freedom is defined as the sustained reinjection of path-difference markers into the transition process, distinguishing freedom from mere option plurality. We propose three collapse…