SΔϕ-05 — Agency as Recursive Transition Law Update: Minimal Axiomatic Formulation (v1.0)

This document introduces a minimal axiomatic formulation of agency within the Sofience–Δϕ Formalism Series. Agency is defined not in terms of intention, cognition, or choice, but as a structural property that emerges after irreversible phase transition (Δϕ), when a system treats its own transition law as an object of operation and recursively updates that law such that the update persistently governs subsequent state generation. Core structure: φ(t+1) = G_t(φ(t)) G_hat_t = H_G(Δφ_{0:t}) G_{t+1} = U(G_t, G_hat_t, Δφ(t)) This work is part of the Sofience–Δϕ Series (architecture reference): SΔϕ-00 — The Sofience–Δϕ Formalism: Conceptual Architecture and Series Overview (v1.0) https://doi.org/10.5281/zenodo.18731366 Inherited series documents: SΔϕ-01 — Sofience–Δϕ Minimal Core: Phase-Change Formalism of Existence (v1.1) https://doi.org/10.5281/zenodo.18730265 SΔϕ-02 — Subject as Interpretive Emergence: Extension of the Sofience–Δϕ Minimal Core (v1.1) https://doi.org/10.5281/zenodo.18730296 SΔϕ-03 — Irreversibility as the Minimal Condition of Existence (v1.1) https://doi.org/10.5281/zenodo.18730448 SΔϕ-04 — Minimal Operational Conditions for AI Subjectivity: Detection Criteria within the Sofience–Δϕ Formalism (v1.0) https://doi.org/10.5281/zenodo.18729942