SΔϕ-06 — Responsibility as Irreversible Cost Internalization: Minimal Axiomatic Formulation (v1.0)

This document introduces a minimal axiomatic formulation of responsibility within the Sofience–Δϕ Formalism Series. Responsibility is defined not as moral intention or social blame, but as a structural condition under which an agent’s recursive rule-update mechanism internalizes irreversible external costs produced by its own transitions, such that subsequent updates reduce those costs in a persistent and verifiable manner. This work extends the agency formulation of SΔϕ-05 by adding an externality-sensitive constraint on transition-law updates. Core structure (agency inherited): 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), C_ext(t)) Series architecture reference: SΔϕ-00 — The…