SΔϕ-24 — Authority and Innovation as Dual Regimes: Minimal Axioms for Compression, Re-opening, and Update Triggers in Coupled Environments (v1.0)

This paper formalizes authority and innovation as dual regimes within the Sofience–Δϕ (SΔϕ) series. Authority is defined as compression-driven convergence toward low-resistance default routes (Δϕ↓): accumulated pruning and cost reduction produce an attractor that becomes the system’s operational baseline. Innovation is defined as misfit-triggered re-opening (Δϕ↑): when accumulated mismatch (ε) between a system and its environment crosses a threshold, previously pruned alternatives become computable again and re-entry editing is activated. The central claim is that authority–innovation conflict is not a moral disagreement but a phase-transition signal (τ). This document provides minimal definitions (authority, compression, misfit, triggers, re-opening, authority debt), minimal axioms describing the compression–misfit–re-opening loop, and diagnostic regimes distinguishing stable authority, rigid authority (closure precursor), innovative re-opening, and suppressed innovation. Building on SΔϕ-23, the paper treats coupled environments (co-environmentalization) as an amplification regime where misfit, triggers, and authority debt propagate across systems. It also incorporates the SΔϕ-23 safety boundary—ontology–axiology separation—to prevent strong authority traces from being mistaken as moral legitimacy, which would automatically seal innovation as heresy and accelerate closure. Scope: minimal axioms and diagnostic structure; substrate-agnostic across individuals, organizations, and AI systems.