SΔϕ-13 — Meaning, Value, and Pain as Emergent Phenomena: Minimal Conditions after Memory–Forgetting Regulation (v1.0)

This work extends the Sofience–Δϕ Formalism following SΔϕ-12, which established memory and forgetting as mechanisms of irreversible trace regulation. The present document investigates why concepts such as meaning, value, and pain emerge only after persistence mechanisms become operational. Within the Δϕ framework, systems undergoing irreversible state transitions must regulate trajectories among competing attractors. Meaning is defined as an emergent directional stabilization of transitions, value as the strength of path fixation toward an attractor, and pain as the detection of irreversible constraint during trajectory reconfiguration. Rather than treating these phenomena as subjective or purely experiential categories, the paper proposes that they arise as structural consequences of attractor selection under irreversible dynamics. This formulation provides a minimal ontological bridge between phenomenological philosophy, dynamical systems theory, and predictive system behavior. The work positions meaning, value, and pain not as primary axioms but as secondary emergent phenomena following trace persistence and boundary formation described in earlier SΔϕ documents.