SΔϕ-12 — Memory and Forgetting as Irreversible Trace Regulation: Minimal Persistence Mechanism after SΔϕ-11 (v1.0)

This paper fixes memory and forgetting as the minimal regulation mechanism required for persistence under irreversibility within the Sofience–Δϕ (SΔϕ) series. Memory is defined as selective re-entry of irreversible traces into next transition selection (constraint injection), while forgetting is defined as compression/pruning that preserves directional constraints while reopening feasible path space. The paper provides minimal axioms, a Trace Regulation Loop (TRL) diagram, and a three-regime pathology map (drift/repeat, fixation/paralysis, adaptive persistence) to diagnose stability conditions for continued re-entry dynamics.