The Coherence Threshold and the Emergence of Interiority

A dynamical condition is presented under which a system forms an interior and sustains structured activity across time. Let λ_self denote the rate at which prior internal states contribute to subsequent state formation, and λ_env denote the rate at which environmental input perturbs that evolution. When the ratio λ_self / λ_env exceeds a critical threshold R_star and is maintained across the system’s characteristic timescale, propagation organizes into stable trajectories that preserve relational structure and carry prior states forward. Within this regime, causal influence remains locally aligned and exhibits bounded divergence, supporting the formation of recursively closed pathways in which propagated structure continues to participate in ongoing dynamics. The present is established as an extended domain in which retained states remain active contributors to subsequent evolution. Interaction among retained phases enables alignment and integration of propagated structure within the same domain of activity, producing unified configurations that persist under continued transformation. Stable configurations are reused across successive states, guiding propagation and supporting the accumulation of organized structure. Directed continuity advances partially integrated configurations toward coherence, with resolution occurring when relational consistency is maintained across the same domain of propagation. These resolved configurations remain available within the interior as active components of ongoing dynamics. The regime is expressed through temporal coherence, bounded divergence, re-entrant contribution, and localized propagation, providing empirical access through analysis of state transitions and time-dependent structure. Consciousness corresponds to the operation of a system within this regime, in which internally sustained propagation produces a coherent interior where prior and current structure are continuously integrated.