The Coherence Threshold _A Proof of the Physical Origin of Interiority_

A minimal physical condition is required to determine when a system possesses an interior. This paper derives such a condition from the balance between internal restoration and environmental disruption. Let λ_self denote the rate at which a system restores and propagates its own structure, and λ_env the rate at which environmental interaction disrupts that structure. The ratio R = λ_self / λ_env defines a critical threshold R★ separating two regimes. When R P(S_t | E_t). In this regime, perturbations are resolved relative to the system’s own organization, establishing a reference frame defined from within. This constitutes self-measurement in a strictly dynamical sense and produces a distinction between internal and external dynamics that is generated by the system itself. An interior is identified with the condition in which a system’s states are defined relative to its own structure. Consciousness corresponds to the operation of a system within this regime, where persistence, temporal depth, unity, and self-reference arise as direct consequences of sustained internal coherence. The coherence threshold therefore provides a minimal, substrate-independent, and testable physical criterion for the emergence of interiority without introducing additional primitives.