Chronic Approval-Checking as Permission-Seeking Wrong Attractor: The Validation-Loop Architecture, Self-Authorization Foreclosure Basin, and the Return to Calibrated Internal Sanction

Chronic approval-checking—the compulsive solicitation of external validation before, during, or after action—constitutes a structurally stable wrong attractor in the behavioral phase space of autonomous agents. Unlike episodic uncertainty resolution, chronic approval-checking persists across contexts in which internal sanction is fully adequate, progressively forecloses the capacity for self-authorization, and generates a self-reinforcing feedback architecture that deepens the validation-loop basin with each cycle.

We formalize this phenomenon using the displacement framework: defining S^0 as the ground state of calibrated internal sanction, D() as the scalar displacement cost associated with permission-seeking behavior along the behavioral trajectory, and = D()\,dt as the accumulated permission-seeking field over time. We prove nine formal propositions characterizing the attractor geometry, the foreclosure mechanism, the phase structure of approval-dependence, intervention conditions, recovery dynamics, systemic propagation effects, and the ethical asymmetry between calibrated internal sanction and externally-sourced permission.

The framework yields a tractable account of why chronic approval-seeking is not merely inefficient but constitutes a form of self-directed harm: it is a basin that the agent deepens by inhabiting it, a wrong answer that strengthens by being repeatedly chosen.