Addiction Relapse as Wrong Attractor Return: Neurobiological Displacement and the Incomplete Recovery Path

We apply the displacement framework to addiction and relapse. The central thesis is that addiction is a neurobiological wrong attractor: a pathological stable state that the reward system converges to despite its displacement from S^0_baseline, the pre-addiction dopaminergic ground state. Addictive substances produce allostatic displacement: each use cycle shifts the hedonic setpoint downward through tolerance, making S^0_true progressively less accessible and conferring stability on the addicted configuration.

Craving is the wrong attractor's pull — the displacement gradient of a system whose reference point has been captured. Relapse is return to the wrong attractor after partial recovery, driven by cue-induced incentive salience, stress-induced allostatic load, or insufficiently deep recovery basin. Recovery is the active construction of a new S^0 with sufficient basin depth to resist wrong attractor pull.

Medication-assisted treatment operates by reshaping the attractor landscape — flattening the wrong attractor or deepening the recovery basin — rather than by demanding that willpower override attractor dynamics. We provide formal definitions, propositions, and a displacement-framework interpretation table for the key phenomena of the addiction cycle.