Addiction Withdrawal as Wrong Attractor Exit Cost: Allostatic Shift as Basin Redefinition, the Withdrawal Spiral, and the Neuroscience of Return Path Re-Engineering

We apply the Displacement Framework to addiction withdrawal, formalizing it as the exit cost from the addiction wrong attractor W_addiction — the energy barrier that must be crossed to leave the allostatic basin established by chronic substance use. Eleven formal propositions are derived covering: allostatic basin redefinition (the addicted brain's reward set-point shifts such that S°_pre-addiction is no longer accessible without substance), withdrawal as exit-cost trough (D(ξ_withdrawal) > D(ξ_addiction) during cessation, explaining the gradient toward relapse), the withdrawal spiral (cessation drives acute D(ξ) above the wrong-attractor cost, creating a return gradient toward the substance), substance-specific landscape differences (opioid noradrenergic storm with PAWS, alcohol/benzodiazepine GABAergic rebound requiring medical management, nicotine dopamine depletion, stimulant hedonic depletion plateau), PAWS as extended wrong-attractor liminal state with peak relapse vulnerability, craving as gradient-proximity signal from conditioned environmental cues, and medication-assisted treatment as landscape intervention (methadone as surrogate basin, buprenorphine as floor-ceiling stabilizer, naltrexone as basin wall blocking re-entry).

The abstinence paradox is formalized as a path-geometry tradeoff between maximum-gradient direct routes and lower-gradient longer routes. Neuroplasticity-based S° restoration is modeled with documented dopamine receptor density recovery timelines.