Sleep as Nightly Ground State Return: Wakefulness Displacement, Sleep Architecture, and Insomnia as Wrong Attractor

We apply the displacement framework to sleep and sleep disorders. The central claim is that sleep is biology's most universal mandatory return: wakefulness is a controlled, high-displacement condition in which metabolic, synaptic, and neural systems accumulate displacement _wake whose cost must be serviced nightly. We define the biological sleep ground state S^0_sleep, model wakefulness as controlled departure from it, and identify adenosine as the primary signal of accumulated displacement cost.

NREM sleep is formalized as deep ground-state restoration, and REM sleep as active emotional-displacement processing. Insomnia is analyzed as a wrong attractor in the return pathway — a stable high- configuration that prevents entry into the return path. Chronic sleep restriction is modeled as the accumulation of unresolved displacement = D()\,dt whose recovery cost exceeds prevention cost by DC5 (irreversibility).

Sleep medicine — CBT-I, pharmacology, stimulus control — is reinterpreted as return-pathway facilitation: interventions that lower the attractor basin of the wrong state or clear obstructions on the return path. The framework provides a unified quantitative language for phenomena previously described only empirically.