Sleep as Mandatory Displacement Recovery: Accumulated $$, Forced Return, and the Cost of Deprivation

Sleep is not rest. Sleep is mandatory displacement recovery --- the periodic forced return of biological and cognitive systems toward their ground states after the accumulated cost of waking. We apply the displacement framework to sleep physiology, identifying wake-state displacement (), accumulated displacement cost (), and sleep as the minimum-cost path back toward. We show that sleep deprivation is accumulated $D()$), and REM sleep as active displacement processing --- not rest, but managed re-traversal of accumulated displacement.

The framework explains why sleep cannot be compressed, replaced, or fully recovered, and why the subjective experience of sleep onset is precisely a felt movement away from waking displacement toward ground.