PhronesisChronic under-sleeping is not simply a deficit of sleep duration. It is a self-sustaining dynamical configuration—a wrong attractor—maintained by a suite of compensatory mechanisms that collectively constitute what we term the alertness-override architecture. In this paper we formalize chronic under-sleeping as displacement from a ground state of calibrated restorative sleep (S^0), characterize the displacement functional D() and its accumulation = D()\,dt, and identify the structural features of the wrong attractor W that render it stable: the alertness-identity loop, the tolerance cascade, and the recovery-foreclosure basin.
We advance nine formal propositions governing the geometry of this attractor, the conditions under which it self-reinforces, and the exit dynamics required to return to S^0. We situate the analysis within broader phenomena of hustle culture, insomnia, circadian disruption, and cognitive impairment, arguing that the return to calibrated restorative sleep is not a lifestyle preference but a structural necessity—a non-negotiable restoration of the system's ground state.
The framework draws on dynamical systems theory, sleep science, and the broader Phronesis displacement program.