Does Your Model Need Sleep? Constitutive Gap Dependence and the Stability Problem in Self-Modifying AI

Self-modifying AI systems drift toward ordered-phase dynamics through consolidative self-modification. This paper introduces weight-change DFA as a metric for self-modification dynamics, demonstrates that periodic state perturbation maintains criticality (p = 5.0 × 10⁻³⁰), and maps four failure modes of self-modifying AI onto distinct dynamical signatures. A therapeutic window spans the full phase transition from sealed to dissolved, with the first 2% of correction producing 27% of the total effect. Ten experimental protocols are proposed for production-scale verification.