Name | Quadratic Metric-Flow Lyapunov Decrease
Object | $S(x)=\tfrac12 x^\top A x$, $G\succ 0$
Type | Exact local descent identity
Identity | $S(x-\varepsilon G^{-1}\nabla S)<S(x)$ unless $\nabla S=0$, for admissible $\varepsilon$
Evidence | E0 + E1
Boundary | Quadratic local descent only. Nonlinear stationary operators remain ARR-C014.
Parents: FPV20-C08, ARR-C012, ARR-C013.
Witness: PF-FPV20-FOUND-007.