Name | Exact Quadratic Taylor Descent Identity
Object | $S(x)=\tfrac12 x^{\mathsf T} A x$
Type | Exact Taylor identity of a quadratic
Identity | $S(x-\varepsilon\nabla S)=S(x)-\varepsilon\|\nabla S\|^2+(\varepsilon^2/2)\nabla S^{\mathsf T}A\nabla S$
Evidence | E0 + E1
Boundary | Finite Euclidean quadratic. Distinct from LYAP-C01 (inequality).
Parents: PF-FPV20-LYAP-C01, FPV20-C08.
Witness: PF-FPV20C-FOUND-006 · residual $1.39\times 10^{-17}$.