Name | Discrete Dirichlet Energy Identity
Object | Combinatorial Laplacian $L=D-A$
Type | Exact quadratic-form identity
Identity | $x^\top L x=\tfrac12\sum_{ij}A_{ij}(x_i-x_j)^2$
Evidence | E0 + E1
Boundary | Finite undirected graphs. FPV20-C06 NS residual remains a typed field witness and does not alter this identity.
Parents: FPV20-C01, FPV20-C06.
Witness: PF-FPV20-GRAPH-007.