  Factorization of the Gaussian RBF kernel is developed for free-mesh
interpolation in the flat, polynomial limit corresponding to Taylor expansion
and the Vandermonde basis of geometric moments. With this spectral
approximation, a top-down octree-scoping of an interpolant is found by
recursively decomposing the residual, similar to the work of Driscoll and
Heryudono (2007), except that in the current approach the grid is decoupled
from the low rank approximation, allowing partial separation of sampling errors
(the mesh) from representation errors (the polynomial order). Then, it is
possible to demonstrate roughly 5 orders of magnitude improvement in free-mesh
interpolation errors for the three-dimensional Franke function, relative to
previous benchmarks. As in related work on $N$-body methods for factorization
by square root iteration (Challacombe 2015), some emphasis is placed on
resolution of the identity.
