  The many-body entanglement between two finite (size-$d$) disjoint vacuum
regions of non-interacting lattice scalar field theory in one spatial dimension
-- a $(d_A \times d_B)_{\rm mixed}$ Gaussian continuous variable system -- is
locally transformed into a tensor-product "core" of $(1_A \times 1_B)_{\rm
mixed}$ entangled pairs. Accessible entanglement within these core pairs
exhibits an exponential hierarchy, and as such identifies the structure of
dominant region modes from which vacuum entanglement could be extracted into a
spatially separated pair of quantum detectors. Beyond the core, remaining modes
of the "halo" are determined to be AB-separable in isolation, as well as
separable from the core. However, state preparation protocols that distribute
entanglement in the form of $(1_A \times 1_B)_{\rm mixed}$ core pairs are found
to require additional entanglement in the halo that is obscured by classical
correlations. This inaccessible (bound) halo entanglement is found to mirror
the accessible entanglement, but with a step behavior as the continuum is
approached. It remains possible that alternate initialization protocols that do
not utilize the exponential hierarchy of core-pair entanglement may require
less inaccessible entanglement. Entanglement consolidation is expected to
persist in higher dimensions and may aid classical and quantum simulations of
asymptotically free gauge field theories, such as quantum chromodynamics.
