  A novel method for constructing a Bethe-Salpeter kernel for the meson
bound-state problem is described. It produces a closed-form kernel that is
symmetry-consistent (discrete and continuous) with the gap equation defined by
any admissible gluon-quark vertex. Applicable even when the diagrammatic
content of that vertex is unknown, the scheme can foster new synergies between
continuum and lattice approaches to strong interactions. The framework is
illustrated by demonstrating that the presence of a dressed-quark anomalous
magnetic moment in the gluon-quark vertex, an emergent feature of strong
interactions, can remedy many defects of widely used meson bound-state kernels,
including the level ordering of pseudoscalar and vector meson radial
excitations.
