© 2023, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.Focusing on the continuum meson bound-state problem, a novel method is used to calculate closed-form Bethe–Salpeter kernels that are symmetry consistent with any reasonable gluon-quark vertex, ??, and therewith deliver a Poincaré-invariant treatment of the spectrum and decay constants of the ground- and first-excited states of u, d, s mesons. The predictions include masses of as-yet unseen states and many unmeasured decay constants. The analysis reveals that a realistic, unified description of meson properties (including level orderings and mass splittings) requires a sound expression of emergent hadron mass in bound-state kernels; alternatively, that such properties may reveal much about the emergence of mass in the standard model.