A symmetry-preserving truncation of the strong-interaction bound-state equations is used to calculate the spectrum of ground-state J = 1/2 + , 3/2 + (qq q )-baryons, where q, q , q ∈ {u, d, s, c, b}, their first positive-parity excitations and parity partners. Using two parameters, a description of the known spectrum of 39 such states is obtained, with a mean-absolute-relativedifference between calculation and experiment of 3.6(2.7)%. From this foundation, the framework is subsequently used to predict the masses of 90 states not yet seen empirically.Keywords Poincaré-covariant Faddeev equation · baryon spectrum · light and heavy quarks · Dyson-Schwinger equations · emergence of mass 1 IntroductionThe Faddeev equation was introduced almost sixty years ago [1]. It treats the quantum mechanical problem of three-bodies interacting via pairwise potentials by reducing it to a sum of three terms, each of which describes a solvable scattering problem in distinct two-body subsystems. The Faddeev formulation of that three-body problem has a unique solution.An analogous approach to the three-valence-quark (baryon) bound-state problem in quantum chromodynamics (QCD) was explained in Refs. [2][3][4][5][6]. In this case, owing to dynamical mass generation, expressed most simply in QCD's one-body Schwinger functions in the gauge [7][8][9][10][11][12][13][14][15][16][17][18] and matter sectors [19][20][21][22][23][24], and the importance of symmetries [25][26][27], one requires a Poincaré-covariant quantum field theory generalisation of the Faddeev equation. Like the Bethe-Salpeter equation for mesons, it is natural to consider such a Faddeev equation as one of the tower of QCD's Dyson-Schwinger equations (DSEs) [28], which are being used to develop a systematic, symmetry-preserving, continuum approach to the strong-interaction bound-state problem [29][30][31][32][33][34].The Poincaré-covariant Faddeev equation for baryons is typically treated in a quark-diquark approximation, where the diquark correlations are nonpointlike and dynamical [35]. This amounts to a simplified treatment of the scattering problem in the two-body subchannels (as explained, e.g. in Ref. [36], Sec. II.A.2), which is founded on an observation that the same interaction which describes