Emergence XXII: The Inhabitant Sector — How Matter and Forces Emerge from Coupling to Spacetime

The canvas model divides all fundamental fields into two classes. Structural fields (Emergence XXI) create the spacetime lattice and determine its properties. Inhabitant fields—the subject of this paper—exist on that lattice. They include all matter and force fields of the Standard Model: quarks, leptons, gauge bosons, and the Higgs. This paper presents a unified framework for how inhabitant fields acquire their physical properties. All properties—spin, chirality, mass, and gauge charges—are determined by a single mathematical object: the coupling tensor that characterizes how the field couples to the emergent spacetime field \Phi_{\mathcal{L}}. Spin is determined by the tensor rank of the coupling. Chirality is determined by the projection onto the chirality-imprinted subspace. Mass is determined by the overlap with the Higgs modulation direction. Gauge charges are determined by which gauge-modulated subspaces the coupling accesses. What this paper derives: · The coupling to the spatial part of \Phi_{\mathcal{L}} is characterized by a coupling vector \vec{c} = (c_1, c_2, c_3) in the 3-dimensional internal space of the spatial axes. Stability requires \vec{c} to be an eigenvector of the threshold tensor \hat{T}_{ij}. The threshold tensor is a 3 \times 3 real symmetric matrix determined by the gauge symmetry fields (SU(3), SU(2), U(1)).· Three generations of fermions: The threshold tensor has exactly three eigenvectors that satisfy the existence and stability conditions. These are the three generations. A fourth generation is forbidden. The number of generations equals the number of spatial dimensions—both consequences of the same Planck-scale structure.· Mass hierarchy: The Higgs field modulates \Phi_{\mathcal{L}} in a specific direction \vec{v}_H in coupling space. The mass of each generation is proportional to the projection of its coupling vector onto \vec{v}_H. The mass ratios are geometric, not arbitrary parameters.· Gauge charges: The gauge charges of an inhabitant field follow from which gauge-modulated subspaces its coupling vector accesses. The SU(3) field modulates the full 3D subspace, SU(2) modulates a specific 2D subspace, and U(1) modulates a specific 1D subspace. The coupling patterns of the three eigenvectors reproduce the Standard Model gauge representations: left-handed quarks as SU(3) triplets and SU(2) doublets, left-handed leptons as SU(3) singlets and SU(2) doublets, right-handed fermions as SU(2) singlets. Why this matters: Together with Emergence XXI (The Structural Fields), this paper completes the ontology of fields in the canvas model. The structural fields build the stage. The inhabitant fields act on it. Both are waves. Both are governed by the same primitive dynamics (Order, Amplitude, Acceleration, Polarity). The division into two classes reflects a division of labor: some fields build the stage, others act upon it. No new particles, symmetries, or free parameters are introduced. This paper is part of the Emergence series, building on Paper I (Unified Field Theory), Emergence XXI (The Structural Fields), and the primitive ontology (Emergence XI–XX). It provides the unified framework for the matter and force fields of the Standard Model. Keywords: canvas model, inhabitant fields, structural fields, coupling tensor, threshold tensor, three generations, fermion mass hierarchy, gauge charges, spacetime field, Emergence series