Classical Standard Model and Gravity from a Common Constraint-Governed Source

Target–Source Compatibility, Joint Constraints, and Finite Classical Fermion Realization This paper establishes a target-relative common-source realization joining the structural Standard Model carrier–response framework to classical gravity through one fixed covariant action. It constructs a single classical law datum whose polynomial Standard Model description, metric response, canonical constraints, and Cauchy development are all restrictions of the same source. The fixed target contains: the global Standard Model gauge group; three chiral generations; one Higgs doublet; a real massive scalar clock; a compact hyperbolic Cauchy surface; a torsion-free Levi–Civita metric branch; Yang–Mills, Higgs, Weyl, Yukawa, scalar, and Einstein sectors; a complete source, boundary, continuation, and comparison ledger. The construction begins at the premetric level. Nondegenerate standing governs the admissible comparison regime, while metricity is introduced only as a licensed local realization of the already established gravity role. The resulting metric branch is therefore fixation-local, standing-preserving, and non-generative: it does not retroactively create the target or authorize the upstream structural source. A central theorem proves exact target–source compatibility. An explicit positive coefficient tuple simultaneously occupies the represented polynomial Standard Model chart and the coupled Einstein–matter construction. The same action supplies the Standard Model interactions, metric response, canonical constraints, and classical development, preventing the common-source claim from being reduced to a juxtaposition of independently selected branches. The paper establishes an occupied coupled classical body with: nonzero color, weak, and hypercharge curvature; a nowhere-zero, nonconstant Higgs field; trivial infinitesimal internal stabilizer; vanishing fermion body on the base classical branch; a source-attached globally hyperbolic development; a uniquely attached distributional total metric source; a closed Noether and Ward-response ledger. The total source closes only after Euler–Lagrange residuals vanish and internal exchanges cancel. This makes the gravitational response part of the same action-level source structure rather than an externally appended stress tensor. On the regular body, the full Lorentz, internal-gauge, spatial, and normal constraints form the exact off-shell Dirac-bracket algebra. A mixed-order tame right inverse establishes equality between the characteristic distribution and the Hamiltonian image of the constraints. The resulting regular system admits a local finite-refoliation groupoid, and covariant histories are locally equivalent to complete canonical histories on the stated ordinary body chart. The paper further constructs an independently formed clock-forward continuation category. After the target law is adjoined as inert ancestry data, its standing-domain map intertwines with the corrected coupled development while preserving source ancestry, standing, orientation, composition, failure, and no-repair coordinates. This establishes upstream continuation without allowing downstream metric or solution data to rewrite the source from which the construction began. A finite-algebra classical fermion extension is then developed. For every finite complex exterior algebra, coefficientwise constraint lifting and hyperbolic Cauchy induction produce exact classical anticommuting-field solutions. With at least two generators, nonzero Dirac–Yukawa data yield a nonzero self-adjoint fermionic current and a forced nonzero even coupled response. The result remains strictly classical and finite-algebraic: nilpotent fields are not treated as quantum operators or as possessing ordinary numerical positivity. The final common-source theorem establishes the coexistence of: one frozen structural Standard Model law; one source-attached Einstein/ADM realization; one exact joint constraint and refoliation class; finite classical anticommuting-field solutions; local covariant and canonical-history equivalence; exact source, target, boundary, anomaly, representation, and comparison bookkeeping. Scope and realization boundary The result is target-relative and local in its refoliation and clock claims. It does not assert an interacting quantum Standard Model, a dynamical quantum-gravity theory, an unrestricted global refoliation group, global path independence, a CAR representation, a functional integral, physical pole completion, confinement, scattering completeness, or a universal physical apex. The operator-valued mass-matching and quantum-projection branches remain explicitly unactivated. Their positive realization would require additional extension fibres and independent source certificates. The chosen coefficient tuple provides a constructive existence point, not a phenomenological fit or numerical prediction. The theorem establishes compatibility and classical realization on the declared target rather than deriving measured coupling constants, pole masses, or cosmological parameters. Role in the AASC programme CSPC is a classical common-source capstone. It connects the AASC premetric gravity role, the Standard Model carrier structure, the BCRS bosonic realization, the Wheeler–DeWitt constraint architecture, and finite classical fermionic response within one source-faithful classical target. Its principal result is that a nontrivial classical Standard Model–gravity configuration can be constructed with exact joint constraints, local refoliation, coupled metric response, and finite classical fermion strengthening, while preserving a strict boundary between classical realization and later quantum or asymptotic projection. Keywords AASC; classical Standard Model; Einstein–matter theory; common-source realization; target–source compatibility; joint constraint algebra; ADM constraints; hypersurface-deformation algebra; finite refoliation; Wheeler–DeWitt theory; gauge–Higgs–gravity coupling; classical Grassmann fields; Dirac–Yukawa response; source-attached metric response; canonical–covariant equivalence