A restricted-framework uniqueness theorem for the leading-order Einstein-Dirac-Maxwell action from local Lorentz covariance, diffeomorphism covariance, first-order minimality, U(1) gauge invariance, and universal coupling

The leading-order matter Lagrangian for a spin-1/2 field coupled to a U(1) gauge field and to a Lorentzian spacetime is shown to be uniquely determined, within an explicitly restricted framework, by a list of orthodox hypotheses. The framework restrictions are (F1) torsion-free metric-compatible geometry, (F2) bilinear-quadratic matter Lagrangian, (F3) first-derivative minimality with no non-minimal field-strength or curvature-spinor couplings, (F4) no higher-order effective-field-theory corrections in either the matter sector or the gauge sector together with gauge-sector positivity on the perturbative vacuum, and (F5) no preferred-frame or background-dependent structures on the matter Lagrangian. The hypotheses are then local Lorentz covariance, spin-structure-preserving diffeomorphism covariance, first-order minimality on the matter sector, U(1) gauge invariance with a preserved global U(1) in the neutral limit, universal metric-tetrad coupling, tangent-space parity selection on the kinetic term, Hermiticity, and a classical commuting-spinor action setting. Under these conditions the matter Lagrangian is the standard curved-space Dirac Lagrangian with minimal U(1) coupling, and the canonical gravity source for the spin-1/2 field is the symmetric Hilbert / Belinfante-Rosenfeld stress-energy tensor obtained by metric variation. Combined with the Lovelock 1971/1972 uniqueness theorem on the geometric sector (subject to the quasilinear-in-second-derivatives caveat and modulo topological terms) and the spin-2 bootstrap as historical support, the Einstein-Hilbert geometric action plus the unique matter Lagrangian gives a leading-order uniqueness statement for the full Einstein-Dirac-Maxwell system at the classical action level. The theorem is integrative rather than internally novel. The constituent constructions and partial uniqueness / equivalence results have been established in the published literature across the lineages of Wigner-Bargmann-Wigner representation theory, the Tetrode-Weyl-Fock-Ivanenko tetrad construction, the Belinfante-Rosenfeld and Hilbert symmetric stress-energy procedures, the Gotay-Marsden / Forger-Römer equivalence between canonical and Hilbert stress tensors, and Lovelock's theorem on the geometric sector. The collected restricted-framework uniqueness statement on Einstein-Dirac-Maxwell with framework restrictions made explicit has not been written down before in this form. The Colella-Overhauser-Werner 1975 neutron-interferometry result is presented as the leading-order Newtonian weak-field empirical receipt for the gravitationally-induced matter-wave phase, with an explicit identification of which Dirac and geometric terms COW does and does not test. An explicit excluded-theories section catalogues the alternative geometric and matter frameworks the theorem does not cover (Einstein-Cartan-Sciama-Kibble with torsion, Horndeski scalar-tensor, f(R), metric-affine and teleparallel, bimetric and massive gravity, Pauli non-minimal magnetic couplings, four-fermion Nambu-Jona-Lasinio interactions, higher-derivative EFT corrections, nonlinear electrodynamics in the Born-Infeld and Heisenberg-Euler lineage, alternative spin structures, and Lorentz-violating Standard-Model-Extension structures), with each exclusion paired to the framework hypothesis it lifts. The Maxwell-θ topological term is permitted by the theorem as part of its modulo-topological-terms clause and is not excluded.