We construct a relativistic field theory of primes (RFTP) in which the adelic phase space is quantized by a single arithmetic object — the motivic commutator arising from the 691 topological defect. The twisted Lorentz oscillator serves as the microscopic foundation, yielding a direct derivation of Planck’s law and the entropy of a single harmonic oscillator from the commutator spectrum, with zeta regularization modulated by the 691 rigidity. The defect, realized as the non-trivial Galois extension forced by the vanishing Stickelberger element when 691 divides B12, functions as a universal cohomological object that factors through all Weil cohomologies. Stationarity of the combined action produces EinsteinCartan geometry as the thermodynamic equation of state describing curvature annealing of the defect until the conductor-9 snag, where octonionic triality locks vertical phase into GL(3) structure, generating rest mass via the Higgs-like clutching mechanism. Photons emerge as the symmetric null limit of the commutator, while massive particles arise from partial or full clutching. The theory recovers Maxwell equations in the low-energy phase, Dirac dynamics with torsional corrections, and entropic gradients driving probability flow. Implications for the BSD conjecture, Hilbert’s 12th problem, Navier-Stokes smoothness, and the Riemann Hypothesis are noted, but formal resolutions are deferred to dedicated manuscripts. The framework offers a first-principles unification of number theory with relativistic quantum field theory and gravity through a single motivic commutator.