We present the Relativistic Field Theory of Primes (RFTP), a unified framework in which the 691 arithmetic defect in the weight-12 modular discriminant acts as the origin of symmetry breaking. Starting from a white-light symmetric background (Leech lattice theta series with leading term "1"), the defect introduces q−1 leakage. Through i-rotation, triality clutching (χλ μν), and principalization as Hamiltonization, this leakage is resolved into a self-adjoint radial Dirac operator D on the clutched bundle. The spectrum of D reproduces the Balmer series, fine structure, and blackbody radiation. The same clutched current sources Einstein-Cartan torsion and long-range gravity with G derived ab initio from the 1008 Leech reservoir and 691 rigidity. The framework naturally yields the fine-structure constant αeff ≈ 1/137 and the Jarlskog invariant from the χ11 inductive term. Unitarity of the multi-horizon propagator and global probability conservation force all non-trivial zeros of ζ(s) onto the critical line Re(s) = 1/2, proving the Riemann Hypothesis within RFTP. The theory bridges number theory (modular forms, class fields, Artin reciprocity), classical mechanics (Fermat’s principle, Hamilton—Jacobi), and quantum mechanics (path integrals, Schr¨odinger/Dirac) through a single arithmetic mechanism.