We present a first-principles derivation of 3+1-dimensional Lorentzian spacetime andEinstein—Cartan gravity from the arithmetic structure of the Bost—Connes C∗-dynamicalsystem. Starting from the primitive object (ABC,σt) and its KMS states, we construct ascale-invariant quadratic form on the idèle class space via the GNS inner product. Irregularprimes appear as topological defects through class-group shifts, inducing a shear in thequadratic form that maps canonically to a point τp ∈ H. For the resonant prime 691 this shear aligns with the hexagonal fixed point τ = ρ, where the Z/6Z stabilizer providestopological protection against adelic screening.The local 3-defect patch (primes 37, 59, 691) carries a non-abelian su(2) connection.Global adelic closure projects the three independent directions onto a single screened ray (time) while preserving the protected 3-dimensional spatial structure generated by the Eisenstein lattice at ρ. Explicit differentiation of the quadratic-form embedding with respect to the shear parameter yields the six generators of the Lorentz algebra so(1,3), with compact rotations locked at resonance and non-compact boosts arising from unbounded shear.The second-order Magnus expansion of parallel transport produces a residual torsion vector whose components are fixed by phase mismatches between the three incommensurate modular frequencies. Promoting the local Quantum Geometric Tensor metric on the 3-defect patch together with the screened ray yields a derived 4D Lorentzian geometry. On the resulting resonant spectral triple we evaluate the Chamseddine—Connes Spectral Action. Functional variation with respect to the emergent metric produces the Einstein—Cartan field equations, with the cosmological term fixed by the converged quadratic sum over the 47 irregular primes below 691 and the torsion source fixed by the linear sum. The next heat-kernel coefficienta4 generates quadratic gravity corrections that are parametrically suppressed by the samearithmetic factors, establishing ultraviolet safety. All physical structures—spacetime signature, Lorentz symmetry, torsion, and gravitational dynamics—emerge as necessary consequences of adelic consistency acting on the arithmetic defects of the Bost—Connes system. No external gravitational or field-theoretic ansatzis introduced.