We establish a complete proof of the Goldbach conjecture within the Conservative Motion Theory (CMT) framework by embedding the even-integer decomposition problem into a reflection–positive Fredholm operator. The key construction is a trace-class kernel K_\kappa(x,y)\in S_2 whose CMT determinant \Xi_\kappa(E)=\det_2(I-\alpha K_\kappa(E)) encodes the pairwise additive structure of primes. Using a Gaussian-regularized prime kernel and analytic continuation of Dirichlet series on the CMT Fredholm manifold, we show that the spectral flow corresponding to “two-prime decomposition” is strictly conservative: no gap in the prime pair spectrum is compatible with the nonnegativity of the reflection–positive transform \widehat{\Phi_\kappa}. The CMT real–zero persistence principle forces every even integer greater than 2 to admit a representation N = p + q,\qquad p,q\ \text{prime}. The analysis reveals that Goldbach’s conjecture is not a probabilistic phenomenon but a deterministic consequence of Fredholm continuity under conserved analytic rank. This result forms the second part of the CMT–D Series, after the resolution of the Collatz conjecture, and demonstrates the universality of discrete conservation in additive prime dynamics.