Conservative Motion Theory – D II: Fredholm–Analytic Resolution of the Goldbach Conjecture

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.