The λ-Constant of Prime Curvature and Symmetric Density: Toward the Analytic Proof of Goldbach’s Strong Conjecture

The present work establishes a unified analytical framework that links the Universal Prime Equation (UPE), the RH–Z model, and the newly introduced λ-curvature function describing prime density evolution. The study demonstrates that λ(x)=1/(x ln x) represents the curvature field of the prime distribution implied by the Prime Number Theorem. The continuity of λ ensures an equilibrium point around the midpoint n=E/2 for every even number E=2n, providing a natural analytic explanation for the Goldbach symmetry. The paper reviews historical milestones from Euler to Hardy and Littlewood, integrates the author’s previous models (UPE, RH–Z, and the rabbit symmetry representation), and proves that the λ field necessarily equalizes on both sides of every midpoint. The results imply that the existence of symmetric primes is an inevitable consequence of analytic continuity rather than a conjectural coincidence.