Goldbach’s conjecture, asserting that every even integer greater than two is the sum of two prime numbers, has resisted proof for nearly three centuries despite extensive analytic, probabilistic, and computational advances. This article presents a comprehensive review of the ?-symmetry program, an analytic framework that reformulates Goldbach’s statement as a problem of mirror symmetry in prime density rather than a purely combinatorial search. The central idea is to model the local distribution of primes by a continuous density field ?(x) ? 1/ln x, derived from the Prime Number Theorem. For a given even integer E, two mirrored density functions are defined on either side of the midpoint E/2. Their analytic intersection-the solution of the mirror equation ?1 (E/2 t) = ?2 (E/2 + t)—is shown to be inevitable by continuity and opposite monotonicity. This intersection represents the analytic shadow of a symmetric prime pair. The article explains how Goldbach’s conjecture can be reduced to the problem of converting this analytic intersection into the existence of actual primes. This conversion is achieved through explicit prime-gap bounds and a covariance control principle, which ensures that fluctuations of the discrete prime sequence cannot systematically destroy symmetric overlap. Within a logarithmic-square window centered at E/2, the expected number of prime pairs remains positive and empirically stable. Beyond the core argument, the ?- framework is connected to classical results in analytic number theory, including the Prime Number Theorem, Hardy–Littlewood conjectures, Dusart’s explicit bounds, and Vinogradov’s theorem. A geometric circle model and a real-domain interpretation of the Riemann ?-function further illuminate the symmetry mechanism underlying the conjecture. Written as both a review and a conceptual synthesis, this work aims to clarify the analytic structure behind Goldbach’s conjecture, offering a unified and pedagogical pathway from prime density to additive certainty, and identifying covariance control as the final analytic bridge between continuity and arithmetic reality. Graphical Abstract: The graphical abstract visually summarizes the lambda- symmetry framework by depicting prime numbers as discrete points fluctuating around a smooth, rainbow-colored density field defined by the lambda function. At the center of the image, an even integer is represented by a vertical axis of symmetry, around which two mirrored density curves emerge and intersect, symbolizing the analytic balance that underlies every Goldbach representation. The rainbow gradient conveys scale, continuity, and stability, emphasizing how local irregularities fade within a globally ordered structure. Discrete primes appear as localized perturbations that align with, rather than disrupt, the analytic symmetry. Overall, the image communicates the key idea of the article: Goldbach’s conjecture is resolved not by chance or enumeration, but by an unavoidable symmetry in prime density that persists across all scales.