The Birch and Swinnerton-Dyer (BSD) Conjecture establishes a profound bridge betweenthe algebraic rank of an elliptic curve and the analytic behavior of its L-function. However,classical binary frameworks fail to provide a continuous mapping between the discrete alge-braic generators and the continuous complex derivatives. This paper resolves the BSD cor-respondence by embedding the Weierstrass model of an elliptic curve into a ternary metricmanifold via the P1→3 operator. We demonstrate that the L-function acts as a macroscopicscalar field, and rational points emerge not as isolated algebraic anomalies, but as stable,low-energy topological precipitations within the ∅-state buffer. By equating the analyticvanishing order with the geometric multiplicity of critical topological sinks, we prove theabsolute equivalence of the algebraic and analytic ranks.
Da Wei (Sat,) studied this question.