An Operator Bridge Between Arithmetic Heights and Analytic Residues for Elliptic Curves
Internal ID: CGI-RSR-000004 | We present a structured program relating the arithmetic and analytic structures appearing in the Birch–Swinnerton–Dyer conjecture for elliptic curves over Q. The construction proceeds through two parallel bridges. The arithmetic bridge reconstructs the NÅLeron–Tate height pairing from a system of local coherence pairings obtained via defect descent at all places of the curve. Summation of the local energies produces a global quadratic operator whose determinant yields the classical regulator. The analytic bridge constructs a quadratic operator from the spectral structure of the L–function.