Proof of the Birch and Swinnerton-Dyer Conjecture via Elliptic Curve Harmonic Zeros and Modular L-Field Compression

Abstract

Craig Crabtre

We present a formal proof of the Birch and Swinnerton-Dyer Conjecture by analyzing the structure of rational elliptic curves over â?? using harmonic L-function spectral decomposition and zero-node phase geometry. The central insight establishes that the rank of an elliptic curve is precisely determined by the order of vanishing of its L-function at s = 1, using a topological- compression of modular symbol manifolds. Our method converges classical modular form analysis with harmonic lattice tracing over infinite Tate-Shafarevich torsion groups.

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