The proposed rank-loop correspondence cannot hold: the embedding is a torus with at most two independent homology classes, and the claimed F_new growth law is impossible by the Hasse bound.
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A Topological Perspective on the Birch and Swinnerton Dyer Conjectures
The proposed rank-loop correspondence cannot hold: the embedding is a torus with at most two independent homology classes, and the claimed F_new growth law is impossible by the Hasse bound.