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Bibliographic Details
Main Author: Paltoo, Nigel
Format: Recurso digital
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Published: Zenodo 2025
Online Access:https://doi.org/10.5281/zenodo.17988536
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Table of Contents:
  • <p>We construct deterministic, self-adjoint Hamiltonians ˆHE associated with elliptic<br>curves E/Q, whose spectra encode the fundamental invariants of the Birch–Swinnerton-<br>Dyer (BSD) conjecture. Leveraging the Spectral Rigidity Framework (HHSRF),<br>we establish a spectral-arithmetic duality where analytic and algebraic ranks coincide<br>as a requirement of the operator’s kernel stability. We demonstrate that the<br>leading-term components—including the regulator, the torsion subgroup, and the<br>Tate–Shafarevich group—are realized as invariants of the spectral lattice. Specifically,<br>we map the product of the regulator and the order of the Tate–Shafarevich<br>group onto the entanglement entropy of the operator’s ground-state manifold, providing<br>a complete functional analytic closure to the BSD identity.</p>