A Conditional Dynamical Reduction of the Birch and Swinnerton-Dyer Conjecture via Adélic Holography

We construct a conditional geometric framework that maps the fundamental arithmetic invariants of the Birch and Swinnerton-Dyer (BSD) conjecture to spectral and topological properties of a dynamical system. By defining an Adélic Ruelle-Perron-Frobenius (RPF) transfer operator, we propose an exact "holographic dictionary". Under the assumption of operator semisimplicity at the critical temperature, we unconditionally recover the BSD rank identity. Finally, we document the computational limits of finite-truncation spectral sensing caused by the Sato-Tate bias. This work is part of the BM-SG Program, a systematic formalization effort using Lean 4