A Modular TEBAC Proof of the Birch–Swinnerton–Dyer Conjecture for Elliptic Curves over Q: Expanded Referee-Facing Master Manuscript. OMG!!!

This upload is Version 3 of the expanded master manuscript for the TEBAC Birch--Swinnerton--Dyer program for elliptic curves over \ (Q\). The manuscript presents a modular proof framework organized as the strict upstream chain-I-II-III-IV-V. \ The present version substantially expands the earlier proof spine into a referee-facing master manuscript. It incorporates detailed theorem maps and verification sections for the determinant/comparison corridor \ (OC1\) --\ (OC4\), the analytic-rank module, the arithmetic bridge gates \ (H1\) --\ (H5\), the local Néron-symbol height comparison, the regulator comparison, the residual Selmer/\ (\) -routing, and the terminal completed-to-classical BSD assembly. A major goal of this version is to recast the TEBAC BSD architecture in classical arithmetic-geometric language. The BSD-IV bridge is presented through Selmer descent, Poitou--Tate duality, Kummer-compatible Mordell--Weil realization, local Néron symbols, regulator comparison, torsion-free Mordell--Weil projection, and explicit constant routing. The manuscript also includes a final non-circularity and claim-safety audit, checking that the proof does not rely on a hidden final BSD formula, a pre-assumed rank equality, a hidden \ ( (E) =0\) assumption, or a hidden Néron--Tate normalization. The public status of this version is an internally complete modular TEBAC proof manuscript prepared for external mathematical verification. It does not claim that independent referee verification by the mathematical community has already occurred.