TEBAC Birch–Swinnerton–Dyer Program: Unified Master Proof Dossier for Elliptic Curves over Q

This record contains the unified master proof dossier for the TEBAC Birch--Swinnerton--Dyer program for elliptic curves over \( Q\). The manuscript integrates the five-module chain\[{BSD-I}{BSD-II}{BSD-III}{BSD-IV}{BSD-V}\]into a single continuously organized master document. BSD-I fixes the centered operator and parity package at the arithmetic center \(s=1\). BSD-II supplies the determinant, parity/reference-factor, and completed comparison framework, including the centered determinant in the variable\[σ=(s-1)^2\]and the completed comparison object used to read the central order of the completed elliptic \(L\)-function. BSD-III extracts the analytic-rank identity by identifying the order of vanishing at the center with the central spectral multiplicity. BSD-IV is the arithmetic bridge module: it constructs the Selmer/cohomological interface, the spectral realization map, the Mordell--Weil bridge, and the height/regulator comparison. BSD-V performs the terminal assembly, transferring the completed leading-term identity to the classical Birch--Swinnerton--Dyer formula. The proof architecture is designed to keep determinant comparison, analytic rank, arithmetic rank, height/regulator comparison, residual Selmer/Sha routing, and final leading-term assembly in separate theorem homes. The master dossier records the full TEBAC proof chain, the module interfaces, the non-circularity discipline, and the final assembly route toward the classical Birch--Swinnerton--Dyer rank statement and leading-term formula. This version is a full-source verification package intended for external mathematical review. It presents the completed internal TEBAC BSD proof dossier while preserving the distinction between internal module closure and independent referee-level validation.