TEBAC BSD-II: Referee-Facing Merged Synthesis of the Finalized Split Trilogy BSD-IIA / BSD-IIB / BSD-IIC

This preprint presents a referee-facing merged synthesis of the finalized BSD-II split trilogy in the TEBAC Birch–Swinnerton–Dyer program: BSD-IIA, BSD-IIB, and BSD-IIC. Its purpose is to consolidate, in a single manuscript, the finished determinant, parity, and comparison package of BSD-II after closure across the three split components. The manuscript does not serve as a new first-proof home for the hard internal steps. Instead, it assembles in one place the finalized split outputs: the centered heat/zeta/determinant route from BSD-IIA, the normalized reference-factor/parity layer from BSD-IIB, and the completed comparison/no-spurious-center layer from BSD-IIC. In this merged form, the BSD-II package is presented as a single referee-readable determinant/parity/comparison module. This preprint should therefore be read as a merged BSD-II synthesis manuscript, not as a claim that the entire BSD program is already complete in this one file alone. In particular, the downstream analytic-rank, arithmetic-bridge, and final assembly layers belong to BSD-III, BSD-IV, and BSD-V.