TEBAC BSD-IIB: Normalized Reference-Factor Routing and the Completed Determinant for Elliptic Curves over $\mathbb{Q}$

This preprint presents the BSD-IIB split component of the TEBAC Birch--Swinnerton--Dyer program. Its scope is restricted to the normalized reference-factor layer and the completed determinant role inside BSD-II. The manuscript assumes the centered heat/zeta/determinant package upstream and isolates the parity-routing burden forced by the odd root-number case, together with the normalization principle for the reference factor and the corrected determinant object \(D_{\mathrm{comp}}(s) = D_{\mathrm{ref}}(s)\,D_{\mathrm{cen}}\bigl((s-1)^2\bigr)\). The paper should be read as a BSD-IIB split preprint rather than as a claim that the full BSD-II module is already closed. In particular, it does not claim analytic-rank identification, the Mordell--Weil bridge, or final BSD assembly. Its purpose is to make referee-readable the normalized reference-factor mechanism, the exact central germ required at \(s = 1\), and the corrected determinant role needed before the downstream completed comparison layer.