TEBAC BSD-IIC: Completed Comparison, Central Compatibility, and No-Spurious-Center Closure for Elliptic Curves over $\mathbb{Q}$

This preprint presents the BSD-IIC split component of the TEBAC Birch–Swinnerton–Dyer program. Its scope is restricted to the completed comparison layer inside BSD-II, including central compatibility and no-spurious-center control. The manuscript treats the centered determinant package and the normalized reference-factor/corrected determinant role as imported upstream input from BSD-IIA and BSD-IIB, and closes the comparison-side burden on the declared BSD-IIC scope. The paper should be read as a BSD-IIC split preprint rather than as a claim that the full BSD-II module is already closed in a single file. 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 completed comparison mechanism, the exact central compatibility needed at \(s = 1\), and the no-spurious-center package required before downstream BSD-III use.