TEBAC BSD-IIA: Centered Heat-Trace Closure, Mellin/Zeta Regularization, and the Centered Determinant Route (Version 2)

This preprint presents Version 2 of the BSD-IIA split component in the TEBAC Birch--Swinnerton--Dyer program. Its scope is restricted to the upstream BSD-IIA layer: the centered heat-trace package, the Mellin/zeta regularization route, and the centered determinant package. Relative to the earlier nearly closed version, the present v2 is intended as the finalized split-scope BSD-IIA preprint. In the present version, the OC1 theta/heat package is closed in-file, and the OC2 direct-attack centered-determinant route is also closed in-file on the declared BSD-IIA route. The manuscript should therefore be read as a split-closed BSD-IIA preprint on its own stated scope. This paper does not claim closure of the full BSD-II module. In particular, the normalized reference-factor/parity layer and the completed comparison/no-spurious-center layer are deferred to the downstream BSD-IIB and BSD-IIC split components. Accordingly, the present file is best read as the finalized upstream BSD-IIA split manuscript, exporting the centered determinant package for downstream use.