TEBAC BSD-IIA: Centered Heat-Trace Closure and the Direct-Attack OC2 Determinant Route

This preprint is the BSD-IIA split component of the TEBAC Birch–Swinnerton–Dyer program. Its scope is restricted to the centered heat-trace package and the direct-attack determinant route inside BSD-IIA. In the present version, the OC1 theta/heat package is closed in-file, and the OC2 direct-attack determinant route is also closed in-file on the present BSD-IIA route. The manuscript is therefore intended as a standalone split preprint documenting the heat-side and determinant-side closure achieved inside BSD-IIA itself. The paper does not claim closure of the full BSD-II module. In particular, the parity/reference-factor layer and the completed comparison / no-spurious-center layer are deferred to the downstream BSD-IIB and BSD-IIC split components. Accordingly, this manuscript should be read as a route-closed BSD-IIA preprint rather than as a final proof of the full BSD-II package.