TEBAC BSD-IV Split: Actual Coefficient Calculus for the Primitive Spectral Extractor
Tosho Lazarov Karadzhov · Zenodo (CERN European Organization for Nuclear Research) · 2026
This preprint continues the BSD-IV split sequence by supplying the actual coefficient-calculus construction needed after the primitive-frame reduction. It constructs a source-complete actual coefficient calculus for the primitive spectral extractor \(\Theta^{\spec}_{E,\ell}\), admits coordinate probes on each local footprint space, and obtains the identity response matrix for the corresponding local response functionals. Consequently, the raw Mordell--Weil verification residue closes for the strengthened source-complete actual extractor:\[E_M^{\ver}=0.\] The manuscript is status-explicit. It should be read as a Mordell--Weil bridge gate closure for the source-complete actual extractor, not as an unconditional closure of BSD-IV and not as a completed proof of the full Birch--Swinnerton--Dyer conjecture. The remaining BSD-IV front after this upload is the raw height comparison\[q^{\raw}_{E,\spec}=B_E^{\arith,*}\langle\, ,\,\rangle_{\NT}.\]