This preprint continues the BSD-IV split sequence after the primitive-frame and actual coefficient-calculus manuscripts. The preceding split manuscripts reduce and discharge the raw Mordell--Weil verification residue for the source-complete primitive spectral extractor. The present split isolates the remaining height front: ^₄, =BE^, *\, , \, _. \ The manuscript defines the raw height comparison defect\^H, E (v, w): =q^₄, (v, w) - BE^v, BE^w_, records the exact local Neron-symbol calibration theorem needed for its vanishing: ^₄, ₗ, (v, w) =^₄, ₗ (BE^v, BE^w) every place x. \ It proves that exact local Neron-symbol calibration impliesH^=0, agreement\_ (E) = (E), , together with the source-complete Mordell--Weil bridge front, the vanishing of the raw BSD-IV verification ledger^₁ₒ₃₈ₕ (E) = (0, 0, 0, 0, 0) the stated calibration hypothesis. The manuscript is status-explicit. It does not claim to complete the full Birch--Swinnerton--Dyer conjecture, nor does it close BSD-IV by a normalization convention. Its purpose is to isolate the final height-comparison front after the Mordell--Weil bridge reduction and to make the exact local Neron-symbol calibration burden referee-readable.
Tosho Lazarov Karadzhov (Tue,) studied this question.