Split: Raw Height Comparison and Néron-Symbol Calibration

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:\[q^{}E,=B_E,*\, ,\,_{}.\] The manuscript defines the raw height comparison defect\[ΔH,_E(v,w):=q^{}E,(v,w)- B_E^{}v,B_E^{}w_{},\]and records the exact local Neron-symbol calibration theorem needed for its vanishing:\[q^{}E,x,(v,w)=λ^{}E,x(B_E^{}v,B_E^{}w) every place x.\] It proves that exact local Neron-symbol calibration implies\[E_H^{}=0,\]regulator agreement\[_{}(E)=(E),\]and, together with the source-complete Mordell--Weil bridge front, the vanishing of the raw BSD-IV verification ledger\[R^{}BSDIV(E)=(0,0,0,0,0)\]under 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.