TEBAC BSD-IV: Primitive Coordinate-Symbol Right Inverse and Finite Frame Attack

This preprint is Split in the TEBAC BSD-IV series. Its purpose is to attack the raw external Mordell--Weil bridge residue in the BSD-IV arithmetic module by reducing it to a finite and explicitly auditable primitive-frame construction. The central object of the manuscript is the primitive response map\[\Sigma^\Theta:\mathcal P^\Theta_{E,\ell,w}(v,\eta)\longrightarrow\bigl(\mathcal F^\Theta_{E,\ell,w}(v,\eta)\bigr)^\vee .\]The main Path A objective is to construct a primitive coordinate-symbol right inverse\[\mathfrak C^\Theta:(\mathcal F^\Theta)^\vee\longrightarrow\mathcal P^\Theta\quad\text{with}\quad\Sigma^\Theta\circ\mathfrak C^\Theta=\operatorname{id}.\] The manuscript develops a full sequence of…