Central Image from Local Selmer Inclusion Certificates

This preprint is Core II of the TEBAC BSD program. It proves a claim-safe central-image criterion: two unreduced Selmer inclusion certificates imply the reduced central image equality \(\rho_E(K_{E,\mathbb{Q}})=\kappa_E(M_{E,\mathbb{Q}})\subset S^{\mathrm{red}}_{E,\mathrm{cen}}\). The module does not claim a standalone proof of the Birch--Swinnerton--Dyer conjecture. It supplies the structural bridge needed after Core I and identifies the remaining arithmetic burden as the construction of local spectral-to-Kummer response identities.