Visible Residual Transport in Isogeny Descent: A Computational Certification of the Paper13 Core Ledger

Paper14 extends the Paper13 Selmer-ratio ledger by computing the exact φ/φ̂-visible Sha-kernel displacement from Magma exact isogeny-Selmer groups and Mordell-Weil quotient data. We define V = s_φ - s_φ̂ = V_Sel + μ_MW, where s_φ = v_ℓ|Sha(E/Q)[φ]| is extracted from exact Selmer groups and MW quotients. The diagnostic framework is applied to all 74 supported ℓ=2,3 edges of the Paper13 Full80 ledger, completing 63 cases and accounting for 11 pending B=0 cases. Across 45 rank-zero edges (S1) and 29 rank-positive edges (S2), all 14 nonzero-residual core edges satisfy V = B_φ = -S_φ. No mismatch is observed. The computations distinguish certification levels from Magma-certified rank-zero torsion quotients to rank-one height-ratio free-part diagnostics. One edge (13095) is heavy generator-pending with B=0; ten rank≥2 edges are deferred. Six higher-degree edges (ℓ=5,11) are blocked by online Magma availability.