Structural Decoupling of Root Reciprocity and 2-Isogeny Descent in Quadratic Twist Models

This manuscript proposes a structural analysis of elliptic curve L-functions focusing on the relationship between root number symmetry and second-order arithmetic information. We argue that first-order reciprocity encoded in functional equation sign does not, in general, determine higher-order behavior associated with analytic rank. By distinguishing root reciprocity from deeper arithmetic structure, we identify a structural decoupling between global sign data and derivative-level vanishing at the central point. The analysis does not claim resolution of the Birch and Swinnerton-Dyer conjecture; rather, it isolates a layer mismatch between first-order symmetry and second-order arithmetic invariants. The results clarify why sign-based heuristics alone cannot determine rank and suggest that analytic and arithmetic layers must be treated as structurally distinct components within L-function theory.