The Kenuli-Resonance Operator: A Functional Approach to Predicting the Rank of Elliptic Curves

This manuscript introduces the \textbf{Kenuli-Resonance Operator} and the associated global constant $\delta=0.875$, designed to empirically probe arithmetic invariants of elliptic curves over $\mathbb{Q}$. Using a 3-adic resonance filter (the Kenuli Filter), this framework predicts the algebraic rank for tested conductors in the range $0 \le r \le 5$. Numerical correctness has been rigorously verified across multiple tested curves, ensuring confidence in the results. Observed systematic shifts in curves with non-trivial Tate-Shafarevich groups ($|\text{Ш}|>1$) suggest a heuristic link between the analytic order of vanishing of $L$-series and 3-adic arithmetic resonance. Full authorship and priority of these findings are asserted by the author.