Resonance Acceleration and Morphic Scans: A Heuristic Framework for Detecting BSD Rank Signatures

This repository contains the LaTeX source and supplementary materials for the paper “Resonance Acceleration and Morphic Scans: A Heuristic Framework for Detecting BSD Rank Signatures” by Navoda Hasaranga Baddewithana. The work introduces the Kenuli–Baddewithana Resonance Law, a deterministic heuristic method for probing the algebraic rank of elliptic curves over $\mathbb{Q}$ without explicit differentiation of $L$-series. The method is based on a digit-root resonance filter applied to Frobenius trace coefficients $a_p$, combined with a discrete kinetic acceleration term designed to distinguish coherent rank signals from statistical noise. Empirical validation against verified datasets from the LMFDB demonstrates exact agreement with known algebraic ranks for curves with conjecturally trivial Tate–Shafarevich group. For curves with nontrivial $\Sha$, a consistent positive resonance shift is observed, motivating a conjectural morphic invariant relating rank and the Tate–Shafarevich group. This repository is intended to support: Reproducibility of the resonance calculations, Independent verification of the empirical observations, Further computational exploration of resonance-based invariants related to the Birch and Swinnerton-Dyer conjecture. Important note:This work is heuristic and empirical in nature. It does not claim a proof of the Birch and Swinnerton-Dyer conjecture but proposes a computationally lightweight indicator of rank structure and a testable hypothesis regarding $\Sha$-dependent resonance behavior.