test-1

We introduce R_BSD, the ratio of analytic instability C(E) to geometric-local structure α_BSD(E), and show on 368,314 rank-0 elliptic curves that (C, α_BSD) exhibits a robust two-phase structure in which Ghost curves (|Ш|>1) occupy a distinct coherence phase with low instability and high structure. The separation is recoverable by unsupervised clustering (GMM accuracy 99.95%), is not driven by conductor or Sha alone, is strongest after torsion control, and is accompanied by spectral null results indicating the effect is local-analytic rather than due to global zero-spacing.