Analytic-rank split of the height murmuration

Stage M5 / PR-2 (pre-registration). The committed 2¹⁶ statistic (ap reused from the persisted partials, no recompute) split by analytic rank r=ords=1L(E,s) (PARI, never Mordell–Weil rank): the full family, the leave-out F∖S₂ (the PRIMARY test), and S₂/S₀, overlaid on the conjectured density D(u) and the R2 targets. Gates applied mechanically, then interpreted. Renders emitted JSON only.

D̂(u): full family, leave-out F∖S₂, S₂, S₀ — vs the conjectured D(u)

full family F∖S₂ (leave-out, primary) S₂ (analytic-rank-2) S₀ (rank-0) conjectured D(u) R2 targets

The gates, and the branch taken