Empirical statistic (1) vs the conjectured density D(u)
empirical D̂(u) bins
empirical (line)
conjectured density D(u)
committed R2 targets (hump/zero/trough)
Stage M4 — Sawin & Sutherland (arXiv:2504.12295), Conjecture 1. Elliptic curves EA,B: y²=x³+Ax+B ordered by naive height H=max(4|A|³,27B²), with the root-number-weighted average of ap(E) taken over u = p/N(E) (the prime-to-conductor ratio, not p/X). The empirical curve is the computed statistic — ap from scratch (point counts, twinned against the frozen referee); only the conductor N and root number ε are oracle-supplied (PARI, certified vs Cremona over 5676 classes). It is overlaid on the conjectured density D(u), the in-house Bessel-J₁ sum of eq. (2). Renders emitted JSON only.