A1 atom products p_j x_j = r tau g_j (both signs), sum p_j = 1, mean 0: OK
A2 two-coordinate values 2 tau (1-q)(c+d), 2 tau c, 2 tau d: OK
A3 half-angle parametrisation, quartic tail constant 27/256, target unimodality: OK
B0 U_LO < u0 = sqrt(1+sqrt2) and U_HI >= u3 = sqrt(2+sqrt6): OK
B1 one-coordinate cells: 784 rectangles tile [1553773/1000000,1054691/500000] x [0,9/20]: OK
B2 two-coordinate boxes, s=+1: 38631 boxes (374 with a1 <= A_S) tile [1553773/1000000,1054691/500000] x [0,20711/50000] x [9/20,1]: OK
B2 two-coordinate boxes, s=-1: 16884 boxes (307 with a1 <= A_S) tile [1553773/1000000,1054691/500000] x [0,20711/50000] x [9/20,1]: OK
C one-coordinate cells (k=2 target): 784 re-verified exactly, 2s: OK
D two-coordinate six-moment boxes: 49999 re-verified exactly (16 sign patterns x 2 half-lines, strict objective; 1189 of them m-split boxes with two certificates each), 178s: OK
E near-circle boxes: 4835 re-verified (mpmath intervals, prec 120, strict), 1s: OK
ALL SELECTED PARTS PASSED: A B C D E
