R  data range U = [12/5, 2543/1000], s in [3/80, 3/20], a in [a_Z, a_S] = [480/6409, 120/409] = [0.074895, 0.293399]; u_lo <= 12/5, u_hi > u4 = sqrt(3+2sqrt3), u_lo^2 > 5, s_hi < 1: True
K  kappa_1..4 = 0, 1, u - 1/u, u^2 - 4 + u^-2: True; kappa_3..8 monotone on U (no root of kappa_j' in U): True
K  EM^0..4 = 1, 0, 1, K3, 3 + K4: True; EM^5..8 have [2, 4, 4, 7] monomials
K  EM^5..8 equal the hand formulas K5 + 10K3, K6 + 15K4 + 10K3^2 + 15, K7 + 21K5 + 35K3K4 + 105K3, K8 + 28K6 + 56K3K5 + 35K4^2 + 210K4 + 280K3^2 + 105: True
Z  d log T/du = (5-u^2)/(u(1+u^2)) < 0 on U: True; C' = (u^2-1)(u^4+4u^2+1)/(2u^2(1+u^2)^2) > 0: True; C = (q^2+(1-q)^2)/(2 tau): True
Z  at u = u_hi = 2543/1000: T - sqrt(2/pi) - C a_Z in [0.00260108447389, 0.00260108447389] > 0: True (so part (a) holds on all of U for a <= a_Z = a(3/80) = 480/6409)
I  identity (9.1) on 60 random exact examples (n-1 = 1..5 remainder terms, EM = 0): 0 mismatches
data: 4229 cells from RQ-AUD/audit/rqb/c15_data/k3_smalla_certs.json
T  4229 cells inside U x [3/80, 3/20]: True; exact area sum = region area: True; pairs with overlapping interiors: 0
D  domination P > Gh_C on all four pieces: failures 0/4229
M  my moment bound and target: failures 0/4229; min exact slack 3.733e-04; my (a1 + C) minus RQ-B's lhs: min -5.290e-03, max -3.608e-04; rho equal to the stored one: True (2s)
RESULT: ALL CHECKS PASSED (2s)

real	0m12.062s
user	0m18.474s
sys	0m0.100s
