PASS  Proposition 5.3: E(Y) = -(2/25)Y^5 + (3/10)Y^4 + (2/5)Y^3 - (8/5)Y^2 - (8/5)Y + 209/50
PASS  the intermediate integral: int_1^Y (A - y^2)^2 dy with A = Y^2 - 2
PASS  E'(Y) = -(2/5)(Y-2)(Y^3 - Y^2 - 5Y - 2)
PASS  Y^3 - Y^2 - 5Y - 2 = Y(Y^2 - 5) - (Y^2 + 2)
PASS  E(2) = 1/50
PASS  E(1) = phi(0) = 8/5 and E(sqrt 5) > 0   E(sqrt5) = 0.10229124
PASS  E(Y) = phi(s) - gamma^(-1/2) int_0^s phi(tau) q(s-tau) dtau with Y = sqrt(1+4s) (numerical, four values of s)
PASS  condition (C), Certificate A (gamma = 2/3, phi = 1): smallest slack on a grid of 201 points >= 0 (equality at s = 0 and s = 1)   min slack 0.0
PASS  condition (C), Certificate B (gamma = 1/2, phi = 1 + (3/5)(2s-1)^2): smallest slack on the grid > 0   min slack 0.0141421 = sqrt(1/2)/50 = 0.0141421 at s = 3/4 and s = 1/4
      (for comparison: with gamma = 0.48 and the same phi the smallest slack is -0.01032)
PASS  Lemma 5.1, certificate A: (Th)_n / h_n <= 2 sqrt(1+gamma) = 2.5819889 on 120 random configurations, n <= 6 (numerical)   largest ratio found 2.4139762; no margin is to be read from it (Remark 5.4(1))
PASS  Lemma 5.1, certificate A: the identity of step (iii) on the same configurations (numerical)
PASS  Lemma 5.1, certificate B: (Th)_n / h_n <= 2 sqrt(1+gamma) = 2.4494897 on 120 random configurations, n <= 6 (numerical)   largest ratio found 2.3039804; no margin is to be read from it (Remark 5.4(1))
PASS  Lemma 5.1, certificate B: the identity of step (iii) on the same configurations (numerical)
      n = 3, s = 0.2999999999999999889: L/h_n = 0.901692126, formula 0.901692126;  (Th)_n/h_n = 2.1586808, sqrt(g+2s)+sqrt(g+2-2s)-2sqrt(g)/n = 1.9558092, difference*n^2 = 1.826
      n = 6, s = 0.5: L/h_n = 1.134936592, formula 1.134936592;  (Th)_n/h_n = 2.2698732, sqrt(g+2s)+sqrt(g+2-2s)-2sqrt(g)/n = 2.2137875, difference*n^2 = 2.019
      n = 12, s = 0.5: L/h_n = 1.17180401, formula 1.17180401;  (Th)_n/h_n = 2.343608, sqrt(g+2s)+sqrt(g+2-2s)-2sqrt(g)/n = 2.3316386, difference*n^2 = 1.724
PASS  Remark 5.4(1): the formula for L/h_n at n coincident points (n = 3, 6, 12)
PASS  Remark 8.4: U(1) = 0, U(B1) = s, U(B^2 1) = s x3, U(B^3 1) = 2s + (3/2)s^2 + s x3^2
PASS  R B^n 1 = B^n 1 for n < 12 (literal maps)
PASS  Remark 8.5: sum_n z^(-n-1) B^n (x1 - x3) = (sqrt((z-x3)^2-2s) - sqrt((z-x1)^2-2(1-s)))/(z-x1-x3), coefficients of z^(-1)..z^(-13) (exact; a test, not a proof)
PASS  Theorem 1.3: b Pi(f) = Pi(Bf) + 2<f> Omega for the 28 monomials x1^a x3^b s^c with a, b <= 3, c <= 2, a+b+2c <= 5 (exact; operators from the definition, Pi from Lemma 8.1)
PASS  Section 1.3: for alpha = beta = gamma = t = 1 the formula of Gu-Hasebe-Skoufranis equals (g(w) - g(z))/(z - w), g(z) = (z^2-2)^(-1/2)
PASS  the coefficient of z^(-i-1) w^(-j-1) is the arcsine moment m_(i+j)(1) for i + j <= 6: the two faces have the joint law of (X, X)
PASS  moments of 2X: 4, 24, 160; the sixth moment of mu is 464/3
TOTAL failures: 0
