E  [0.9161] A = 4/(3c) = 40000/27483 = 1.455445; base = 0.916066900; slope = -2.1815e-07; V(A) = 9160669/10000000 = 0.916066900; c - V = 3.310e-05
E  [0.9161] min_[0,3] (phi(z) - z) ~ 4.9965e-05 at z ~ 0.8508
E  [0.92] A = 4/(3c) = 100/69 = 1.449275; base = 0.916150000; slope = 1.0192e-04; V(A) = 138475569361/151114140000 = 0.916364077; c - V = 3.636e-03
E  [0.92] min_[0,3] (phi(z) - z) ~ 2.0934e-04 at z ~ 0.8519
E  exact checks: 13/13 hold []
Q  bound < 1 iff q < q* = 0.288832268403 (certified: B(q*-1e-12) < 1 < B(q*+1e-12): True); stated 0.28883 / 0.2888
Q  q = 0.1: bound in [0.940768320848, 0.940768320848] <= stated 0.9408: True
Q  q = 0.2: bound in [0.969662760871, 0.969662760871] <= stated 0.9697: True
Q  q = 0.25: bound in [0.986111120512, 0.986111120512] <= stated 0.9862: True
Q  sup over (0, 1/4] of bound/M(q): 1.0790148 at q = 0.1835034191 (= 1 - sqrt(2/3) = 0.1835034191); grid max 1.0790124; the text says 'within 7.4%': FALSE
Q  limit q -> 0 of the ratio: c sqrt(e/2) = 1.0680095
S  3000 random probability K on [-A, A] (Gaussian part + 1-3 atoms, |atom| >= 0.35): min E phi - E|Z| = 5.768e-02, min V(A) - E phi = 4.121e-05, max E|Z| = 0.857762 (sqrt(2/e) = 0.857764)
F  Lemma 8.2 (i) first-variation formula: max |D+ E|V + Y_eps| - G_V(a)| over 60 random (V, a) = 5.12e-07
F  K = delta_sqrt2: E|Z| = 0.857763884961 (sqrt(2/e) = 0.857763884961); u = 0.3934693403 (1 - e^-1/2 = 0.3934693403); P(-sqrt2 < Z <= 0) - R sqrt2/2 = 1.11e-16; max |Q - claimed Q| = 3.55e-15; max over a<0 of G(a) - R/2 = -2.144e-01
RESULT: ALL CHECKS PASSED (parts EQSF, 7s); note: the 7.4% side remark is checked separately above
