=== d' = (9/100, 9/100, 9/100, 6/25) ===
radicands of the sqrt(d_i): [2, 3]
Q1 = 107811/100000000 ~ 1.078110e-03
Q2 (from the definition, exact in Q(sqrt6)) = 2368521/1280000000000 ~ 1.850407e-06
claimed Q2 = 1/2 (57/100)^2 (15/100)^6: True
Q1 == 107811/10^8: True
Q1 > Q2: True ; Q1/Q2 ~ 582.6
in cube [0,1/4]^4: True
f(d') exactly = ['1/10', '1/10', '1/10', '2/5'] ; polygon at 4: f(d4) - (f(d1)+f(d2)+f(d3)) = 1/10

=== d* = (3/50, 3/50, 3/50, 171/1000) ===
radicands: [2, 3, 5, 19]
Q1 = 110937519/1000000000000  claimed 110937519/10^12: True
Q2 = 254677515836793921/2000000000000000000000000 ~ 1.273388e-07 ; equals 1/2 (9a-b)^2 (a-b)^6: True
Q1 - Q2 ~ 1.108102e-04 > 0: True
rigorous lower bound for f(d4) - sum f(d1..3) (interval sqrt, 40 digits): 2.660030e-02 > 0: True

=== padded points (d*, 0, ..., 0), n = 5..8, Q2 from the definition ===
n=5: Q1 ~ 3.8939e-05, Q2 ~ 3.2430e-14, Q1 > Q2: True, polygon defect lower bound 2.6600e-02 > 0: True
n=6: Q1 ~ 1.3668e-05, Q2 ~ 2.1035e-27, Q1 > Q2: True, polygon defect lower bound 2.6600e-02 > 0: True
n=7: Q1 ~ 4.7973e-06, Q2 ~ 8.8490e-54, Q1 > Q2: True, polygon defect lower bound 2.6600e-02 > 0: True
n=8: Q1 ~ 1.6839e-06, Q2 ~ 1.5661e-106, Q1 > Q2: True, polygon defect lower bound 2.6600e-02 > 0: True

=== boundary companion (9/100,9/100,9/100,x), x in (21/100, 1/4]: Q1 - Q2 > 0 on the whole segment? ===
grid check of Q1 > Q2 on [21/100, 1/4] (401 points): True
rigorous bounds on the segment: Q1 >= 5.400e-04 > 3.020e-06 >= Q2: True
polygon at x = 21/100: f(21/100) = 3/10 (= 3/10, tight); for x > 21/100 f(x) > 3/10 since f is increasing
