(1) family d(x) = (x,x,x,3x-x^2)
   identities (3R1-2)^2 - R4^2 = 4(3-6x-x^2-3R1) and (3-6x-x^2)^2 - 9R1^2 = 30x^2+12x^3+x^4: verified (deg<=4, 59 pts)
   => for 0 < x < 5/36 (so 3R1-2 > 0 and 3-6x-x^2 > 0): 3R1 - R4 > 2 (polygon fails) <=> 30x^2+12x^3+x^4 > 0: TRUE
   x, (3R1-2-R4) [>0 = polygon fails], (3R1-2) - (1-6x-x^2) [the write-up implicitly needs >= 0]:
     x=0.00694  5.120e-04  -2.452e-04
     x=0.02778  1.004e-02  -4.135e-03
     x=0.04861  3.980e-02  -1.339e-02
     x=0.06944  1.183e-01  -2.900e-02
   Q1 = x^5(4-x)^3, Q2 = x^8(6+x)^2(2-x)^6/2 (Q2 from the definition), Q1 > Q2 at 5 rational x: True
   c=1: Q1 > c*Q2 on the family already for x <= 1/10
   c=10: Q1 > c*Q2 on the family already for x <= 1/10
   c=1e+06: Q1 > c*Q2 on the family already for x <= 1/1000
(2) Monte Carlo volume fractions in [0,1/4]^n (Q2 from the product definition in floating point)
   n=4: |locus| 0.6961, |{Q1>=Q2}| 0.8332, conj-not-locus 0.1371, locus-not-conj 0.00000
   n=5: |locus| 0.8827, |{Q1>=Q2}| 0.9585, conj-not-locus 0.0758, locus-not-conj 0.00000
(3) attainment: LP for an even-weight distribution with marginals lambda, for random lambda in P_n
   n=2: 40 random lambda in P_n (30% on facets): LP feasible every time; max |det - lambda(1-lambda)|, |norm-1| = 2.2e-16
   n=3: 40 random lambda in P_n (30% on facets): LP feasible every time; max |det - lambda(1-lambda)|, |norm-1| = 2.2e-16
   n=4: 40 random lambda in P_n (30% on facets): LP feasible every time; max |det - lambda(1-lambda)|, |norm-1| = 2.2e-16
   n=5: 40 random lambda in P_n (30% on facets): LP feasible every time; max |det - lambda(1-lambda)|, |norm-1| = 2.2e-16
   n=6: 40 random lambda in P_n (30% on facets): LP feasible every time; max |det - lambda(1-lambda)|, |norm-1| = 2.2e-16
   n=7: 40 random lambda in P_n (30% on facets): LP feasible every time; max |det - lambda(1-lambda)|, |norm-1| = 2.2e-16
(4) attainment by direct numerical inversion of the Gram map (no construction), n = 4, 5
   n=4: 25 random targets h(lambda), lambda in P_n: worst residual of G(A)=target, |A|=1: 2.8e-13
   n=5: 25 random targets h(lambda), lambda in P_n: worst residual of G(A)=target, |A|=1: 1.8e-13
(5) vertices of P_4 by brute force over active constraint sets
   #vertices = 12 (2^n - n = 12); equal to {0} U {(1/2) 1_K : |K| >= 2}: True
