(1) Monte Carlo, uniform points in [0,1/4]^n
  n=4 N=400000: locus 0.6973 | conj {Q1>=Q2} 0.8336 | conj but NOT locus 0.1363 | locus but NOT conj 0.00000
  n=5 N=400000: locus 0.8828 | conj {Q1>=Q2} 0.9586 | conj but NOT locus 0.0757 | locus but NOT conj 0.00000
  n=6 N=400000: locus 0.9619 | conj {Q1>=Q2} 0.9919 | conj but NOT locus 0.0301 | locus but NOT conj 0.00000
(2) sup of Q2/Q1 over the exact locus (Q1>0 there except at degenerate points):
    multistart SLSQP in lambda-coordinates (d = lambda(1-lambda)) + random sampling
  n=4: sup Q2/Q1 found = 0.052734 at lambda = [0.5 0.5 0.5 0. ] ; random sampling (166713 locus pts) max = 0.051573
  n=5: sup Q2/Q1 found = 0.000724 at lambda = [0.5 0.5 0.5 0.5 0.5] ; random sampling (191729 locus pts) max = 0.000699
  n=6: sup Q2/Q1 found = 0.000000 at lambda = [0.     0.4992 0.5    0.5    0.5    0.4999] ; random sampling (49587 locus pts) max = 0.000000
(3) exact family d(x) = (x,x,x,3x-x^2)
  x=1/12: in cube True, Q1-Q2 = 2.3933e-04 > 0: True, polygon violated (exact): True
  x=1/20: in cube True, Q1-Q2 = 1.9220e-05 > 0: True, polygon violated (exact): True
  x=1/100: in cube True, Q1-Q2 = 6.3520e-09 > 0: True, polygon violated (exact): True
  x=1/1000: in cube True, Q1-Q2 = 6.3952e-14 > 0: True, polygon violated (exact): True
  x=1/1000000: in cube True, Q1-Q2 = 6.4000e-29 > 0: True, polygon violated (exact): True
  identity (1-6x-x^2)^2 - (1-4(3x-x^2)) == 30x^2 + 12x^3 + x^4: True
  identity Q1(d(x)) == x^5 (4-x)^3: True ; Q2(d(x)) == x^8 (6+x)^2 (2-x)^6 / 2: True
  on (0,1/12]: (4-x)^3 >= 103823/1728 = 60.083 > 5329/7776 = 0.6853 >= x^3(6+x)^2(2-x)^6/2  ->  Q1 > Q2
DONE
