(1) finite-difference check of d/d eps = -p Q:
    p=3.0, r=0.5: finite difference -3.41615912   -p*Q = -3.41615911
    p=8.0, r=0.45: finite difference -9.39438550   -p*Q = -9.39438533
    p=20.0, r=0.47: finite difference -21.74924754   -p*Q = -21.74924459
(2) check of the decomposition of Q:
    p=28.946, x=0.2450:  Q = 0.7618296097   decomposition = 0.7618296097
    p=4.215, x=0.2283:  Q = 0.1366810754   decomposition = 0.1366810754
    p=24.565, x=0.1383:  Q = 2.0935682386   decomposition = 2.0935682386
(3) first-order threshold at the identity:  p,  x*(p) from the matrix,  zero of the hypergeometric condition,  r_id = sqrt(x*)
    p=    2.5   0.4481345363   0.4481345363   r_id = 0.669429
    p=    3.0   0.4115647803   0.4115647803   r_id = 0.641533
    p=    4.0   0.3635591788   0.3635591788   r_id = 0.602959
    p=    5.0   0.3333333333   0.3333333333   r_id = 0.577350
    p=    6.0   0.3124212744   0.3124212744   r_id = 0.558947
    p=    8.0   0.2851193396   0.2851193396   r_id = 0.533966
    p=   10.0   0.2678752304   0.2678752304   r_id = 0.517567
    p=   12.0   0.2558707516   0.2558707516   r_id = 0.505837
    p=   13.0   0.2511153086   0.2511153086   r_id = 0.501114
    p=   14.0   0.2469668299   0.2469668299   r_id = 0.496958
    p=   16.0   0.2400615748   0.2400615748   r_id = 0.489961
    p=   20.0   0.2299750373   0.2299750373   r_id = 0.479557
    p=   30.0   0.2154415123   0.2154415123   r_id = 0.464157
    p=   50.0   0.2023120808   0.2023120808   r_id = 0.449791
    p=  100.0   0.1906613855   0.1906613855   r_id = 0.436648
    p= 1000.0   0.1755953201   0.1755953201   r_id = 0.419041
    x*(p) = 1/4 (r_id = 1/2) at p ~ 13.25614
(4) p = 5, x = 1/3, G = (1-z)^2:  T g = [ 0.  0. -0.  0. -0. -0.]  (zero vector)
