min over grid of majorant - Phi_t: 0.000e+00 (should be >= -1e-12)
middle case: max over a in [3/10,5/7] of a + 3b^2/(20a) + b/4 = 0.993485 (< 1)
large case : max over a in [5/7,1] of a + 5b^2/(12a) = 1.000000 (<= 1)
small case : sqrt(2/pi) + 0.3*17/(8 sqrt15) = 0.962486 < 2 tau = 0.968246
cubic signs at -1, 0, 31/100, 21/20, 2: ['-476', '9', '-2473/10000', '-729/80', '649']
s-range of the middle case: [3/sqrt(91), 5/sqrt(24)] = [np.float64(0.3144854510165755), np.float64(1.0206207261596576)]
random unit vectors, n<=12: max E|L| = 0.968246 <= 2 tau = 0.968246
