(a) Theorem A, r=1/2: max over 300 random phi of lam_max(A_p)-1:
      p=0.5: -2.283e-05
      p=1.0: -4.418e-05
      p=1.5: -6.405e-05
      p=2.0: -8.246e-05
(b) Lemma 3.2: max eigenvalue of M_N^*M_N - diag(1,..,1,alpha^2): 5.082e-16  (must be <= 0 up to rounding)
(c) Lemma 3.3: max of ||V||^2 - gamma over 400 random (phi, r): -1.832e-06  (must be <= 0 up to rounding)
(d) Theorem C at p = P1(r), r in 0.42..0.49: max of Lambda^(p-2)*gamma - 1: -1.371e-04;  max of lam_max(A_p) - 1: -8.886e-04
    (both must be <= 0 up to rounding)
lower bound r_1(p) of Theorem C: p=2.5: 0.46609, p=3: 0.45227, p=4: 0.43933, p=6: 0.42927, p=8: 0.42499, p=12: 0.42109, p=16: 0.41926, p=20: 0.41820, p=30: 0.41683, p=50: 0.41576, p=100: 0.41498, p=1000: 0.41429
