PART 1: full matrix, exact mu, 60-digit eigenvalues
 d=2 n=4: 51 values of p; flags {'level_const': True, 'w_decr': True, 'w_logconvex': True, 'mean': True, 'var': True, 'dirichlet_eq': True, 'H_le_tau': True, 'lump': True, 'level_law': True}
      min tau/H_d = 1.0 at p=999999/1000000 ; max |tau_full - tau_level| = 9.33e-61 ; tau(1/d)=1.68094663676 vs d(d-1)/15=0.13333333 ; max_grid tau=2.0 at p=999999/1000000 (tau(0)=1.0, d=2)  -> OK
 d=3 n=8: 52 values of p; flags {'level_const': True, 'w_decr': True, 'w_logconvex': True, 'mean': True, 'var': True, 'dirichlet_eq': True, 'H_le_tau': True, 'lump': True, 'level_law': True}
      min tau/H_d = 1.0 at p=999999/1000000 ; max |tau_full - tau_level| = 2.18e-60 ; tau(1/d)=2.67487992637 vs d(d-1)/15=0.4 ; max_grid tau=3.11437049533 at p=31/40 (tau(0)=1.5, d=3)  -> OK
 d=4 n=16: 51 values of p; flags {'level_const': True, 'w_decr': True, 'w_logconvex': True, 'mean': True, 'var': True, 'dirichlet_eq': True, 'H_le_tau': True, 'lump': True, 'level_law': True}
      min tau/H_d = 1.0 at p=999999/1000000 ; max |tau_full - tau_level| = 7.47e-60 ; tau(1/d)=3.87408754101 vs d(d-1)/15=0.8 ; max_grid tau=4.44214996276 at p=3/5 (tau(0)=2.0, d=4)  -> OK
 d=5 n=32: 51 values of p; flags {'level_const': True, 'w_decr': True, 'w_logconvex': True, 'mean': True, 'var': True, 'dirichlet_eq': True, 'H_le_tau': True, 'lump': True, 'level_law': True}
      min tau/H_d = 1.0 at p=999999/1000000 ; max |tau_full - tau_level| = 1.49e-59 ; tau(1/d)=5.29591351708 vs d(d-1)/15=1.3333333 ; max_grid tau=5.98340174482 at p=19/40 (tau(0)=2.5, d=5)  -> OK
 d=6 n=64: 53 values of p; flags {'level_const': True, 'w_decr': True, 'w_logconvex': True, 'mean': True, 'var': True, 'dirichlet_eq': True, 'H_le_tau': True, 'lump': True, 'level_law': True}
      min tau/H_d = 1.0 at p=999999/1000000 ; max |tau_full - tau_level| = 3.48e-59 ; tau(1/d)=6.96277942694 vs d(d-1)/15=2.0 ; max_grid tau=7.74772008579 at p=5/13 (tau(0)=3.0, d=6)  -> OK
PART 1 ALL OK

PART 2: full matrix (double precision) against the level chain, d = 7..10
 d=7 (n=128): max relative |tau_full - tau_level| over 8 values of p = 1.77e-14
 d=8 (n=256): max relative |tau_full - tau_level| over 8 values of p = 2.29e-14
 d=9 (n=512): max relative |tau_full - tau_level| over 8 values of p = 2.57e-14
 d=10 (n=1024): max relative |tau_full - tau_level| over 8 values of p = 4.16e-14

PART 3: level chain for larger d (tau_level is an eigenvalue of the full chain, see report; lower bound for tau)
   d | min_p tau/H_d | tau(1/d) | d(d-1)/15 | ratio | max_p tau (p*d at max) | max tau/d^2 | max tau/tau(0) | max tau/d
    8 | 1.000064543 | 11.107562 | 3.733333 | 2.9752 | 11.989033 (2.000) | 0.18733 | 2.9973 | 1.4986
   12 | 1.000032445 | 22.950576 | 8.800000 | 2.6080 | 23.629424 (1.500) | 0.16409 | 3.9382 | 1.9691
   16 | 1.000019407 | 39.765255 | 16.000000 | 2.4853 | 40.021325 (1.500) | 0.15633 | 5.0027 | 2.5013
   17 | 1.000017378 | 44.756752 | 18.133333 | 2.4682 | 44.842421 (1.500) | 0.15516 | 5.2756 | 2.6378
   24 | 1.000009172 | 88.562709 | 36.800000 | 2.4066 | 88.562709 (1.000) | 0.15375 | 7.3802 | 3.6901
   32 | 1.000005320 | 157.663006 | 66.133333 | 2.3840 | 159.530993 (0.600) | 0.15579 | 9.9707 | 4.9853
   48 | 1.000002439 | 356.878623 | 150.400000 | 2.3729 | 370.925232 (0.400) | 0.16099 | 15.4552 | 7.7276
   64 | 1.000001393 | 637.530021 | 268.800000 | 2.3718 | 676.829390 (0.300) | 0.16524 | 21.1509 | 10.5755
   96 | 1.000000629 | 1443.343530 | 608.000000 | 2.3739 | 1576.265035 (0.200) | 0.17104 | 32.8389 | 16.4194
  128 | 1.000000356 | 2575.343131 | 1083.733333 | 2.3764 | 2864.118173 (0.100) | 0.17481 | 44.7518 | 22.3759
  192 | 1.000000160 | 5818.296909 | 2444.800000 | 2.3799 | 6603.926519 (0.100) | 0.17914 | 68.7909 | 34.3955
  256 | 1.000000090 | 10366.838631 | 4352.000000 | 2.3821 | 11918.570435 (0.050) | 0.18186 | 93.1138 | 46.5569
  400 | 1.000000037 | 25375.496203 | 10640.000000 | 2.3849 | 29585.675645 (0.050) | 0.18491 | 147.9284 | 73.9642
done
