
=======================================================================
  FRACTAL HABIT ??? 100k steps in Clear Water
  Init: Hysteresis C80 | omega = 1.0 | nu = 0.166667
=======================================================================
  Steps:     100000  (200 batches of 500)
  Samples:   2  (every 50000 steps)
  Diffusive: tau_d = 159364 steps  (run = 0.6 tau_d)
=======================================================================

[CUDA] NVIDIA GeForce RTX 4090  SM 8.9  SMs: 128
[NVML] Idle: 149.6 W

[LOAD] Loading Hysteresis C80...
  Loaded build/f_state_post_relax.bin (36.0 MB)
  Initial mean rho: 1.0614981871
[INIT] Computing step-0 spectrum...
    0 |         0 | Ev=7.497e-10 H=0.89 sl=-3.82 pk=  1 | Er=2.438e-09 H=0.94 sl=-4.04 kx0=100.0% | 149.6W

[RUN] 100k steps at omega=1.0  (0.6 diffusive times)
  sam |     step  | Velocity spectrum              | Density spectrum                | Power
  ----|-----------|--------------------------------|---------------------------------|------
    1 |     50000 | Ev=6.140e-10 H=0.95 sl=-3.59 pk=  1 | Er=2.097e-09 H=0.95 sl=-3.56 kx0=100.0% | 149.8W
    2 |    100000 | Ev=5.084e-10 H=1.25 sl=-3.83 pk=  1 | Er=1.723e-09 H=1.23 sl=-3.94 kx0=100.0% | 150.0W


=======================================================================
  FRACTAL HABIT ??? ANALYSIS  (3 samples, 0.4 minutes)
=======================================================================

--- 1. VELOCITY SPECTRUM: Initial vs Mid vs Final ---
  k   |  E_v(init)       |  E_v(mid)        |  E_v(final)      | Ratio f/i
  ----|------------------|------------------|------------------|----------
     1 | 6.4666698992e-10 | 4.8603309918e-10 | 3.4044761167e-10 |    0.5265
     2 | 2.7701677954e-11 | 1.0377991789e-10 | 1.3784740698e-10 |    4.9761
     3 | 4.0027417030e-11 | 2.4910534671e-14 | 1.8785426838e-11 |    0.4693
     4 | 2.0190087259e-11 | 1.4560685231e-11 | 9.3623213430e-13 |    0.0464
     5 | 2.1530509826e-12 | 6.9938242284e-12 | 5.2124629382e-12 |    2.4210
     8 | 2.2684950727e-12 | 5.0909940932e-13 | 1.2139821724e-13 |    0.0535
    10 | 4.8252514746e-13 | 6.9430903028e-14 | 1.3235758645e-13 |    0.2743
    16 | 9.4454480580e-14 | 5.6137441569e-14 | 3.2244043284e-13 |    3.4137
    20 | 1.2165471397e-14 | 1.7860994428e-14 | 3.4714647830e-14 |    2.8535
    32 | 5.9723118332e-15 | 1.6237757223e-15 | 2.7340193305e-16 |    0.0458
    50 | 1.0269094465e-15 | 8.4627031816e-16 | 3.1927982262e-16 |    0.3109
    64 | 2.7408807441e-17 | 6.7315355235e-17 | 1.0852167085e-16 |    3.9594
   100 | 9.8419229447e-17 | 1.1885762190e-17 | 2.9625880665e-17 |    0.3010
   128 | 2.7322111106e-17 | 1.6504235546e-19 | 1.4138116520e-18 |    0.0517
   200 | 4.4206099119e-18 | 1.7908179214e-18 | 1.2163588649e-18 |    0.2752
   256 | 1.3827084945e-18 | 9.2088363234e-19 | 7.7134261248e-19 |    0.5578
   400 | 1.6755309271e-18 | 1.6138958403e-19 | 2.2688009038e-19 |    0.1354
   512 | 1.3652278520e-17 | 5.6817381915e-20 | 3.1393158608e-20 |    0.0023

--- 2. DENSITY SPECTRUM: Initial vs Mid vs Final ---
  k   |  E_r(init)       |  E_r(mid)        |  E_r(final)      | Ratio f/i
  ----|------------------|------------------|------------------|----------
     1 | 2.0871275819e-09 | 1.6593266761e-09 | 1.1633931596e-09 |    0.5574
     2 | 1.0933642533e-10 | 3.5486544259e-10 | 4.6319539870e-10 |    4.2364
     3 | 1.2051467463e-10 | 6.8643773662e-14 | 5.7748748492e-11 |    0.4792
     4 | 5.6428410555e-11 | 4.8100136721e-11 | 2.3129042084e-12 |    0.0410
     5 | 1.5446013392e-11 | 2.3642465589e-11 | 2.1210640883e-11 |    1.3732
     8 | 1.2004679802e-11 | 2.0219845763e-12 | 3.7086165302e-13 |    0.0309
    10 | 1.6233168238e-12 | 5.8030064586e-14 | 3.9798768664e-13 |    0.2452
    16 | 3.8023666789e-13 | 4.0870800667e-13 | 1.1027189361e-12 |    2.9001
    20 | 4.1352707527e-14 | 7.1320428269e-14 | 4.3985546813e-14 |    1.0637
    32 | 6.1639631116e-14 | 6.0912714217e-15 | 9.1599794630e-15 |    0.1486
    50 | 3.7351436116e-15 | 1.2761197742e-15 | 2.1920899273e-15 |    0.5869
    64 | 1.2937232894e-15 | 2.6720428562e-16 | 5.2105999374e-16 |    0.4028
   100 | 2.5790150805e-16 | 2.3492668069e-17 | 4.8518206451e-18 |    0.0188
   128 | 3.4454484571e-17 | 7.7759584976e-18 | 2.8441951890e-17 |    0.8255
   200 | 1.8260318079e-17 | 6.9624493608e-17 | 1.8488800253e-17 |    1.0125
   256 | 1.3688052428e-17 | 1.8566962204e-17 | 4.6078592331e-19 |    0.0337
   400 | 2.5469244267e-17 | 1.0774724895e-18 | 9.9294605635e-19 |    0.0390
   512 | 1.3023978597e-17 | 3.0493186101e-18 | 1.0977546996e-18 |    0.0843

--- 3. SPECTRAL ENTROPY ---
  Velocity:
    Initial: H = 0.8892 bits  (0.0988 normalized)  slope = -3.822  modes = 5
    Final:   H = 1.2460 bits  (0.1384 normalized)  slope = -3.827  modes = 4
  Density:
    Initial: H = 0.9371 bits  (0.1041 normalized)  slope = -4.043  modes = 5
    Final:   H = 1.2255 bits  (0.1362 normalized)  slope = -3.940  modes = 4

  Reference slopes: Kolmogorov -5/3 = -1.667, Kraichnan -3

--- 4. ENERGY BUDGET ---
  Initial kinetic energy: 7.497160e-10
  Final kinetic energy:   5.084132e-10
  Ratio (final/init):     0.678141
  Initial density energy: 2.437637e-09
  Final density energy:   1.723119e-09
  Ratio (final/init):     0.706881

=======================================================================
  V E R D I C T
=======================================================================

  VELOCITY: PERSISTENT ??? 67.8% of kinetic energy survived
  DENSITY:  PERSISTENT ??? 70.7% of spectral power survived

  >>> STABLE: Structure maintained with similar complexity <<<

  Output:
    /build/fractal_habit.csv             (summary per sample)
    /build/fractal_habit_vel_spectra.csv  (full E_v(k) per sample)
    /build/fractal_habit_rho_spectra.csv  (full E_rho(k) per sample)
=======================================================================

