Loading Freckles v40 + CIFAR-10...
Collecting spatial friction maps (full test set)...


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Collected 10000 images, 2000 individual maps

======================================================================
  1. SPATIAL STRUCTURE — Do friction maps have spatial variance?
======================================================================

  Per-image spatial friction variance (across 256 patches):
  Mode 0 (S₀): mean=0.0359 std=0.0196
  Mode 1 (S₁): mean=0.0207 std=0.0143
  Mode 2 (S₂): mean=0.3235 std=0.1607
  Mode 3 (S₃): mean=0.0000 std=0.0000

  Per-image spatial CV (std/mean):
    Mode 0: CV mean=0.0145 median=0.0145 max=0.0300
    Mode 1: CV mean=0.0109 median=0.0106 max=0.0272
    Mode 2: CV mean=0.0294 median=0.0297 max=0.0533
    Mode 3: CV mean=0.0000 median=0.0000 max=0.0000

  VERDICT: SPATIALLY UNIFORM (mean CV = 0.0137)

======================================================================
  2. PER-CLASS SPATIAL PATTERNS — Do classes have different friction maps?
======================================================================

  Inter-class friction map L2 distances:
              airpl   auto   bird    cat   deer    dog   frog  horse   ship  truck
    airplane  0.000  5.791  5.016  6.309  6.924  5.982  7.640  5.202  3.186  4.733
        auto  5.791  0.000  3.181  3.194  3.779  3.585  3.552  3.158  3.951  2.838
        bird  5.016  3.181  0.000  2.093  2.065  2.115  2.931  1.535  4.403  4.120
         cat  6.309  3.194  2.093  0.000  1.806  1.493  1.996  2.043  5.563  4.821
        deer  6.924  3.779  2.065  1.806  0.000  2.135  1.485  2.355  6.168  5.364
         dog  5.982  3.585  2.115  1.493  2.135  0.000  2.682  2.474  5.349  5.220
        frog  7.640  3.552  2.931  1.996  1.485  2.682  0.000  3.063  6.488  5.457
       horse  5.202  3.158  1.535  2.043  2.355  2.474  3.063  0.000  4.650  3.783
        ship  3.186  3.951  4.403  5.563  6.168  5.349  6.488  4.650  0.000  3.010
       truck  4.733  2.838  4.120  4.821  5.364  5.220  5.457  3.783  3.010  0.000

  Mean inter-class distance: 3.8820
  Mean cosine similarity:    0.999958
  Min cosine similarity:     0.999881
  VERDICT: NEARLY IDENTICAL PATTERNS

======================================================================
  3. CENTER vs EDGE — Do boundary patches have higher friction?
======================================================================

  Class        Center     Edge  Edge/Center
  ----------------------------------------
  airplane     12.155   12.126       0.9975
  auto         12.203   12.219       1.0013
  bird         12.193   12.177       0.9987
  cat          12.206   12.212       1.0005
  deer         12.207   12.198       0.9993
  dog          12.179   12.200       1.0017
  frog         12.201   12.222       1.0018
  horse        12.214   12.183       0.9974
  ship         12.147   12.166       1.0015
  truck        12.210   12.185       0.9980

======================================================================
  4. PER-PATCH-POSITION DISCRIMINABILITY
======================================================================

  F-statistic (inter-class var / intra-class var) per mode:
    Mode 0: mean=0.054267 max=0.113004 top 5% threshold=0.096192
    Mode 1: mean=0.165008 max=0.262047 top 5% threshold=0.254798
    Mode 2: mean=0.069616 max=0.170688 top 5% threshold=0.149573
    Mode 3: mean=0.000000 max=0.000000 top 5% threshold=0.000000
    Mode 0 best position: (1, 15) F=0.113004
    Mode 1 best position: (1, 13) F=0.262047
    Mode 2 best position: (0, 14) F=0.170688
    Mode 3 best position: (0, 0) F=0.000000

  Overall best discriminative patch position: 0, 14 F=0.133089
  Overall mean F-statistic: 0.072223
  VERDICT: POSITIONALLY DISCRIMINATIVE

======================================================================
  5. PER-MODE SPATIAL VARIANCE — Which mode has the most structure?
======================================================================
  Mode 0: map_mean=12.5844 map_var=0.000355 map_cv=0.0015
  Mode 1: map_mean=12.4741 map_var=0.000701 map_cv=0.0021
  Mode 2: map_mean=18.6994 map_var=0.004943 map_cv=0.0038
  Mode 3: map_mean=5.0000 map_var=0.000000 map_cv=0.0000

======================================================================
  6. SAMPLE FRICTION MAPS — Individual images
======================================================================

  Class      Img     Mean      Std      Max  Entropy  HotSpots
  -------------------------------------------------------
  airplane     0    12.11     0.22    19.60    1.000         0
  airplane     1    12.09     0.11    19.89    1.000         0
  auto         0    12.35     0.26    20.45    1.000         0
  auto         1    12.15     0.24    20.03    1.000         0
  bird         0    12.18     0.23    20.62    1.000         0
  bird         1    12.30     0.26    20.28    1.000         0
  cat          0    12.19     0.20    19.87    1.000         0
  cat          1    12.07     0.18    20.44    1.000         0
  deer         0    12.30     0.09    19.88    1.000         0
  deer         1    12.26     0.24    20.43    1.000         0
  dog          0    12.26     0.23    20.28    1.000         0
  dog          1    12.19     0.30    20.55    1.000         0
  frog         0    12.18     0.19    20.18    1.000         0
  frog         1    12.23     0.17    20.43    1.000         0
  horse        0    12.38     0.34    20.69    1.000         0
  horse        1    12.15     0.21    19.89    1.000         0
  ship         0    12.16     0.29    20.76    1.000         0
  ship         1    12.17     0.23    20.06    1.000         0
  truck        0    12.17     0.26    20.30    1.000         0
  truck        1    12.21     0.23    20.33    1.000         0

======================================================================
  7. LINEAR PROBE — Can flattened friction maps classify?
======================================================================

  Features: flattened friction map (1024 dims)
  Train: 1600, Test: 400
  Train accuracy: 92.6%
  Test accuracy:  24.3%
  Chance:          10.0%

  Class         Acc
  ------------------
  airplane   32.6% ██████
  auto       24.4% ████
  bird       20.6% ████
  cat        15.7% ███
  deer       10.3% ██
  dog        21.9% ████
  frog       37.8% ███████
  horse      22.9% ████
  ship       24.1% ████
  truck      27.8% █████

  VERDICT: DISCRIMINATIVE spatial friction signal

======================================================================
  8. SETTLE MAP — Spatial convergence patterns
======================================================================
  Settle map linear probe:
  Test accuracy: 10.5%
  VERDICT: NOT DISCRIMINATIVE

======================================================================
  9. COMBINED CONDUIT — All evidence stacked
======================================================================

  Collecting eigenvalue spatial maps...

  Linear probe comparison (all use same train/test split):

  Eigenvalues (S) spatial        dims= 1024  test_acc=21.0%
  Friction spatial               dims= 1024  test_acc=24.3%
  Settle spatial                 dims= 1024  test_acc=10.5%
  Combined (S+fric+settle)       dims= 3072  test_acc=22.0%

  Chance: 10.0%
  VERDICT: Combined vs eigenvalues-only lift = +1.0 percentage points

======================================================================
  SPATIAL FRICTION ANALYSIS — SUMMARY
======================================================================
  1. Spatial structure within images:   CV = 0.0137
  2. Inter-class pattern distance:      cos_min = 0.999881
  3. Center vs edge asymmetry:          (see table above)
  4. Per-position F-statistic:          max = 0.133089
  5. Friction map linear probe:         24.3%
  6. Settle map linear probe:           10.5%
  7. Eigenvalue map linear probe:       21.0%
  8. Combined conduit linear probe:     22.0%
  9. Conduit lift over eigenvalues:     +1.0pp