Create notebook_cell_2_try_1_output.txt

notebook_cell_2_try_1_output.txt

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+Device: cuda
+Setup complete.
+
+
+======================================================================
+  1. PARITY VERIFICATION
+======================================================================
+
+  Tests:          100
+  Passed:         100/100
+  Max eval error: 0.00e+00
+  Max evec error: 2.98e-07
+  VERDICT:        PASS
+
+======================================================================
+  2. CHARACTERISTIC COEFFICIENTS VALIDATION
+======================================================================
+
+  Prescribed eigenvalues: [1, 2, 3, 4]
+  Recovered eigenvalues:  [0.9999998211860657, 1.9999996423721313, 2.9999988079071045, 3.999999761581421]
+  Char coeffs (sample):   [0.4266666769981384, -2.4343225955963135, 4.6666669845581055, -3.6514837741851807]
+
+  Coefficient ratios (should be consistent across batch):
+    c[0]: mean=0.4267 std=0.000000 cv=0.0000
+    c[1]: mean=-2.4343 std=0.000000 cv=0.0000
+    c[2]: mean=4.6667 std=0.000000 cv=0.0000
+    c[3]: mean=-3.6515 std=0.000000 cv=0.0000
+
+  VERDICT: Coefficients consistent across batch
+
+======================================================================
+  3. FRICTION vs SPECTRAL GAP CORRELATION
+======================================================================
+
+  Samples: 512 matrices, 2048 eigenvalues
+  Gap range:      [0.0377, 4.6139]
+  Friction range: [0.85, 847.31]
+  Correlation (gap vs friction): -0.0449
+  Expected: NEGATIVE (small gap → high friction)
+  VERDICT: WEAK
+
+  Binned friction by gap size:
+    Gap [0.038-0.525]: friction mean=12.70 std=35.88
+    Gap [0.527-0.839]: friction mean=8.13 std=19.13
+    Gap [0.841-1.151]: friction mean=6.94 std=14.87
+    Gap [1.151-1.551]: friction mean=8.29 std=43.83
+    Gap [1.552-4.614]: friction mean=6.51 std=20.56
+
+======================================================================
+  4. CONTROLLED GAP SWEEP
+======================================================================
+
+  Fixed eigenvalues: λ₀=1.0, λ₁=3.0, λ₃=10.0
+  Sweeping: λ₂ from 3.001 to 8.0 (gap to λ₁)
+
+       Gap      λ₂   fric[0]   fric[1]   fric[2]   fric[3]        settle
+  ----------------------------------------------------------------------
+     0.001   3.001     13.54   2179.23   2060.23      5.00  [1.21875, 3.1875, 2.3125, 1.0]
+     0.010   3.010     16.34   1226.98    418.81      5.00  [1.15625, 3.3125, 2.21875, 1.0]
+     0.050   3.050     15.36    447.83    154.27      6.48  [1.1875, 3.0625, 1.96875, 1.0]
+     0.100   3.100     10.53    240.25    108.60      5.07  [1.1875, 3.03125, 2.0625, 1.0]
+     0.500   3.500      9.64     96.32     15.93      5.86  [1.15625, 2.4375, 2.03125, 1.0]
+     1.000   4.000      9.67     63.08     13.24      6.58  [1.1875, 2.1875, 2.03125, 1.0]
+     2.000   5.000     12.39     51.44      9.97      6.35  [1.15625, 2.28125, 2.34375, 1.0]
+     5.000   8.000     14.13     20.95     17.38      7.73  [1.375, 1.875, 2.625, 1.0]
+
+  Expected: friction[1] and friction[2] spike as gap → 0
+
+======================================================================
+  5. SETTLE TIME ANALYSIS
+======================================================================
+
+  Samples: 1024 matrices
+
+  Settle distribution per root position:
+    Root 0: mean=1.22 mode=1 min=1 max=3
+    Root 1: mean=2.61 mode=3 min=1 max=5
+    Root 2: mean=2.81 mode=3 min=1 max=5
+    Root 3: mean=1.00 mode=1 min=1 max=1
+
+  All roots settle in 1 iter: 0.0%
+  Any root needs ≥3 iters:   85.2%
+  VERDICT: DENSE settle signal at n=4
+
+======================================================================
+  6. EXTRACTION ORDER DETERMINISM
+======================================================================
+
+  Same matrix repeated 32 times
+  Extraction order[0]: [0.0, 1.0, 2.0, 3.0]
+  All identical: True
+
+  64 different matrices
+  Unique extraction orders: 1
+  VERDICT: Order is deterministic for identical inputs, fixed across inputs
+
+======================================================================
+  7. NEAR-DEGENERATE BEHAVIOR
+======================================================================
+
+  Two eigenvalues converging: λ₂ = 5.0, λ₃ = 5.0 + ε
+
+             ε   fric[2]   fric[3]   settle[2]   settle[3]  refine_res    eval_err
+  ---------------------------------------------------------------------------
+       1.0e+00     21.22      6.32         2.5         1.0    1.51e-07    1.91e-06
+       1.0e-01     96.96      6.89         4.3         1.0    3.65e-07    1.43e-06
+       1.0e-02    366.61      7.32         4.5         1.0    7.28e-06    1.91e-06
+       1.0e-03   1581.30  38780.37         4.2         1.2    8.30e-02    3.56e+00
+       1.0e-04    402.81  46227.47         2.8         1.8    5.78e-01    3.69e+00
+       1.0e-05    205.76  23394.54         2.0         2.2    9.95e-01    3.75e+00
+       1.0e-07     71.99     34.94         2.2         2.2    1.12e+00    3.75e+00
+       1.0e-10  42139.94   6887.26         3.2         2.2    9.84e-01    3.75e+00
+
+  Expected: friction spikes, settle increases, eigenvalue error grows as ε → 0
+
+======================================================================
+  8. SIGN CANONICALIZATION
+======================================================================
+
+  Canonicalization preserves positive max entry: True
+  Eigenvector drift under 1e-6 perturbation: 2.72e-06
+  VERDICT: Canonicalization STABLE
+
+  Near-degenerate (gap=0.001):
+  Max-entry row consistent: [False, False, False, False]
+  CONCERN: Degenerate columns may have inconsistent gauge
+
+======================================================================
+  9. REFINEMENT RESIDUAL
+======================================================================
+
+  Samples: 1024
+  Mean:    1.15e-07
+  Std:     4.46e-08
+  Min:     8.78e-09
+  Max:     2.76e-07
+  < 1e-6:  100.0%
+  < 1e-4:  100.0%
+  VERDICT: UNIFORMLY TINY — no discriminative signal
+
+======================================================================
+  10. STATIC RECONSTRUCTION — char_coeffs from eigenvalues
+======================================================================
+
+  Mstore[1]: off-diag norm = 6.11e-08, diag norm = 2.00e+00, ratio = 3.05e-08
+  Mstore[2]: off-diag norm = 8.08e-08, diag norm = 2.58e+00, ratio = 3.13e-08
+  Mstore[3]: off-diag norm = 7.64e-08, diag norm = 2.47e+00, ratio = 3.09e-08
+  Mstore[4]: off-diag norm = 3.28e-08, diag norm = 1.08e+00, ratio = 3.05e-08
+
+  VERDICT: Mstore IS diagonal in eigenbasis → CONFIRMED reconstructible from (λ,V)
+
+======================================================================
+  11. DYNAMIC NON-RECONSTRUCTIBILITY
+======================================================================
+
+  Root 0: corr(actual, static_proxy) = 0.0080, residual mean = 8.92, residual std = 53.34
+  Root 1: corr(actual, static_proxy) = 0.2306, residual mean = 6.64, residual std = 15.64
+  Root 2: corr(actual, static_proxy) = 0.0248, residual mean = 6.11, residual std = 36.72
+  Root 3: corr(actual, static_proxy) = -0.0070, residual mean = 12.89, residual std = 171.57
+
+  Total friction variance:    8465.3789
+  Static proxy variance:      35.8844
+  Residual (dynamic) variance: 8490.7451
+  Dynamic fraction:            100.3%
+
+  VERDICT: Dynamic excess is SIGNIFICANT
+
+======================================================================
+  12. DIMENSION AGNOSTIC SCALING
+======================================================================
+
+  n=3: packet OK, parity=True, friction=[1.2, 112.4], settle=[1, 4], time=6.2ms
+  n=4: packet OK, parity=True, friction=[1.6, 966.6], settle=[1, 5], time=6.9ms
+  n=5: packet OK, parity=True, friction=[0.8, 43.5], settle=[1, 5], time=8.7ms
+  n=6: packet OK, parity=True, friction=[1.2, 18981.9], settle=[1, 5], time=10.7ms
+  n=8: packet OK, parity=True, friction=[1.2, 543.6], settle=[1, 5], time=15.4ms
+
+  VERDICT: Scales cleanly across dimensions
+
+======================================================================
+  13. RESEARCH MODE
+======================================================================
+
+  Mstore shape:        torch.Size([5, 8, 4, 4])
+  z_trajectory shape:  torch.Size([8, 4, 5])
+  dp_trajectory shape: torch.Size([8, 4, 5])
+
+  Laguerre trajectory for patch 0:
+    Root 0 (final λ=-1.8706):
+      iter 0: z= -0.9732  |p'|=    0.3093
+      iter 1: z= -0.5809  |p'|=    1.9045
+      iter 2: z= -0.3366  |p'|=    1.6568
+      iter 3: z= -0.3167  |p'|=    1.6084
+      iter 4: z= -0.3167  |p'|=    1.6084
+    Root 1 (final λ=-0.4204):
+      iter 0: z= -0.2495  |p'|=    1.4321
+      iter 1: z=  0.4084  |p'|=    1.7178
+      iter 2: z=  0.6268  |p'|=    1.2384
+      iter 3: z=  0.6361  |p'|=    1.2117
+      iter 4: z=  0.6361  |p'|=    1.2117
+    Root 2 (final λ=0.8443):
+      iter 0: z=  0.3411  |p'|=    0.8630
+      iter 1: z=  1.2285  |p'|=    2.6377
+      iter 2: z=  1.2285  |p'|=    2.6377
+      iter 3: z=  1.2285  |p'|=    2.6377
+      iter 4: z=  1.2285  |p'|=    2.6377
+    Root 3 (final λ=1.6307):
+      iter 0: z=  1.0203  |p'|=    1.0000
+      iter 1: z= -1.4092  |p'|=    1.0000
+      iter 2: z= -1.4092  |p'|=    1.0000
+      iter 3: z= -1.4092  |p'|=    1.0000
+      iter 4: z= -1.4092  |p'|=    1.0000
+
+  Mstore diagonal progression for patch 0:
+    Mstore[1] diag: [1.0000, 1.0000, 1.0000, 1.0000]
+    Mstore[2] diag: [-0.3882, 0.8816, -1.1118, 0.2024]
+    Mstore[3] diag: [-1.6200, -0.9681, -0.2902, -1.1024]
+    Mstore[4] diag: [0.9069, -0.3164, 0.2354, -0.3093]
+
+======================================================================
+  14. FRECKLES CIFAR-10 — CLASS DISCRIMINABILITY
+======================================================================
+
+  Loading Freckles v40 and CIFAR-10...
+
+  Per-class friction statistics (mean across patches):
+
+  Class       fric_mean   fric_std  settle_mean
+  --------------------------------------------
+  airplane        12.14       4.79         1.25
+  auto            12.21       4.89         1.25
+  bird            12.17       4.85         1.25
+  cat             12.21       4.90         1.25
+  deer            12.20       4.89         1.25
+  dog             12.18       4.86         1.25
+  frog            12.23       4.93         1.25
+  horse           12.18       4.87         1.25
+  ship            12.15       4.80         1.25
+  truck           12.18       4.86         1.25
+
+  Inter-class friction spread: 0.08
+  Mean friction: 12.19
+  Spread/Mean ratio: 0.68%
+
+  VERDICT: NOT DISCRIMINATIVE friction signal
+
+======================================================================
+  SUMMARY — ALL TESTS COMPLETE
+======================================================================
+
+  Review each section's VERDICT above.
+  Key questions answered:
+    1. Does FLEighConduit match FLEigh?
+    2. Does friction correlate with spectral gaps?
+    3. Does friction spike at near-degeneracy?
+    4. Is the dynamic signal non-trivial at n=4?
+    5. Are static conduits reconstructible from eigenvalues?
+    6. Is sign canonicalization stable?
+    7. Does friction differ across CIFAR-10 classes?
+    8. Is refinement residual uniformly tiny?
+    9. Does settle time carry signal?
+   10. Does the system scale to higher n?