| Device: cuda |
| Setup complete. |
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| ====================================================================== |
| 1. PARITY VERIFICATION |
| ====================================================================== |
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| Tests: 100 |
| Passed: 100/100 |
| Max eval error: 0.00e+00 |
| Max evec error: 2.98e-07 |
| VERDICT: PASS |
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| ====================================================================== |
| 2. CHARACTERISTIC COEFFICIENTS VALIDATION |
| ====================================================================== |
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| 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] |
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| 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 |
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| VERDICT: Coefficients consistent across batch |
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| ====================================================================== |
| 3. FRICTION vs SPECTRAL GAP CORRELATION |
| ====================================================================== |
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| 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 |
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| 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 |
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| ====================================================================== |
| 4. CONTROLLED GAP SWEEP |
| ====================================================================== |
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| Fixed eigenvalues: λ₀=1.0, λ₁=3.0, λ₃=10.0 |
| Sweeping: λ₂ from 3.001 to 8.0 (gap to λ₁) |
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| 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] |
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| Expected: friction[1] and friction[2] spike as gap → 0 |
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| ====================================================================== |
| 5. SETTLE TIME ANALYSIS |
| ====================================================================== |
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| Samples: 1024 matrices |
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| 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 |
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| All roots settle in 1 iter: 0.0% |
| Any root needs ≥3 iters: 85.2% |
| VERDICT: DENSE settle signal at n=4 |
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| ====================================================================== |
| 6. EXTRACTION ORDER DETERMINISM |
| ====================================================================== |
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| Same matrix repeated 32 times |
| Extraction order[0]: [0.0, 1.0, 2.0, 3.0] |
| All identical: True |
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| 64 different matrices |
| Unique extraction orders: 1 |
| VERDICT: Order is deterministic for identical inputs, fixed across inputs |
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| ====================================================================== |
| 7. NEAR-DEGENERATE BEHAVIOR |
| ====================================================================== |
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| Two eigenvalues converging: λ₂ = 5.0, λ₃ = 5.0 + ε |
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| 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 |
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| Expected: friction spikes, settle increases, eigenvalue error grows as ε → 0 |
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| ====================================================================== |
| 8. SIGN CANONICALIZATION |
| ====================================================================== |
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| Canonicalization preserves positive max entry: True |
| Eigenvector drift under 1e-6 perturbation: 2.72e-06 |
| VERDICT: Canonicalization STABLE |
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| Near-degenerate (gap=0.001): |
| Max-entry row consistent: [False, False, False, False] |
| CONCERN: Degenerate columns may have inconsistent gauge |
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| ====================================================================== |
| 9. REFINEMENT RESIDUAL |
| ====================================================================== |
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| 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 |
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| ====================================================================== |
| 10. STATIC RECONSTRUCTION — char_coeffs from eigenvalues |
| ====================================================================== |
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| 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 |
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| VERDICT: Mstore IS diagonal in eigenbasis → CONFIRMED reconstructible from (λ,V) |
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| ====================================================================== |
| 11. DYNAMIC NON-RECONSTRUCTIBILITY |
| ====================================================================== |
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| 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 |
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| Total friction variance: 8465.3789 |
| Static proxy variance: 35.8844 |
| Residual (dynamic) variance: 8490.7451 |
| Dynamic fraction: 100.3% |
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| VERDICT: Dynamic excess is SIGNIFICANT |
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| ====================================================================== |
| 12. DIMENSION AGNOSTIC SCALING |
| ====================================================================== |
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| 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 |
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| VERDICT: Scales cleanly across dimensions |
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| ====================================================================== |
| 13. RESEARCH MODE |
| ====================================================================== |
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| Mstore shape: torch.Size([5, 8, 4, 4]) |
| z_trajectory shape: torch.Size([8, 4, 5]) |
| dp_trajectory shape: torch.Size([8, 4, 5]) |
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| 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 |
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| 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] |
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| ====================================================================== |
| 14. FRECKLES CIFAR-10 — CLASS DISCRIMINABILITY |
| ====================================================================== |
|
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| Loading Freckles v40 and CIFAR-10... |
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| Per-class friction statistics (mean across patches): |
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| 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 |
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| Inter-class friction spread: 0.08 |
| Mean friction: 12.19 |
| Spread/Mean ratio: 0.68% |
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| VERDICT: NOT DISCRIMINATIVE friction signal |
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| ====================================================================== |
| SUMMARY — ALL TESTS COMPLETE |
| ====================================================================== |
|
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| 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? |
