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?