/home/pc/.venv/global-python/lib/python3.12/site-packages/scipy/stats/_axis_nan_policy.py:423: RuntimeWarning: Precision loss occurred in moment calculation due to catastrophic cancellation. This occurs when the data are nearly identical. Results may be unreliable.
  return hypotest_fun_in(*args, **kwds)
======================================================================
  Fractal Correction Engine -- Scientific Validation Suite
======================================================================

======================================================================
  1. Quantitative Benchmarks
======================================================================

Quantitative Validation Against Analytical References
===============================================================================================
Metric                                 Simulated    Reference        Error    Rel Err Source              
-----------------------------------------------------------------------------------------------
[+] F(rho, rho) = 1                      1.000000     1.000000     0.00e+00   0.00e+00 Uhlmann identity    
[+] F(|0>, |1>) = 0                      0.000000     0.000000     0.00e+00   0.00e+00 Orthogonality       
[+] F(|+>, I/2) = 0.5                    0.500000     0.500000     3.89e-16   7.77e-16 Mixed state formula 
[+] F(A,B) = F(B,A) symmetry             0.860000     0.860000     4.44e-16   5.16e-16 Fidelity symmetry   
[+] S(I/2) = ln(2)                       0.693147     0.693147     0.00e+00   0.00e+00 Maximum entropy     
[+] S(I/4) = ln(4)                       1.386294     1.386294     0.00e+00   0.00e+00 Maximum entropy d=4 
[+] S(pure state) = 0                   -0.000000     0.000000     0.00e+00   0.00e+00 Pure state entropy  
[+] Purity(pure) = 1                     1.000000     1.000000     0.00e+00   0.00e+00 Pure state purity   
[+] Purity(I/2) = 0.5                    0.500000     0.500000     0.00e+00   0.00e+00 Max mixed purity    
[+] Bures(rho, rho) = 0                  0.000000     0.000000     0.00e+00   0.00e+00 Bures self-distance 
[+] Bures(|0>,|1>) = sqrt(2)             1.414214     1.414214     0.00e+00   0.00e+00 Max Bures distance  
[+] Tr(normalized rho) = 1               1.000000     1.000000     0.00e+00   0.00e+00 Trace preservation  
[+] Tr(U rho U^dag) = 1                  1.000000     1.000000     2.22e-16   2.22e-16 Unitary trace pres. 
[+] Purity(U rho U^dag) = Purity(rho)     1.000000     1.000000     0.00e+00   0.00e+00 Unitary purity pres.
[+] F(U rho U^dag, U rho U^dag) = 1      1.000000     1.000000     0.00e+00   0.00e+00 Evolved self-fidelity
[+] Lindblad decay timescale             0.909365     0.818731     9.06e-02   1.11e-01 Breuer & Petruccione
[+] Max trace error (50 steps)           0.000000     0.000000     2.22e-16   2.22e-16 Trace conservation  
[+] Max positivity violation             0.000000     0.000000     0.00e+00   0.00e+00 Positivity          
[+] T1 decay: rho_11(t)                  0.951229     0.951229     1.55e-08   1.62e-08 Breuer & Petruccione (2002)
[+] T2 dephasing: |rho_01(t)|            0.452419     0.452419     1.51e-08   3.33e-08 Breuer & Petruccione (2002)
[+] FCE error reduction > 1.0            1.080658     1.000000     8.07e-02   8.07e-02 FCE emergent prediction
[+] d_H(low noise) <= d_H(high noise)     0.984028     0.937236     4.68e-02   4.99e-02 FCE emergent prediction
[+] N_corr(thresh=0.001) >= N_corr(thresh=0.01)    50.000000    45.000000     5.00e+00   1.11e-01 FCE emergent prediction
-----------------------------------------------------------------------------------------------
Passed: 23/23 (100%)

======================================================================
  2. Ablation Study (20 trials)
======================================================================

Ablation Study Results
==========================================================================================
Configuration             Final F (mean) Final F (std)  Err Reduction  Runtime (s)
------------------------------------------------------------------------------------------
A_physics_only                  0.970882      0.000000           1.00       0.0747
B_full_fce                      0.987294      0.000000           2.29       0.0795
C_random_fce                    0.990019      0.003461           2.03       0.0781
------------------------------------------------------------------------------------------
Trials per configuration: 20

Conservation & Stability per Mode
==========================================================================================
Configuration                Trace Err   Positivity       Purity   F Variance
------------------------------------------------------------------------------------------
A_physics_only                7.16e-18     0.00e+00     0.943897     7.54e-05
B_full_fce                    1.43e-17     0.00e+00     0.974993     1.45e-05
C_random_fce                  5.73e-18     1.94e-17     0.959443     1.04e-05
------------------------------------------------------------------------------------------

Pairwise Comparisons (B_full_fce vs others)
==========================================================================================
Comparison                      Cohen d     Effect   t-stat    p-value               95% CI  Sig?
------------------------------------------------------------------------------------------
B vs A_physics_only               0.000 negligible      inf   0.00e+00   [+0.0164, +0.0164]     *
B vs C_random_fce                -0.768     medium   -3.433   2.79e-03   [-0.0044, -0.0011]     *
------------------------------------------------------------------------------------------
* = significant at alpha=0.05
Effect sizes: negligible (|d|<0.2), small (0.2-0.5), medium (0.5-0.8), large (>0.8)

======================================================================
  3. Multi-Observable Convergence
======================================================================

Multi-Observable Convergence Study
===========================================================================
Observable                   Order p        R^2      Richardson         Flag
---------------------------------------------------------------------------
final_fidelity                -9.294   0.750000      0.95241870 NEGATIVE_ORDER
mean_fidelity                  1.403   0.994484      0.97581330           OK
hausdorff_dim                  0.951   0.985249      0.99749191           OK
---------------------------------------------------------------------------
Status: CHECK WARNINGS

--- final_fidelity ---
Convergence Study: final_fidelity
======================================================================
   n_steps           dt      Observable      Error E(h)      Ratio
----------------------------------------------------------------------
        50     1.00e-06      0.95241870    1.909584e-14        ---
       100     5.00e-07      0.95241871    7.527682e-09       0.00
       200     2.50e-07      0.95241871    7.527676e-09       1.00
       400     1.25e-07      0.95241870             ---        ---
----------------------------------------------------------------------
Convergence order p: -9.294
R^2 of log-log fit: 0.750000
Richardson extrapolation: 0.9524187042
Finest grid value:       0.9524187042
WARNING: NEGATIVE_ORDER
  Error increases with resolution -- possible instability

--- mean_fidelity ---
Convergence Study: mean_fidelity
======================================================================
   n_steps           dt      Observable      Error E(h)      Ratio
----------------------------------------------------------------------
        50     1.00e-06      0.97582084    6.934307e-06        ---
       100     5.00e-07      0.97581688    2.972948e-06       2.33
       200     2.50e-07      0.97581490    9.917894e-07       3.00
       400     1.25e-07      0.97581391             ---        ---
----------------------------------------------------------------------
Convergence order p: 1.403
R^2 of log-log fit: 0.994484
Richardson extrapolation: 0.9758133037
Finest grid value:       0.9758139069

--- hausdorff_dim ---
Convergence Study: hausdorff_dim
======================================================================
   n_steps           dt      Observable      Error E(h)      Ratio
----------------------------------------------------------------------
        50     1.00e-06      0.98335803    1.098480e-02        ---
       100     5.00e-07      0.98780894    6.533893e-03       1.68
       200     2.50e-07      0.99140383    2.938999e-03       2.22
       400     1.25e-07      0.99434283             ---        ---
----------------------------------------------------------------------
Convergence order p: 0.951
R^2 of log-log fit: 0.985249
Richardson extrapolation: 0.9974919123
Finest grid value:       0.9943428299

======================================================================
  4. Uncertainty Quantification
======================================================================

Uncertainty Quantification Results
===========================================================================
Metric                                 Mean          Std               95% CI
---------------------------------------------------------------------------
final_fidelity                     0.978246     0.008997 [0.959577, 0.989917]
mean_fidelity                      0.989458     0.005125 [0.979076, 0.995953]
error_reduction                    1.024133     0.008919 [1.011939, 1.044855]
n_corrections                     29.660000     0.514198 [29.000000, 30.000000]
hausdorff_dimension                1.002710     0.001876 [1.000212, 1.006815]
max_trace_error                    0.000000     0.000000 [0.000000, 0.000000]
---------------------------------------------------------------------------
Monte Carlo samples: 50

Parameter Ranges:
  feedback_gain: 0.1 +/- 0.01
  T1: 0.001 +/- 0.00015
  T2: 0.0005 +/- 7.5e-05
  gate_fidelity: 0.999 +/- 0.0005
  dt: 1e-06 +/- 5e-08

--- Parameter Importance Ranking ---
Parameter Importance Ranking: final_fidelity
======================================================================
  Rank Parameter                     Variance   Fraction
----------------------------------------------------------------------
     1 T2                            2.10e-05     0.2567
     2 dt                            2.02e-06     0.0247
     3 feedback_gain                 3.69e-09     0.0000
     4 T1                            4.40e-17     0.0000
     5 gate_fidelity                 2.35e-17     0.0000
----------------------------------------------------------------------
Total variance (all-vary): 8.18e-05
Sum of fractions: 0.2815
  (>1 indicates parameter interactions; <1 indicates correlated effects)

======================================================================
  5. Conservation Law Monitoring
======================================================================

Conservation Law Monitoring Report
=================================================================
Quantity                         Max Violation     Status
-----------------------------------------------------------------
Trace preservation                    2.22e-16       PASS
Hermiticity                           1.11e-16       PASS
Positivity (min eigenvalue)          -0.00e+00       PASS
Mean purity Tr(rho^2)                 0.913709        ---
-----------------------------------------------------------------
Steps monitored: 101

Time-Series Samples
=================================================================
  Step     Trace Err        Purity    Min Eigval     ||rho||_F
-----------------------------------------------------------------
     0      2.22e-16      1.000000      0.00e+00      1.000000
    25      0.00e+00      0.952723      2.42e-02      0.976076
    50      0.00e+00      0.910555      4.69e-02      0.954230
    75      0.00e+00      0.873020      6.81e-02      0.934355
   100      0.00e+00      0.839688      8.79e-02      0.916345

Lindblad Integrator Verification
=================================================================
Max ||drho/dt - L[rho]||_F            9.48e-04      CHECK
Mean ||drho/dt - L[rho]||_F           8.62e-04        ---

======================================================================
  6a. Alpha Sweep
======================================================================

Parameter Sensitivity: feedback_gain (alpha)
=====================================================================================
   alpha      Final F    F (std)    Err Red  Corrections      d_H    Runtime
-------------------------------------------------------------------------------------
  0.0000     0.970882   0.000000       1.00            0   1.0168     0.0745
  0.0100     0.970971   0.000000       1.00           30   1.0110     0.0786
  0.0500     0.971320   0.000000       1.02           30   1.0034     0.0869
  0.1000     0.971744   0.000000       1.03           30   1.0014     0.0788
  0.5000     0.974686   0.000000       1.15           30   1.0014     0.0784
  1.0000     0.977518   0.000000       1.30           30   0.9779     0.0793 <--
-------------------------------------------------------------------------------------
Optimal alpha: 1.0000
Optimal fidelity: 0.97751838

======================================================================
  6b. Threshold Sweep
======================================================================

Parameter Sensitivity: correction_threshold
=====================================================================================
 threshold      Final F    F (std)    Err Red  Corrections      d_H    Runtime
-------------------------------------------------------------------------------------
   0.00000     0.971744   0.000000       1.03           30   1.0014     0.0788 <--
   0.00010     0.971744   0.000000       1.03           30   1.0014     0.0862
   0.00100     0.971744   0.000000       1.03           30   1.0014     0.0784
   0.01000     0.971739   0.000000       1.03           25   1.0013     0.0780
   0.10000     0.970882   0.000000       1.00            0   1.0168     0.0749
-------------------------------------------------------------------------------------
Optimal threshold: 0.00000
Optimal fidelity: 0.97174351

======================================================================
  6c. 2D Sweep (alpha x threshold)
======================================================================

2D Parameter Sweep: alpha x correction_threshold
================================================================================
alpha \\ thresh     0.0000     0.0010     0.0100
--------------------------------------------------------------------------------
        0.0000   0.970882   0.970882   0.970882
        0.0500   0.971320   0.971320   0.971318
        0.1000   0.971744   0.971744   0.971739
        0.5000   0.974686   0.974686   0.974669
--------------------------------------------------------------------------------
Optimal: alpha=0.5000, threshold=0.00000, fidelity=0.97468591

======================================================================
  Validation Complete
======================================================================

  Benchmarks:      23/23 passed
  Ablation modes:  3
  Convergence:     3 observables
  UQ samples:      50
  Importance:      5 parameters ranked
  Lindblad resid:  9.48e-04
  Alpha optimal:   1.0
  Thresh optimal:  0.0
  2D optimal:      alpha=0.5, thresh=0.0
