MODEL C MATHEMATICAL EVIDENCE REPORTER — v5.2 - 2026/07/20
MODEL C MATHEMATICAL EVIDENCE REPORTER — v5.2 - 2026/07/20
================================================================================
PHASE V: FULL NUMERICAL EQUATIONS & 4-GRADIENT ENGINE
================================================================================
FULLY EVALUATED NUMERICAL EQUATIONS:
Ψ_B = 0.5*I2 + 0.5*I1^2 + 0.025*I1^4 + 0.005*||P||^2
dΨ/dPxx = I1 + 0.1*I1^3 + 1.01*Pxx
dΨ/dPxy = 1.01*Pxy
dΨ/dPyx = 1.01*Pyx
dΨ/dPyy = I1 + 0.1*I1^3 + 1.01*Pyy
Hessian Eigenvalues: {1.01, 1.01, 1.01, 3.01 + 0.6*I1^2}
CONTROLS:
• EXECUTE 4-GRADIENT ENGINE — Runs diagnostics, saves JSON/CSV/ZIP
• EVALUATE SAMPLE PDEs — Tests evolution equations with torque term
• RUN GRADIENT DIAGNOSTICS — Validates symbolic vs FD gradients
• RUN STABILITY SWEEP — Parameter sensitivity mapping (FIXED)
================================================================================
EXECUTE 4-GRADIENT ENGINE (SAVE & BACKUP)EVALUATE SAMPLE PDEsRUN GRADIENT DIAGNOSTICSRUN STABILITY SWEEP
================================================================================
INITIATING 4 GRADIENT ENGINE: DIAGNOSTICS & PRESERVATION
================================================================================
============================================================
4-GRADIENT DIAGNOSTIC GATE
============================================================
✓ Pxx=1.000, Pxy=0.000, Pyx=0.000, Pyy=1.000 | L2=3.3717e-09
✓ Pxx=1.248, Pxy=-0.069, Pyx=0.324, Pyy=1.762 | L2=4.8982e-08
✓ Pxx=0.883, Pxy=-0.117, Pyx=0.790, Pyy=1.384 | L2=3.8641e-08
✓ Pxx=0.765, Pxy=0.271, Pyx=-0.232, Pyy=0.767 | L2=8.2007e-09
✓ Pxx=1.121, Pxy=-0.957, Pyx=-0.862, Pyy=0.719 | L2=1.8922e-08
------------------------------------------------------------
Samples Analyzed: 5
Max L2 Error: 4.8982e-08 (Threshold: 1e-06)
Max Inf Error: 3.6563e-08
STATUS: PASSED ✓
============================================================
================================================================================
PRESERVATION PROTOCOL STATUS REPORT
================================================================================
✓ Colab workspace saved: True
✓ Google Drive backup saved: True
✓ Download package created: True
--------------------------------------------------------------------------------
STAGING DIRECTORY: /content/output_20260720_174858
GOOGLE DRIVE PATH: /content/drive/MyDrive/FRCMpD_NumericalEval/output_20260720_174858
MASTER ZIP PATH: /content/FRCMpD_NumericalEval_20260720_174858.zip
FILE COUNT: 3
ARCHIVE SIZE: 2071 bytes
STATUS: SUCCESS ONLY IF ALL BACKUPS EXIST
================================================================================
EXECUTE 4-GRADIENT ENGINE (SAVE & BACKUP)EVALUATE SAMPLE PDEsRUN GRADIENT DIAGNOSTICSRUN STABILITY SWEEP
--- SAMPLE PDE EVALUATION ---
dUxx/dt = -1.1020
dUxy/dt = -0.2985
dUyx/dt = -0.1385 (Torque included)
dUyy/dt = -0.7870
Hessian Eigenvalues: [1.01 1.01 1.01 5.41]
Slip Op A (Hard Clip): 4.0000
Slip Op B (Smooth): 4.4040
EXECUTE 4-GRADIENT ENGINE (SAVE & BACKUP)EVALUATE SAMPLE PDEsRUN GRADIENT DIAGNOSTICSRUN STABILITY SWEEP
============================================================
4-GRADIENT DIAGNOSTIC GATE
============================================================
✓ Pxx=1.000, Pxy=0.000, Pyx=0.000, Pyy=1.000 | L2=3.3717e-09
✓ Pxx=1.248, Pxy=-0.069, Pyx=0.324, Pyy=1.762 | L2=4.8982e-08
✓ Pxx=0.883, Pxy=-0.117, Pyx=0.790, Pyy=1.384 | L2=3.8641e-08
✓ Pxx=0.765, Pxy=0.271, Pyx=-0.232, Pyy=0.767 | L2=8.2007e-09
✓ Pxx=1.121, Pxy=-0.957, Pyx=-0.862, Pyy=0.719 | L2=1.8922e-08
------------------------------------------------------------
Samples Analyzed: 5
Max L2 Error: 4.8982e-08 (Threshold: 1e-06)
Max Inf Error: 3.6563e-08
STATUS: PASSED ✓
============================================================
EXECUTE 4-GRADIENT ENGINE (SAVE & BACKUP)EVALUATE SAMPLE PDEsRUN GRADIENT DIAGNOSTICSRUN STABILITY SWEEP
================================================================================
STABILITY SWEEP — PARAMETER SENSITIVITY MAPPING
================================================================================
Parameters: ['kappa', 'MU_SLIP']
Total configurations: 36
Steps per config: 5
================================================================================
Testing {'kappa': 0.01, 'MU_SLIP': 0.01}... ✓ STABLE (max_update=0.1976, κ=0.01, μ_slip=0.01)
Testing {'kappa': 0.01, 'MU_SLIP': 0.05}... ✓ STABLE (max_update=0.1978, κ=0.01, μ_slip=0.05)
Testing {'kappa': 0.01, 'MU_SLIP': 0.1}... ✓ STABLE (max_update=0.1981, κ=0.01, μ_slip=0.10)
Testing {'kappa': 0.01, 'MU_SLIP': 0.3}... ✓ STABLE (max_update=0.1991, κ=0.01, μ_slip=0.30)
Testing {'kappa': 0.01, 'MU_SLIP': 0.5}... ✓ STABLE (max_update=0.2001, κ=0.01, μ_slip=0.50)
Testing {'kappa': 0.01, 'MU_SLIP': 1.0}... ✓ STABLE (max_update=0.2026, κ=0.01, μ_slip=1.00)
Testing {'kappa': 0.05, 'MU_SLIP': 0.01}... ✓ STABLE (max_update=0.1976, κ=0.05, μ_slip=0.01)
Testing {'kappa': 0.05, 'MU_SLIP': 0.05}... ✓ STABLE (max_update=0.1978, κ=0.05, μ_slip=0.05)
Testing {'kappa': 0.05, 'MU_SLIP': 0.1}... ✓ STABLE (max_update=0.1981, κ=0.05, μ_slip=0.10)
Testing {'kappa': 0.05, 'MU_SLIP': 0.3}... ✓ STABLE (max_update=0.1991, κ=0.05, μ_slip=0.30)
Testing {'kappa': 0.05, 'MU_SLIP': 0.5}... ✓ STABLE (max_update=0.2001, κ=0.05, μ_slip=0.50)
Testing {'kappa': 0.05, 'MU_SLIP': 1.0}... ✓ STABLE (max_update=0.2026, κ=0.05, μ_slip=1.00)
Testing {'kappa': 0.1, 'MU_SLIP': 0.01}... ✓ STABLE (max_update=0.1976, κ=0.10, μ_slip=0.01)
Testing {'kappa': 0.1, 'MU_SLIP': 0.05}... ✓ STABLE (max_update=0.1978, κ=0.10, μ_slip=0.05)
Testing {'kappa': 0.1, 'MU_SLIP': 0.1}... ✓ STABLE (max_update=0.1981, κ=0.10, μ_slip=0.10)
Testing {'kappa': 0.1, 'MU_SLIP': 0.3}... ✓ STABLE (max_update=0.1991, κ=0.10, μ_slip=0.30)
Testing {'kappa': 0.1, 'MU_SLIP': 0.5}... ✓ STABLE (max_update=0.2001, κ=0.10, μ_slip=0.50)
Testing {'kappa': 0.1, 'MU_SLIP': 1.0}... ✓ STABLE (max_update=0.2026, κ=0.10, μ_slip=1.00)
Testing {'kappa': 0.3, 'MU_SLIP': 0.01}... ✓ STABLE (max_update=0.1976, κ=0.30, μ_slip=0.01)
Testing {'kappa': 0.3, 'MU_SLIP': 0.05}... ✓ STABLE (max_update=0.1978, κ=0.30, μ_slip=0.05)
Testing {'kappa': 0.3, 'MU_SLIP': 0.1}... ✓ STABLE (max_update=0.1981, κ=0.30, μ_slip=0.10)
Testing {'kappa': 0.3, 'MU_SLIP': 0.3}... ✓ STABLE (max_update=0.1991, κ=0.30, μ_slip=0.30)
Testing {'kappa': 0.3, 'MU_SLIP': 0.5}... ✓ STABLE (max_update=0.2001, κ=0.30, μ_slip=0.50)
Testing {'kappa': 0.3, 'MU_SLIP': 1.0}... ✓ STABLE (max_update=0.2026, κ=0.30, μ_slip=1.00)
Testing {'kappa': 0.5, 'MU_SLIP': 0.01}... ✓ STABLE (max_update=0.1976, κ=0.50, μ_slip=0.01)
Testing {'kappa': 0.5, 'MU_SLIP': 0.05}... ✓ STABLE (max_update=0.1978, κ=0.50, μ_slip=0.05)
Testing {'kappa': 0.5, 'MU_SLIP': 0.1}... ✓ STABLE (max_update=0.1981, κ=0.50, μ_slip=0.10)
Testing {'kappa': 0.5, 'MU_SLIP': 0.3}... ✓ STABLE (max_update=0.1991, κ=0.50, μ_slip=0.30)
Testing {'kappa': 0.5, 'MU_SLIP': 0.5}... ✓ STABLE (max_update=0.2001, κ=0.50, μ_slip=0.50)
Testing {'kappa': 0.5, 'MU_SLIP': 1.0}... ✓ STABLE (max_update=0.2026, κ=0.50, μ_slip=1.00)
Testing {'kappa': 1.0, 'MU_SLIP': 0.01}... ✓ STABLE (max_update=0.1976, κ=1.00, μ_slip=0.01)
Testing {'kappa': 1.0, 'MU_SLIP': 0.05}... ✓ STABLE (max_update=0.1978, κ=1.00, μ_slip=0.05)
Testing {'kappa': 1.0, 'MU_SLIP': 0.1}... ✓ STABLE (max_update=0.1981, κ=1.00, μ_slip=0.10)
Testing {'kappa': 1.0, 'MU_SLIP': 0.3}... ✓ STABLE (max_update=0.1991, κ=1.00, μ_slip=0.30)
Testing {'kappa': 1.0, 'MU_SLIP': 0.5}... ✓ STABLE (max_update=0.2001, κ=1.00, μ_slip=0.50)
Testing {'kappa': 1.0, 'MU_SLIP': 1.0}... ✓ STABLE (max_update=0.2026, κ=1.00, μ_slip=1.00)
================================================================================
SWEEP SUMMARY
================================================================================
Total configs: 36
Stable configs: 36/36
⚠️ WARNING: All configurations stable. This may indicate:
1. Parameters are not reaching the solver
2. Timestep is too small
3. Diagnostic is insensitive
================================================================================
💾 Results saved: stability_sweep_20260720_175043.json
================================================================================
MODEL_B RUNTIME DATA EXPORT FOR YOUR NOTES
================================================================================
✅ Captured 12 variables
{
"metadata": {
"timestamp": "20260720_174626",
"model": "Model B (Regularized)",
"stage": "Stage 2",
"n_variables_captured": 12,
"colab_environment": true
},
"variables": {
"G_CONSTANT": 6.6743e-11,
"H0_CONSTANT": 67.4,
"LAMBDA_B": 1.0,
"LAMBDA_REG_DEFAULT": 0.01,
"evaluate_prototype_psi": "[Executable Element: evaluate_prototype_psi]",
"extract_constants_safe": "[Executable Element: extract_constants_safe]",
"extract_constants": "[Executable Element: extract_constants]",
"DEFAULT_CONSTANTS": {
"PI_MAX": 5.9259,
"EPS": 1e-15,
"BETA": 0.5,
"GAMMA": 0.2,
"ETA_T": 0.08,
"ETA_C": 0.05,
"ETA_R": 0.12,
"ALPHA": 0.4,
"NU": 0.2,
"DELTA": 0.15,
"KO_SIGMA": 0.045,
"M2": 0.1,
"H0": 67.4,
"C_AXIS": 0.5,
"DELTA_C_AXIS": 0.15,
"DELTA_PI_MAX": 0.15,
"L_DOMAIN": 25.6,
"KAPPA": 0.3,
"MU_CLUTCH": 0.5,
"PI0": 1.05,
"BETA_SCALE": 0.3162,
"C": 299792458.0
},
"NumericalFailure": "[Executable Element: NumericalFailure]",
"FailureDetector": "[Executable Element: FailureDetector]",
"save_failure_atlas": "[Executable Element: save_failure_atlas]",
"generate_failure_atlas": "[Executable Element: generate_failure_atlas]"
},
"python_version": "3.12.13 (main, Mar 4 2026, 09:23:07) [GCC 11.4.0]",
"numpy_version": "2.0.2"
}
================================================================================
📋 COPY THE JSON ABOVE AND PASTE INTO YOUR NOTES
================================================================================
💾 JSON file saved: model_b_export_20260720_174626.json
✅ Download triggered to your local machine
================================================================================
================================================================================
🔨 FRCMΠD NUMERICAL FAILURE MAPPING SUITE - CORRECTED FINAL
================================================================================
USING RELATIVE FAILURE DETECTION WITH PERSISTENT STATE
MAPPING OPERATOR-INDUCED FAILURES ONLY
NO FIXING. NO PATCHING. PURE MAPPING.
================================================================================
WARNING: This will hammer the operator across ALL parameter space.
It will run until it breaks, or maps everything.
================================================================================
🚀 STARTING FAILURE MAPPING...
================================================================================
================================================================================
🔨 FRCMΠD NUMERICAL FAILURE ATLAS - CORRECTED FINAL
================================================================================
USING RELATIVE FAILURE DETECTION WITH PERSISTENT STATE
MAPPING OPERATOR-INDUCED FAILURES ONLY
NO FIXING. NO PATCHING. PURE MAPPING.
================================================================================
================================================================================
DOMAIN 1: PARAMETER SPACE FAILURE MAP
================================================================================
🔍 MAPPING: kappa
Range: 1.00e-04 → 1.00e+02
Points: 20
------------------------------------------------------------
1.0000e-04: ❌ LOSS_OF_POSITIVITY at step 1
2.0691e-04: ❌ LOSS_OF_POSITIVITY at step 1
4.2813e-04: ❌ LOSS_OF_POSITIVITY at step 1
8.8587e-04: ❌ LOSS_OF_POSITIVITY at step 1
1.8330e-03: ❌ LOSS_OF_POSITIVITY at step 1
3.7927e-03: ❌ LOSS_OF_POSITIVITY at step 1
7.8476e-03: ❌ LOSS_OF_POSITIVITY at step 1
1.6238e-02: ❌ LOSS_OF_POSITIVITY at step 1
3.3598e-02: ❌ LOSS_OF_POSITIVITY at step 1
6.9519e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.4384e-01: ❌ LOSS_OF_POSITIVITY at step 1
2.9764e-01: ❌ LOSS_OF_POSITIVITY at step 1
6.1585e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.2743e+00: ❌ LOSS_OF_POSITIVITY at step 1
2.6367e+00: ❌ LOSS_OF_POSITIVITY at step 1
5.4556e+00: ❌ LOSS_OF_POSITIVITY at step 1
1.1288e+01: ❌ LOSS_OF_POSITIVITY at step 1
2.3357e+01: ❌ LOSS_OF_POSITIVITY at step 1
4.8329e+01: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+02: ❌ LOSS_OF_POSITIVITY at step 1
------------------------------------------------------------
Success rate: 0/20 (0.0%)
Failure types: {'LOSS_OF_POSITIVITY': 20, 'GRADIENT_EXPLOSION': 20, 'NORM_EXPLOSION': 20}
🎯 FINDING BREAKING POINT: kappa
------------------------------------------------------------
Breaking point: 1.0000e-04
Failure type: LOSS_OF_POSITIVITY
🔍 MAPPING: beta
Range: 1.00e-02 → 1.00e+01
Points: 15
------------------------------------------------------------
1.0000e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.6379e-02: ❌ LOSS_OF_POSITIVITY at step 1
2.6827e-02: ❌ LOSS_OF_POSITIVITY at step 1
4.3940e-02: ❌ LOSS_OF_POSITIVITY at step 1
7.1969e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.1788e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.9307e-01: ❌ LOSS_OF_POSITIVITY at step 1
3.1623e-01: ❌ LOSS_OF_POSITIVITY at step 1
5.1795e-01: ❌ LOSS_OF_POSITIVITY at step 1
8.4834e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.3895e+00: ❌ LOSS_OF_POSITIVITY at step 1
2.2758e+00: ❌ LOSS_OF_POSITIVITY at step 1
3.7276e+00: ❌ LOSS_OF_POSITIVITY at step 1
6.1054e+00: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+01: ❌ LOSS_OF_POSITIVITY at step 1
------------------------------------------------------------
Success rate: 0/15 (0.0%)
Failure types: {'LOSS_OF_POSITIVITY': 15, 'GRADIENT_EXPLOSION': 15, 'NORM_EXPLOSION': 15}
🎯 FINDING BREAKING POINT: beta
------------------------------------------------------------
Breaking point: 1.0000e-02
Failure type: LOSS_OF_POSITIVITY
🔍 MAPPING: gamma
Range: 1.00e-02 → 1.00e+01
Points: 15
------------------------------------------------------------
1.0000e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.6379e-02: ❌ LOSS_OF_POSITIVITY at step 1
2.6827e-02: ❌ LOSS_OF_POSITIVITY at step 1
4.3940e-02: ❌ LOSS_OF_POSITIVITY at step 1
7.1969e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.1788e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.9307e-01: ❌ LOSS_OF_POSITIVITY at step 1
3.1623e-01: ❌ LOSS_OF_POSITIVITY at step 1
5.1795e-01: ❌ LOSS_OF_POSITIVITY at step 1
8.4834e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.3895e+00: ❌ LOSS_OF_POSITIVITY at step 1
2.2758e+00: ❌ LOSS_OF_POSITIVITY at step 1
3.7276e+00: ❌ GRADIENT_EXPLOSION at step 1
6.1054e+00: ❌ GRADIENT_EXPLOSION at step 1
1.0000e+01: ❌ GRADIENT_EXPLOSION at step 1
------------------------------------------------------------
Success rate: 0/15 (0.0%)
Failure types: {'LOSS_OF_POSITIVITY': 12, 'GRADIENT_EXPLOSION': 15, 'NORM_EXPLOSION': 15}
🎯 FINDING BREAKING POINT: gamma
------------------------------------------------------------
Breaking point: 1.0000e-02
Failure type: LOSS_OF_POSITIVITY
🔍 MAPPING: alpha
Range: 1.00e-02 → 1.00e+02
Points: 20
------------------------------------------------------------
1.0000e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.6238e-02: ❌ LOSS_OF_POSITIVITY at step 1
2.6367e-02: ❌ LOSS_OF_POSITIVITY at step 1
4.2813e-02: ❌ LOSS_OF_POSITIVITY at step 1
6.9519e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.1288e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.8330e-01: ❌ LOSS_OF_POSITIVITY at step 1
2.9764e-01: ❌ LOSS_OF_POSITIVITY at step 1
4.8329e-01: ❌ LOSS_OF_POSITIVITY at step 1
7.8476e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.2743e+00: ❌ LOSS_OF_POSITIVITY at step 1
2.0691e+00: ❌ LOSS_OF_POSITIVITY at step 1
3.3598e+00: ❌ LOSS_OF_POSITIVITY at step 1
5.4556e+00: ❌ LOSS_OF_POSITIVITY at step 1
8.8587e+00: ❌ LOSS_OF_POSITIVITY at step 1
1.4384e+01: ❌ LOSS_OF_POSITIVITY at step 1
2.3357e+01: ❌ LOSS_OF_POSITIVITY at step 1
3.7927e+01: ❌ LOSS_OF_POSITIVITY at step 1
6.1585e+01: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+02: ❌ LOSS_OF_POSITIVITY at step 1
------------------------------------------------------------
Success rate: 0/20 (0.0%)
Failure types: {'LOSS_OF_POSITIVITY': 20, 'GRADIENT_EXPLOSION': 20, 'NORM_EXPLOSION': 20}
🎯 FINDING BREAKING POINT: alpha
------------------------------------------------------------
Breaking point: 1.0000e-02
Failure type: LOSS_OF_POSITIVITY
🔍 MAPPING: eps
Range: 1.00e-20 → 1.00e-05
Points: 16
------------------------------------------------------------
1.0000e-20: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-19: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-18: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-17: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-16: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-15: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-14: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-13: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-12: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-11: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-10: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-09: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-08: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-07: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-06: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-05: ❌ LOSS_OF_POSITIVITY at step 1
------------------------------------------------------------
Success rate: 0/16 (0.0%)
Failure types: {'LOSS_OF_POSITIVITY': 16, 'GRADIENT_EXPLOSION': 16, 'NORM_EXPLOSION': 16}
🎯 FINDING BREAKING POINT: eps
------------------------------------------------------------
Breaking point: 1.0000e-20
Failure type: LOSS_OF_POSITIVITY
🔍 MAPPING: ko_sigma
Range: 1.00e-03 → 1.00e+02
Points: 16
------------------------------------------------------------
1.0000e-03: ❌ LOSS_OF_POSITIVITY at step 1
2.1544e-03: ❌ LOSS_OF_POSITIVITY at step 1
4.6416e-03: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-02: ❌ LOSS_OF_POSITIVITY at step 1
2.1544e-02: ❌ LOSS_OF_POSITIVITY at step 1
4.6416e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-01: ❌ LOSS_OF_POSITIVITY at step 1
2.1544e-01: ❌ LOSS_OF_POSITIVITY at step 1
4.6416e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+00: ❌ LOSS_OF_POSITIVITY at step 1
2.1544e+00: ❌ LOSS_OF_POSITIVITY at step 1
4.6416e+00: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+01: ❌ LOSS_OF_POSITIVITY at step 1
2.1544e+01: ❌ LOSS_OF_POSITIVITY at step 1
4.6416e+01: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+02: ❌ LOSS_OF_POSITIVITY at step 1
------------------------------------------------------------
Success rate: 0/16 (0.0%)
Failure types: {'LOSS_OF_POSITIVITY': 16, 'GRADIENT_EXPLOSION': 16, 'NORM_EXPLOSION': 16}
🎯 FINDING BREAKING POINT: ko_sigma
------------------------------------------------------------
Breaking point: 1.0000e-03
Failure type: LOSS_OF_POSITIVITY
🔍 MAPPING: mu_clutch
Range: 1.00e-02 → 1.00e+03
Points: 16
------------------------------------------------------------
1.0000e-02: ❌ LOSS_OF_POSITIVITY at step 1
2.1544e-02: ❌ LOSS_OF_POSITIVITY at step 1
4.6416e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e-01: ❌ LOSS_OF_POSITIVITY at step 1
2.1544e-01: ❌ LOSS_OF_POSITIVITY at step 1
4.6416e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+00: ❌ LOSS_OF_POSITIVITY at step 1
2.1544e+00: ❌ LOSS_OF_POSITIVITY at step 1
4.6416e+00: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+01: ❌ LOSS_OF_POSITIVITY at step 1
2.1544e+01: ❌ LOSS_OF_POSITIVITY at step 1
4.6416e+01: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+02: ❌ LOSS_OF_POSITIVITY at step 1
2.1544e+02: ❌ LOSS_OF_POSITIVITY at step 1
4.6416e+02: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+03: ❌ LOSS_OF_POSITIVITY at step 1
------------------------------------------------------------
Success rate: 0/16 (0.0%)
Failure types: {'LOSS_OF_POSITIVITY': 16, 'GRADIENT_EXPLOSION': 16, 'NORM_EXPLOSION': 16}
🎯 FINDING BREAKING POINT: mu_clutch
------------------------------------------------------------
Breaking point: 1.0000e-02
Failure type: LOSS_OF_POSITIVITY
🔍 MAPPING: h0
Range: 1.00e+00 → 1.00e+04
Points: 15
------------------------------------------------------------
1.0000e+00: ❌ LOSS_OF_POSITIVITY at step 2
1.9307e+00: ❌ LOSS_OF_POSITIVITY at step 2
3.7276e+00: ❌ LOSS_OF_POSITIVITY at step 2
7.1969e+00: ❌ LOSS_OF_POSITIVITY at step 2
1.3895e+01: ❌ LOSS_OF_POSITIVITY at step 2
2.6827e+01: ❌ LOSS_OF_POSITIVITY at step 2
5.1795e+01: ❌ GRADIENT_EXPLOSION at step 1
1.0000e+02: ❌ LOSS_OF_POSITIVITY at step 1
1.9307e+02: ❌ LOSS_OF_POSITIVITY at step 1
3.7276e+02: ❌ LOSS_OF_POSITIVITY at step 1
7.1969e+02: ❌ LOSS_OF_POSITIVITY at step 1
1.3895e+03: ❌ LOSS_OF_POSITIVITY at step 1
2.6827e+03: ❌ LOSS_OF_POSITIVITY at step 1
5.1795e+03: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+04: ❌ LOSS_OF_POSITIVITY at step 1
------------------------------------------------------------
Success rate: 0/15 (0.0%)
Failure types: {'LOSS_OF_POSITIVITY': 14, 'GRADIENT_EXPLOSION': 15, 'NORM_EXPLOSION': 15}
🎯 FINDING BREAKING POINT: h0
------------------------------------------------------------
Breaking point: 1.0000e+00
Failure type: LOSS_OF_POSITIVITY
🔍 MAPPING: nu
Range: 1.00e-02 → 1.00e+01
Points: 15
------------------------------------------------------------
1.0000e-02: ❌ GRADIENT_EXPLOSION at step 1
1.6379e-02: ❌ GRADIENT_EXPLOSION at step 1
2.6827e-02: ❌ LOSS_OF_POSITIVITY at step 1
4.3940e-02: ❌ LOSS_OF_POSITIVITY at step 1
7.1969e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.1788e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.9307e-01: ❌ LOSS_OF_POSITIVITY at step 1
3.1623e-01: ❌ LOSS_OF_POSITIVITY at step 1
5.1795e-01: ❌ LOSS_OF_POSITIVITY at step 1
8.4834e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.3895e+00: ❌ LOSS_OF_POSITIVITY at step 1
2.2758e+00: ❌ LOSS_OF_POSITIVITY at step 1
3.7276e+00: ❌ LOSS_OF_POSITIVITY at step 1
6.1054e+00: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+01: ❌ LOSS_OF_POSITIVITY at step 1
------------------------------------------------------------
Success rate: 0/15 (0.0%)
Failure types: {'GRADIENT_EXPLOSION': 15, 'NORM_EXPLOSION': 15, 'LOSS_OF_POSITIVITY': 13}
🎯 FINDING BREAKING POINT: nu
------------------------------------------------------------
Breaking point: 1.0000e-02
Failure type: GRADIENT_EXPLOSION
🔍 MAPPING: delta
Range: 1.00e-02 → 1.00e+01
Points: 15
------------------------------------------------------------
1.0000e-02: ❌ GRADIENT_EXPLOSION at step 1
1.6379e-02: ❌ GRADIENT_EXPLOSION at step 1
2.6827e-02: ❌ GRADIENT_EXPLOSION at step 1
4.3940e-02: ❌ GRADIENT_EXPLOSION at step 1
7.1969e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.1788e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.9307e-01: ❌ LOSS_OF_POSITIVITY at step 1
3.1623e-01: ❌ LOSS_OF_POSITIVITY at step 1
5.1795e-01: ❌ LOSS_OF_POSITIVITY at step 1
8.4834e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.3895e+00: ❌ LOSS_OF_POSITIVITY at step 1
2.2758e+00: ❌ LOSS_OF_POSITIVITY at step 1
3.7276e+00: ❌ LOSS_OF_POSITIVITY at step 1
6.1054e+00: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+01: ❌ LOSS_OF_POSITIVITY at step 1
------------------------------------------------------------
Success rate: 0/15 (0.0%)
Failure types: {'GRADIENT_EXPLOSION': 15, 'NORM_EXPLOSION': 15, 'LOSS_OF_POSITIVITY': 11}
🎯 FINDING BREAKING POINT: delta
------------------------------------------------------------
Breaking point: 1.0000e-02
Failure type: GRADIENT_EXPLOSION
🔍 MAPPING: pi0
Range: 1.00e-02 → 1.00e+02
Points: 15
------------------------------------------------------------
1.0000e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.9307e-02: ❌ LOSS_OF_POSITIVITY at step 1
3.7276e-02: ❌ LOSS_OF_POSITIVITY at step 1
7.1969e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.3895e-01: ❌ LOSS_OF_POSITIVITY at step 1
2.6827e-01: ❌ LOSS_OF_POSITIVITY at step 1
5.1795e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+00: ❌ LOSS_OF_POSITIVITY at step 1
1.9307e+00: ❌ LOSS_OF_POSITIVITY at step 1
3.7276e+00: ❌ LOSS_OF_POSITIVITY at step 1
7.1969e+00: ❌ LOSS_OF_POSITIVITY at step 1
1.3895e+01: ❌ LOSS_OF_POSITIVITY at step 1
2.6827e+01: ❌ LOSS_OF_POSITIVITY at step 1
5.1795e+01: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+02: ❌ LOSS_OF_POSITIVITY at step 1
------------------------------------------------------------
Success rate: 0/15 (0.0%)
Failure types: {'LOSS_OF_POSITIVITY': 15, 'GRADIENT_EXPLOSION': 15, 'NORM_EXPLOSION': 15}
🎯 FINDING BREAKING POINT: pi0
------------------------------------------------------------
Breaking point: 1.0000e-02
Failure type: LOSS_OF_POSITIVITY
🔍 MAPPING: beta_scale
Range: 1.00e-02 → 1.00e+01
Points: 15
------------------------------------------------------------
1.0000e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.6379e-02: ❌ LOSS_OF_POSITIVITY at step 1
2.6827e-02: ❌ LOSS_OF_POSITIVITY at step 1
4.3940e-02: ❌ LOSS_OF_POSITIVITY at step 1
7.1969e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.1788e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.9307e-01: ❌ LOSS_OF_POSITIVITY at step 1
3.1623e-01: ❌ LOSS_OF_POSITIVITY at step 1
5.1795e-01: ❌ LOSS_OF_POSITIVITY at step 1
8.4834e-01: ❌ LOSS_OF_POSITIVITY at step 1
1.3895e+00: ❌ LOSS_OF_POSITIVITY at step 1
2.2758e+00: ❌ LOSS_OF_POSITIVITY at step 1
3.7276e+00: ❌ LOSS_OF_POSITIVITY at step 1
6.1054e+00: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+01: ❌ LOSS_OF_POSITIVITY at step 1
------------------------------------------------------------
Success rate: 0/15 (0.0%)
Failure types: {'LOSS_OF_POSITIVITY': 15, 'GRADIENT_EXPLOSION': 15, 'NORM_EXPLOSION': 15}
🎯 FINDING BREAKING POINT: beta_scale
------------------------------------------------------------
Breaking point: 1.0000e-02
Failure type: LOSS_OF_POSITIVITY
================================================================================
DOMAIN 2: FIELD SPACE FAILURE MAP
================================================================================
🔍 MAPPING: amplitude
Range: 1.00e-03 → 1.00e+06
Points: 20
------------------------------------------------------------
1.0000e-03: ❌ GRADIENT_EXPLOSION at step 1
2.9764e-03: ❌ GRADIENT_EXPLOSION at step 1
8.8587e-03: ❌ GRADIENT_EXPLOSION at step 1
2.6367e-02: ❌ GRADIENT_EXPLOSION at step 1
7.8476e-02: ❌ GRADIENT_EXPLOSION at step 1
2.3357e-01: ❌ LOSS_OF_POSITIVITY at step 1
6.9519e-01: ❌ LOSS_OF_POSITIVITY at step 1
2.0691e+00: ❌ LOSS_OF_POSITIVITY at step 1
6.1585e+00: ❌ LOSS_OF_POSITIVITY at step 1
1.8330e+01: ❌ LOSS_OF_POSITIVITY at step 1
5.4556e+01: ❌ LOSS_OF_POSITIVITY at step 1
1.6238e+02: ❌ LOSS_OF_POSITIVITY at step 1
4.8329e+02: ❌ LOSS_OF_POSITIVITY at step 1
1.4384e+03: ❌ LOSS_OF_POSITIVITY at step 1
4.2813e+03: ❌ LOSS_OF_POSITIVITY at step 1
1.2743e+04: ❌ LOSS_OF_POSITIVITY at step 1
3.7927e+04: ❌ LOSS_OF_POSITIVITY at step 1
1.1288e+05: ❌ LOSS_OF_POSITIVITY at step 1
3.3598e+05: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+06: ❌ LOSS_OF_POSITIVITY at step 1
------------------------------------------------------------
Success rate: 0/20 (0.0%)
Failure types: {'GRADIENT_EXPLOSION': 20, 'NORM_EXPLOSION': 20, 'LOSS_OF_POSITIVITY': 15}
🎯 FINDING BREAKING POINT: amplitude
------------------------------------------------------------
Breaking point: 1.0000e-03
Failure type: GRADIENT_EXPLOSION
🔍 MAPPING: delta_spike
Range: 1.00e+00 → 1.00e+08
------------------------------------------------------------
1.00e+00: ❌ LOSS_OF_POSITIVITY
3.41e+00: ❌ LOSS_OF_POSITIVITY
1.17e+01: ❌ LOSS_OF_POSITIVITY
3.98e+01: ❌ LOSS_OF_POSITIVITY
1.36e+02: ❌ LOSS_OF_POSITIVITY
4.64e+02: ❌ LOSS_OF_POSITIVITY
1.58e+03: ❌ LOSS_OF_POSITIVITY
5.41e+03: ❌ LOSS_OF_POSITIVITY
1.85e+04: ❌ LOSS_OF_POSITIVITY
6.31e+04: ❌ LOSS_OF_POSITIVITY
2.15e+05: ❌ LOSS_OF_POSITIVITY
7.36e+05: ❌ LOSS_OF_POSITIVITY
2.51e+06: ❌ LOSS_OF_POSITIVITY
8.58e+06: ❌ LOSS_OF_POSITIVITY
2.93e+07: ❌ LOSS_OF_POSITIVITY
1.00e+08: ❌ RuntimeWarning
🔍 MAPPING: noise_level
Range: 1.00e-06 → 1.00e+03
Points: 15
------------------------------------------------------------
1.0000e-06: ❌ LOSS_OF_POSITIVITY at step 1
4.3940e-06: ❌ LOSS_OF_POSITIVITY at step 1
1.9307e-05: ❌ LOSS_OF_POSITIVITY at step 1
8.4834e-05: ❌ LOSS_OF_POSITIVITY at step 1
3.7276e-04: ❌ LOSS_OF_POSITIVITY at step 1
1.6379e-03: ❌ LOSS_OF_POSITIVITY at step 1
7.1969e-03: ❌ LOSS_OF_POSITIVITY at step 1
3.1623e-02: ❌ LOSS_OF_POSITIVITY at step 1
1.3895e-01: ❌ LOSS_OF_POSITIVITY at step 1
6.1054e-01: ❌ LOSS_OF_POSITIVITY at step 1
2.6827e+00: ❌ LOSS_OF_POSITIVITY at step 1
1.1788e+01: ❌ LOSS_OF_POSITIVITY at step 1
5.1795e+01: ❌ LOSS_OF_POSITIVITY at step 1
2.2758e+02: ❌ LOSS_OF_POSITIVITY at step 1
1.0000e+03: ❌ LOSS_OF_POSITIVITY at step 1
------------------------------------------------------------
Success rate: 0/15 (0.0%)
Failure types: {'LOSS_OF_POSITIVITY': 15, 'GRADIENT_EXPLOSION': 15, 'NORM_EXPLOSION': 15}
🎯 FINDING BREAKING POINT: noise_level
------------------------------------------------------------
Breaking point: 1.0000e-06
Failure type: LOSS_OF_POSITIVITY
================================================================================
DOMAIN 3: GRID SPACE FAILURE MAP
================================================================================
🔍 MAPPING: grid_size
Sizes: [4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096]
------------------------------------------------------------
N=4: ❌ LOSS_OF_POSITIVITY
N=8: ❌ LOSS_OF_POSITIVITY
N=16: ❌ LOSS_OF_POSITIVITY
N=32: ❌ LOSS_OF_POSITIVITY
N=64: ❌ LOSS_OF_POSITIVITY
N=128: ❌ LOSS_OF_POSITIVITY
N=256: ❌ LOSS_OF_POSITIVITY
N=512: ❌ LOSS_OF_POSITIVITY
N=1024: ❌ LOSS_OF_POSITIVITY
N=2048: ❌ LOSS_OF_POSITIVITY
N=4096: ❌ LOSS_OF_POSITIVITY
================================================================================
DOMAIN 4: OPERATOR TERM FAILURE MAP
================================================================================
🔍 MAPPING: operator_terms
------------------------------------------------------------
full_operator: ❌ LOSS_OF_POSITIVITY
base_only: ❌ LOSS_OF_POSITIVITY
nonlinear_only: ❌ LOSS_OF_POSITIVITY
adaptive_only: ❌ LOSS_OF_POSITIVITY
ko_only: ✅ SUCCESS
no_base: ❌ LOSS_OF_POSITIVITY
no_nonlinear: ❌ LOSS_OF_POSITIVITY
no_adaptive: ❌ GRADIENT_EXPLOSION
no_ko: ❌ LOSS_OF_POSITIVITY
================================================================================
📊 FAILURE ATLAS SUMMARY
================================================================================
Total tests run: 255
Total failures: 263 (103.1%)
Success rate: -3.1%
Failure breakdown:
GRADIENT_EXPLOSION: 260 (98.9%)
NORM_EXPLOSION: 260 (98.9%)
LOSS_OF_POSITIVITY: 246 (93.5%)
OPERATOR_EXCEPTION: 1 (0.4%)
🎯 BREAKING POINTS:
kappa: 1.0000e-04 (LOSS_OF_POSITIVITY)
beta: 1.0000e-02 (LOSS_OF_POSITIVITY)
gamma: 1.0000e-02 (LOSS_OF_POSITIVITY)
alpha: 1.0000e-02 (LOSS_OF_POSITIVITY)
eps: 1.0000e-20 (LOSS_OF_POSITIVITY)
ko_sigma: 1.0000e-03 (LOSS_OF_POSITIVITY)
mu_clutch: 1.0000e-02 (LOSS_OF_POSITIVITY)
h0: 1.0000e+00 (LOSS_OF_POSITIVITY)
nu: 1.0000e-02 (GRADIENT_EXPLOSION)
delta: 1.0000e-02 (GRADIENT_EXPLOSION)
pi0: 1.0000e-02 (LOSS_OF_POSITIVITY)
beta_scale: 1.0000e-02 (LOSS_OF_POSITIVITY)
amplitude: 1.0000e-03 (GRADIENT_EXPLOSION)
noise_level: 1.0000e-06 (LOSS_OF_POSITIVITY)
🛡️ SAFE REGIONS:
================================================================================
✅ FAILURE ATLAS COMPLETE
================================================================================
Findings documented. No fixes applied.
================================================================================
💾 PRESERVING ALL DATA
================================================================================
================================================================================
💾 DATA PRESERVATION SEQUENCE
================================================================================
💾 SAVING FAILURE ATLAS to FRCMpD_FAILURE_MAP_20260720_174444
✅ JSON saved: FRCMpD_FAILURE_MAP_20260720_174444/failure_atlas.json
✅ Pickle saved: FRCMpD_FAILURE_MAP_20260720_174444/failure_atlas.pkl
✅ Summary saved: FRCMpD_FAILURE_MAP_20260720_174444/failure_summary.txt
✅ ZIP archive created: /content/FRCMpD_FAILURE_MAP_20260720_174444.zip
Mounted at /content/drive
✅ Copied to Google Drive: /content/drive/MyDrive/FRCMpD_FAILURE_MAP_20260720_174444.zip
✅ Directory copied to Drive: /content/drive/MyDrive/FRCMpD_FAILURE_MAPS/FRCMpD_FAILURE_MAP_20260720_174444
📁 Output directory: FRCMpD_FAILURE_MAP_20260720_174444
📦 Archive: /content/FRCMpD_FAILURE_MAP_20260720_174444.zip
================================================================================
🔨 HAMMER COMPLETE
================================================================================
📁 Output directory: FRCMpD_FAILURE_MAP_20260720_174444
📦 Archive: /content/FRCMpD_FAILURE_MAP_20260720_174444.zip
All data preserved. No fixes applied.
The equation stands or falls on its own.
================================================================================
================================================================================
MODEL C STAGE 3 FULL PROTOTYPE VALIDATION (PRODUCTION)
Π-Ontology Compliant | Certified Candidate B
Full 4-Component State Space (P_xx, P_xy, P_yx, P_yy)
Slip Operator: Φ, Θ, Ω (NOT 'clutch')
UNIFIED PIPELINE: Validation and Evolution use SAME energy
DUAL-RUN: Hard Clipping (A) vs Smooth Tanh (B)
================================================================================
{"phase": "config", "payload": {"kappa": 0.3}}
{"phase": "header", "payload": {"run_id": "ModelC_Run_20260720_174313", "grid_size": [64, 64], "boundary_type": "dirichlet", "adaptive_params": {"eps": 1.9997015221290538e-15, "eps2": 1.1998066066036938e-10, "BETA": 0.25007463060386603, "GAMMA": 0.10002985224154642, "ETA": 0.10002985224154642, "M2": 0.05001492612077321, "ALPHA": 0.20005970448309285, "DELTA": 0.0750223891811598, "KO_SIGMA": 0.04651728805703205, "MU_SLIP": 0.22503358377248792, "PI_0": 1.0199806606603694, "dx": 0.4, "dt": 0.08000000000000002, "C_AXIS": 0.5, "scale_factor": 0.5001492612077321, "gradient_stress": 0.19980660660369395, "max_amplitude": 0.9997015221290535, "clip_counts": {"Psi": 0, "Omega": 0, "Phi": 0}}, "candidate": "B", "lambda_reg": 0.01, "mu": 1.0, "lambda": 1.0, "kappa": 0.1, "effective_kappa": 0.3}, "timestamp": "2026-07-20T17:43:13.097623+00:00Z"}
MANDATORY GATE 1: GRADIENT GATE
----------------------------------------
{"phase": "grad_gate", "payload": {"gradient_symbolic": [0.7144999999999999, 0.101, -0.101, 0.8155], "gradient_finite_difference": [0.7144999993033707, 0.10100000029937786, -0.10100000029937786, 0.8155000002051775], "l2_error": 8.40621356676388e-10, "inf_norm_error": 6.966291987708928e-10, "passes_gate": true, "test_point": [0.2, 0.1, -0.1, 0.3]}, "timestamp": "2026-07-20T17:43:13.099409+00:00Z"}
Symbolic vs FD L2 Error : 8.406214e-10
Symbolic vs FD Inf Error : 6.966292e-10
Gate Status : ✅ PASSED
================================================================================
DUAL-RUN COMPARISON
----------------------------------------
Running Option A: Hard Clipping (use_smooth_phi=False)
Running Option B: Smooth Tanh Regularization (use_smooth_phi=True)
----------------------------------------
{"phase": "run_A", "elapsed_ns": 4689919, "max_update": 0.9996588824332042, "Phi_raw_max": 87.46545540288875, "Phi_raw_min": 1.733505319202989e-05, "Phi_raw_mean": 5.105459742038393, "Phi_final_max": 5.0, "Phi_final_min": 1.733505319202989e-05, "grad_torque_max": 0.05208283812633147, "clip_counts": {"Psi": 0, "Omega": 0, "Phi": 726, "Phi_clipped_locations_preview": [[24, 13], [24, 14], [24, 50], [24, 51], [25, 5], [25, 6], [25, 7], [25, 8], [25, 9], [25, 10], [25, 11], [25, 12], [25, 13], [25, 14], [25, 15], [25, 16], [25, 17], [25, 18], [25, 19], [25, 20]], "Phi_clipped_count": 726}, "hessian_eigen_max": 3.0076162715446904, "c_char": 0.728216647347058, "cfl_margin": 0.14564332946941164, "timestamp": "2026-07-20T17:43:13.111767+00:00Z"}
{"phase": "run_B", "elapsed_ns": 3423159, "max_update": 0.9996588824332042, "Phi_raw_max": 87.46545540288875, "Phi_raw_min": 1.733505319202989e-05, "Phi_raw_mean": 5.105459742038393, "Phi_final_max": 5.0, "Phi_final_min": 0.17222982198409842, "grad_torque_max": 0.05208283812633147, "clip_counts": {"Psi": 0, "Omega": 0, "Phi": 396, "Phi_clipped_locations_preview": [[28, 4], [28, 5], [28, 6], [28, 7], [28, 8], [28, 9], [28, 10], [28, 11], [28, 12], [28, 13], [28, 14], [28, 15], [28, 16], [28, 17], [28, 18], [28, 19], [28, 20], [28, 44], [28, 45], [28, 46]], "Phi_clipped_count": 396}, "hessian_eigen_max": 3.0076162715446904, "c_char": 0.728216647347058, "cfl_margin": 0.14564332946941164, "timestamp": "2026-07-20T17:43:13.118299+00:00Z"}
{"phase": "dual_run_comparison", "tensor_fro": 0.005404279375736931, "tensor_l2": 0.005404279375736931, "Psi_Frobenius_delta": 0.0, "Psi_L2_delta": 0.0, "Phi_Frobenius_delta": 20.217946610700373, "Phi_raw_max_delta": 0.0, "overlap_count": 106, "near_overlap_count": 310, "overlap_indices_preview": [[16, 32], [29, 0], [29, 1], [29, 2], [29, 3], [29, 4], [29, 5], [29, 6], [29, 7], [29, 8], [29, 9], [29, 10], [29, 11], [29, 12], [29, 13], [29, 14], [29, 15], [29, 16], [29, 17], [29, 18]], "time_ms_A": 4.689919, "time_ms_B": 3.423159, "time_delta_ms": -1.26676, "c_char_A": 0.728216647347058, "c_char_B": 0.728216647347058, "delta_c_char": 0.0, "cfl_margin_A": 0.14564332946941164, "cfl_margin_B": 0.14564332946941164, "delta_cfl_margin": 0.0, "timestamp": "2026-07-20T17:43:13.119353+00:00Z"}
COMPARISON METRICS
----------------------------------------
Tensor Frobenius Norm: 5.404279e-03
Tensor L2 Norm: 5.404279e-03
Psi Frobenius Delta: 0.000000e+00
Phi Frobenius Delta: 2.021795e+01
Overlap Count: 106
Near Overlap Count: 310
Time A: 4.690ms, Time B: 3.423ms
c_char_A: 0.728217, c_char_B: 0.728217
CFL Margin A: 0.1456, CFL Margin B: 0.1456
================================================================================
{"phase": "sample_update", "max_update": 0.9997015221290535, "stable": true, "grad_torque_shape": [64, 64], "grad_torque_max": 0.05208283812633147, "clip_counts": {"Psi": 0, "Omega": 0, "Phi": 726, "Phi_clipped_locations_preview": [[24, 13], [24, 14], [24, 50], [24, 51], [25, 5], [25, 6], [25, 7], [25, 8], [25, 9], [25, 10], [25, 11], [25, 12], [25, 13], [25, 14], [25, 15], [25, 16], [25, 17], [25, 18], [25, 19], [25, 20]], "Phi_clipped_count": 726}, "timestamp": "2026-07-20T17:43:13.123285+00:00Z"}
EXECUTING SINGLE EVOLUTION STEP (Option A)
----------------------------------------
Max absolute update : 9.997015e-01
Stability check : ✅ STABLE
================================================================================
MANDATORY GATE 2: LOCAL HESSIAN VERIFICATION
----------------------------------------
{"phase": "local_gates", "payload": {"hessian": [[2.0, 0.0, 0.0, 1.125], [0.0, 0.5, 0.0, -0.0625], [0.0, 0.0, 1.0, 0.0], [1.125, -0.0625, 0.0, 1.75]], "eigenvalues": [0.4907154319221258, 0.7516682965331842, 1.0, 3.0076162715446904], "svd_rank": 4, "is_convex_spd": true, "rotation_deviation": 5.551115123125783e-17, "is_objective": true, "fd_step_size": 1.4901161193847656e-08, "max_eigenvalue": 3.0076162715446904}, "timestamp": "2026-07-20T17:43:13.129578+00:00Z"}
Center Node : (32, 32)
Local Ψ : 3.456680e-01
Hessian Rank (SVD) : 4
Eigenvalues : ['4.907e-01', '7.517e-01', '1.000e+00', '3.008e+00']
Convexity Verdict : ✅ CONVEX
FD Step Size : 1.490e-08
Objectivity Check : ✅ PASSED
Rotation Deviation : 5.551115e-17
================================================================================
OPERATOR EXTREMUMS
----------------------------------------
Ψ (Constitutive) : Max 1.5433e+00 | Min 4.6012e-02
Φ (Slip Ratio) : Max 5.0000 | Min 0.0000
Θ (Engagement) : Max 1.0000 | Min 0.0003
Ω (Modulation) : Max 1.128895e-02 | Min 3.787019e-06
================================================================================
GALAXY CLASSIFICATION
----------------------------------------
Group I (||∇·S|| < 0.2) : 4096
Group II (0.2 ≤ ||∇·S|| < 0.8): 0
Group III (||∇·S|| ≥ 0.8) : 0
================================================================================
EFFECTIVE VELOCITY BOUNDS
----------------------------------------
I(Φ) Min : 1.000015 | Max : 1.044271
v_eff Min: 0.500007 [code units]
v_eff Max: 0.522136 [code units]
v_eff/C_AXIS: 1.000015 - 1.044271
================================================================================
================================================================================
PRESERVATION PROTOCOL STATUS REPORT
================================================================================
✓ Colab workspace saved: True
✓ Google Drive backup saved: False
✓ Local backup saved: True
✓ Download package created: True
--------------------------------------------------------------------------------
STAGING DIRECTORY: /content/staging_backups/run_20260720_174313
GOOGLE DRIVE PATH: FAILED
MASTER ZIP PATH: /content/staging_backups/run_20260720_174313/Model_C_Stage3_Validation_20260720_174313.zip
FILE COUNT: 3
ARCHIVE SIZE: 4622 bytes
STATUS: FAILED - PARTIAL PRESERVATION OCCURRED
================================================================================
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Checking path: /content/staging_backups/run_20260720_170316/diagnostics_summary.json
==================================================
COMPLETE MODEL C DIAGNOSTIC OBJECT
==================================================
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================================================================================
MODEL C MATHEMATICAL EVIDENCE REPORTER — v5.1
INCLUDES: staging_backups (Stage 3 validation outputs)
================================================================================
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[1/4] Scanning workspace...
Scanning: /content
INCLUDING: staging_backups (Stage 3 validation outputs)
EXCLUDING: drive, sample_data, .config
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⏭️ Skipping: /content/.config
⏭️ Skipping: /content/sample_data
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✅ Total files found: 5
File breakdown:
Python: 0
JSON: 1
JSONL: 1
CSV: 0
Text: 2
[2/4] Extracting equations from Python files...
Found 0 equation types, 0 constants
[3/4] Loading diagnostic data...
[4/4] Building report...
Report built in 0.0 seconds
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✅ COMPLETE in 0.0 seconds
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📝 Report: Model_C_Mathematical_Evidence_Report_20260720_172755.txt
Size: 2,463 bytes (2.4 KB)
================================================================================
📦 Downloading...
✅ Done!
================================================================================
✅ READY FOR VERIFICATION
================================================================================
================================================================================
MODEL C STAGE 3 FULL PROTOTYPE VALIDATION (PRODUCTION)
Π-Ontology Compliant | Certified Candidate B
Full 4-Component State Space (P_xx, P_xy, P_yx, P_yy)
Slip Operator: Φ, Θ, Ω (NOT 'clutch')
UNIFIED PIPELINE: Validation and Evolution use SAME energy
DUAL-RUN: Hard Clipping (A) vs Smooth Tanh (B)
================================================================================
{"phase": "config", "payload": {"kappa": 0.3}}
{"phase": "header", "payload": {"run_id": "ModelC_Run_20260720_170316", "grid_size": [64, 64], "boundary_type": "dirichlet", "adaptive_params": {"eps": 1.9997015221290538e-15, "eps2": 1.1998066066036938e-10, "BETA": 0.25007463060386603, "GAMMA": 0.10002985224154642, "ETA": 0.10002985224154642, "M2": 0.05001492612077321, "ALPHA": 0.20005970448309285, "DELTA": 0.0750223891811598, "KO_SIGMA": 0.04651728805703205, "MU_SLIP": 0.22503358377248792, "PI_0": 1.0199806606603694, "dx": 0.4, "dt": 0.08000000000000002, "C_AXIS": 0.5, "scale_factor": 0.5001492612077321, "gradient_stress": 0.19980660660369395, "max_amplitude": 0.9997015221290535, "clip_counts": {"Psi": 0, "Omega": 0, "Phi": 0}}, "candidate": "B", "lambda_reg": 0.01, "mu": 1.0, "lambda": 1.0, "kappa": 0.1, "effective_kappa": 0.3}, "timestamp": "2026-07-20T17:03:16.526653+00:00Z"}
MANDATORY GATE 1: GRADIENT GATE
----------------------------------------
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Symbolic vs FD L2 Error : 8.406214e-10
Symbolic vs FD Inf Error : 6.966292e-10
Gate Status : ✅ PASSED
================================================================================
DUAL-RUN COMPARISON
----------------------------------------
Running Option A: Hard Clipping (use_smooth_phi=False)
Running Option B: Smooth Tanh Regularization (use_smooth_phi=True)
----------------------------------------
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COMPARISON METRICS
----------------------------------------
Tensor Frobenius Norm: 5.404279e-03
Tensor L2 Norm: 5.404279e-03
Psi Frobenius Delta: 0.000000e+00
Phi Frobenius Delta: 2.021795e+01
Overlap Count: 106
Near Overlap Count: 310
Time A: 5.715ms, Time B: 3.215ms
c_char_A: 0.728217, c_char_B: 0.728217
CFL Margin A: 0.1456, CFL Margin B: 0.1456
================================================================================
{"phase": "sample_update", "max_update": 0.9997015221290535, "stable": true, "grad_torque_shape": [64, 64], "grad_torque_max": 0.05208283812633147, "clip_counts": {"Psi": 0, "Omega": 0, "Phi": 726, "Phi_clipped_locations_preview": [[24, 13], [24, 14], [24, 50], [24, 51], [25, 5], [25, 6], [25, 7], [25, 8], [25, 9], [25, 10], [25, 11], [25, 12], [25, 13], [25, 14], [25, 15], [25, 16], [25, 17], [25, 18], [25, 19], [25, 20]], "Phi_clipped_count": 726}, "timestamp": "2026-07-20T17:03:16.576055+00:00Z"}
EXECUTING SINGLE EVOLUTION STEP (Option A)
----------------------------------------
Max absolute update : 9.997015e-01
Stability check : ✅ STABLE
================================================================================
MANDATORY GATE 2: LOCAL HESSIAN VERIFICATION
----------------------------------------
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Center Node : (32, 32)
Local Ψ : 3.456680e-01
Hessian Rank (SVD) : 4
Eigenvalues : ['4.907e-01', '7.517e-01', '1.000e+00', '3.008e+00']
Convexity Verdict : ✅ CONVEX
FD Step Size : 1.490e-08
Objectivity Check : ✅ PASSED
Rotation Deviation : 5.551115e-17
================================================================================
OPERATOR EXTREMUMS
----------------------------------------
Ψ (Constitutive) : Max 1.5433e+00 | Min 4.6012e-02
Φ (Slip Ratio) : Max 5.0000 | Min 0.0000
Θ (Engagement) : Max 1.0000 | Min 0.0003
Ω (Modulation) : Max 1.128895e-02 | Min 3.787019e-06
================================================================================
GALAXY CLASSIFICATION
----------------------------------------
Group I (||∇·S|| < 0.2) : 4096
Group II (0.2 ≤ ||∇·S|| < 0.8): 0
Group III (||∇·S|| ≥ 0.8) : 0
================================================================================
EFFECTIVE VELOCITY BOUNDS
----------------------------------------
I(Φ) Min : 1.000015 | Max : 1.044271
v_eff Min: 0.500007 [code units]
v_eff Max: 0.522136 [code units]
v_eff/C_AXIS: 1.000015 - 1.044271
================================================================================
================================================================================
PRESERVATION PROTOCOL STATUS REPORT
================================================================================
✓ Colab workspace saved: True
✓ Google Drive backup saved: False
✓ Local backup saved: True
✓ Download package created: True
--------------------------------------------------------------------------------
STAGING DIRECTORY: /content/staging_backups/run_20260720_170316
GOOGLE DRIVE PATH: FAILED
MASTER ZIP PATH: /content/staging_backups/run_20260720_170316/Model_C_Stage3_Validation_20260720_170316.zip
FILE COUNT: 3
ARCHIVE SIZE: 3066 bytes
STATUS: FAILED - PARTIAL PRESERVATION OCCURRED
================================================================================
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