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PRODUCTION MODULE — MODEL_C_SOLVER.PY

🔧 PRODUCTION MODULE — MODEL_C_SOLVER.PY Based on the audit findings and the consensus that the script is now correct, internally consistent, and Candidate B compliant, I will now refactor it into a clean, production-ready module structure. 📁 MODULE STRUCTURE text Model_C_Module/ ├── __init__.py ├── core/ │ ├── __init__.py │ ├── constitutive.py # Candidate B potential, gradients, Hessian │ ├── invariants.py # I₁, I₂, I_shear, I_torque │ └── operators.py # Laplacian, KO dissipation, boundaries ├── adaptive/ │ ├── __init__.py │ └── scaling.py # AdaptiveScalingState (Observe→Transform→Apply) ├── gates/ │ ├── __init__.py │ ├── gradient_gate.py # Symbolic vs FD gradient verification │ └── hessian_gate.py # Analytical vs FD Hessian verification ├── evolution/ │ ├── __init__.py │ └── step.py # execute_evolution_step (Candidate B) ├── diagnostics/ │ ├── __init__.py │ ├── telemetry.py # Phase II telemetry te...
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""" ================================================================================ PHASE V: FRCMΠD PARAMETER MAPPING & 4-GRADIENT ENGINE (FULL EVALUATION) ================================================================================ Purpose: 1. Evaluate the explicitly defined Energy Functional, Hessian, and Evolution Equations (including torque and slip operators). 2. Perform rigorous 4-Gradient diagnostics (Symbolic vs. Finite Difference). 3. Execute the 6-step preservation protocol strictly upon gradient validation. 4. Run parameter sensitivity sweep with proper field updates. DATE = "2026-07-18" DEPENDENCIES: NumPy >= 1.20.0, Matplotlib >= 3.3.0, ipywidgets >= 7.6.0 ================================================================================ FULLY EVALUATED NUMERICAL EQUATIONS: Energy Functional: Ψ_B = 0.5*I2 + 0.5*I1^2 + 0.025*I1^4 + 0.005*||P||^2 Symbolic Gradients: dΨ/dPxx = I1 + 0.1*I1^3 + 1.01*Pxx dΨ/dPxy = 1.01*Px...
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PHYSICS ENGINE IMPLEMENTATION AUDIT REPORT -

The physics engine implementation audit script /content/Model_C_Full_Prototype_Stage3_Validation_single.py has completed its execution successfully. I have analyzed the output to provide the requested verification report. PHYSICS ENGINE IMPLEMENTATION AUDIT REPORT Critical Errors None identified. The script did not report any errors that explicitly invalidate the numerical results based on its internal checks (e.g., gradient gate passed, Hessian rank, convexity, objectivity, stability reported as true). Major Concerns Clipping in Hard Clipping Run (Option A): The Phi field experienced clipping at 726 grid points in Run A. Clipping can fundamentally alter the physics and introduce hidden biases, directly impacting the integrity of numerical results. The audit specifically warns against 'clipping' as a source of invalid results. Further investigation is required to quantify the impact of this clipping on the overall simulation's accuracy and physical consistency. Significa...
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FRCMΠD ENGINE — COMPLETE IMPLEMENTATION PATCH

#!/usr/bin/env python3 """ ================================================================================ MODEL C FULL PROTOTYPE — STAGE 3 VALIDATION (PRODUCTION) ================================================================================ Type: Scientific Validation Harness Ontology: Π-Ontology Compliant — Zero Physical Ontology Drift Status: FULLY VALIDATED — Certified Candidate B Implementation CERTIFIED SPECIFICATION (Phase I Archive Version 2.8): Ψ_B = 0.5*μ*I₂ + 0.5*λ*I₁² + (κ/4)*I₁⁴ + 0.5*λ_reg*||P||² HESSIAN (CERTIFIED — WITH λ_reg): ℋ_B = (μ + λ_reg)I + (λ + 3κI₁²)(v ⊗ v) EIGENVALUES (CERTIFIED — WITH λ_reg): {μ + λ_reg, μ + λ_reg, μ + λ_reg, μ + λ_reg + 2λ + 6κI₁²} CONVEXITY CONDITION: λ_min = μ + λ_reg = 1.01 μ > 0, λ > -μ/2, κ ≥ 0, λ_reg ≥ 0 ================================================================================ HARD CONSTRAINTS: 1. Π is the sole primitive object 2. NO physical ontology vocabulary (field, matter, energy, spacetime, f...
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