Complete Symbolic Verification of the Second Bianchi Identity and Kinetic Cartan Sector for Logarithmic-Spiral Tubular Wormholes in Einstein–Cartan–Maxwell Theory

This archive contains the complete symbolic materialization and verification of two central results of the accompanying paper: 1. **The Second Bianchi Identity** in the axial Einstein–Cartan specialization of the logarithmic-spiral tubular wormhole, verified explicitly on all 64 independent components in four spacetime dimensions, both symbolically (exact reduction to zero) and numerically (residual below machine precision). 2. **The Full Kinetic Cartan Equation** for propagating axial torsion in the same geometry, materialized on all 24 independent components. Both results are reproducible from the archived files using Mathematica and the xAct tensor-algebra package. --- 2. Software environment The symbolic computations were performed with: - **Wolfram Mathematica** 15.0.1 (Windows 64-bit)- **xAct** 1.3.0 (tensor-algebra suite) - xPerm 1.2.4 - xTensor 1.3.0 - xCoba 0.8.6 The archive is compatible with any Mathematica version ≥ 13.0 and any xAct version ≥ 1.2. --- 3. Directory structure Bianchi2_Complete_Component_Verification + Kinetic_Cartan_v1.0/│├── README.pdf (this file)│├── Bianchi2/ (Second Bianchi Identity)│ ├── InputForm/ 128 .txt files (64 LHS + 64 RHS)│ ├── MX/ 128 .mx files│ └── LaTeX/ 128 .tex files│└── Kinetic_Cartan/ (Kinetic Cartan Equation) ├── InputForm/ 24 .txt files └── MX/ 24 .mx files