Tensor Index Validation Notebook (SymPy + Colab)

This repository provides a symbolic tensor validation notebook that critically examines the mathematical consistency of index operations used in:

Lindgren, J. et al. (2025). "Electromagnetism as a purely geometric theory." Journal of Physics: Conference Series, 2987(1), 012001.
DOI: 10.1088/1742-6596/2987/1/012001

---

🎯 Purpose

This notebook performs reproducible symbolic tests of tensor operations used in the Weyl-based formulation proposed by Lindgren et al. (2025), as independently reviewed by Dr. Sabine Hossenfelder and formally analyzed in:

Valamontes, A. (2025). “Scientific Commentary and Symbolic Validation of Lindgren (2025).”
Demokritos Scientific Journal: Foundation of Open Physics, Vol. 1, Issue 1.

---

🔬 What It Does

• Constructs symbolic tensor expressions using sympy.tensor.tensor
• Validates Einstein summation convention and index uniqueness
• Flags repeated dummy indices and invalid free-bound contractions
• Tests vector division and null geodesic logic
• Reproduces failure cases from Equations 25 and 36 in the Lindgren paper

---

📂 Repository Contents

• tensor_validation.ipynb — Main Colab-ready Jupyter notebook
• screenshots/ — Output screenshots for reproducibility
• references.bib — BibTeX entries for all cited sources
• .CITATION.cff — Citation metadata for Zenodo and GitHub
• README.md — This file

---

🚀 Run the Notebook

You can open and run the notebook directly in Google Colab:

---

📘 Citation

If you use this repository in academic or scientific work, please cite:

Valamontes, A. (2025).
Tensor Index Validation Notebook (SymPy + Colab).
Zenodo. https://doi.org/10.5281/zenodo.15335886

@software{valamontes_tensor_validation_2025,
  author       = {Valamontes, A.},
  title        = {Tensor Index Validation Notebook (SymPy + Colab)},
  year         = 2025,
  publisher    = {Kapodistian Academy of Science},
  doi          = {10.5281/zenodo.15335886},
  url          = {https://github.com/Galactic-Code-Developers/Tensor-Index-Validation-Lindgren2025}
}