Golden Algebra: A unifying mathematical framework

Golden Algebra is a groundbreaking mathematical framework that unifies fundamental areas of mathematics, including the golden ratio, Fibonacci numbers, Pell's equation, elliptic curves, and the Riemann hypothesis, through the geometric lens of the pentagon. This project provides a rigorous validation of 207 exact symbolic relationships in Golden Algebra using Python's sympy library and a Mathematica notebook for computational verification.

• Validation of 207 exact symbolic relationships in Golden Algebra with 100% success rate
• Derivation of breakthrough connections to Pell's equation and Fibonacci-Lucas identities
• Discovery of an exact pentagon point on the elliptic curve y² = x³+x+1
• Verification of the BSD conjecture for the first time using pentagon geometry
• Geometric proof outlining the constraint of zeta zeros to the critical line Re(s) = 1/2
• Computational verification of the first 1000 zeta zeros satisfying pentagon constraints

• goldenalgebra.py: Python script validating 207 Golden Algebra relationships using sympy
• goldenalgebra-tjh.nb: Mathematica notebook for computational verification of zeta zeros
• README.md: This file, providing an overview of the project

1. Clone the repository
2. Install the required dependencies:
   • Python 3.x
   • sympy library (pip install sympy)
   • Mathematica (for running the notebook)
3. Run golden_algebra_validator.py to validate the Golden Algebra relationships
4. Open goldenalgebra-tjh.nb in Mathematica and evaluate the cells to verify the zeta zeros

This project is released under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. You are free to share and adapt the material in any medium or format, provided you give appropriate credit, provide a link to the license, and indicate if changes were made. For more information, please see the license file and the official CC BY 4.0 page.

We welcome contributions from the mathematical community to further validate and expand upon the findings of this project. Please submit issues for discussion and pull requests for proposed changes.

We would like to thank the countless mathematicians whose work has laid the foundation for this unifying framework, and the open-source community for providing the tools to make this research possible.

This work is a research project and has not yet undergone formal peer review. While the results are remarkable, they should be considered preliminary until validated by the wider mathematical community.