We are open sourcing The Mathematical Universe
a day ago
- #Lie-groups
- #mathematics
- #fractals
- The Golden Seed Fractal is a 96-fold self-similar visualization of the Atlas of Resonance Classes.
- The Atlas of Resonance Classes is a 96-vertex graph that serves as the foundation for constructing all five exceptional Lie groups (G₂, F₄, E₆, E₇, E₈) through categorical operations.
- The Golden Seed Vector is a 96-dimensional configuration in the E₈ root system, encoding the full exceptional group hierarchy.
- The fractal exhibits unique properties: 96-fold self-similarity, fractal dimension ≈4.155, and 8-fold rotational symmetry.
- Applications span quantum computing, AI, physics, and decentralized systems, providing structured embedding spaces and symmetry frameworks.
- The project is implemented in Rust with exact arithmetic, formal verification in Lean 4, and comprehensive documentation.
- The Atlas is derived from first principles as the stationary configuration of an action functional, ensuring mathematical correctness.
- The crate is designed for rigorous peer review, with all mathematical claims verifiable from code and tests serving as formal proofs.