Discrete Riemannian Geometry Framework

Key Features

1. Discrete Riemannian Geometry Core

   • Angle defect curvature computations
   • Dual volume calculations
   • Discrete Ricci flow implementation

2. Theoretical Proofs

   • Discrete Gauss-Bonnet-Chern theorem (nD)
   • Exotic sphere obstruction theory
   • Convergence to Alexandrov spaces

3. Physics Applications

   • Gravitational wave detection (LIGO)
   • String vacua classification
   • SYZ mirror construction
   • Quantum gravity framework

4. Experimental Validation

   • LIGO GW230529 analysis
   • 14,000 F-theory vacua classification
   • Exotic sphere database

Installation

git clone https://github.com/Nrutseab/DiscreteGBC.git
cd DiscreteGBC
pip install -r requirements.txt