Resonant Spacetime Hypothesis 2.0

1. Quantum Gravity Simulations 

- Objective: Derive spacetime eigenmodes from first principles (e.g., loop quantum gravity or string theory compactifications).  

- Methods:  

- Tensor Networks: Simulate holographic boundary conditions using MERA (Multiscale Entanglement Renormalization Ansatz).  

- Quantum Graphity: Model fractal spacetime as a dynamical spin network with emergent eigenmodes.  

- Expected Outcome: Rigorous link between Planck-scale quantum geometry and cosmic-scale resonances.  

2. Fractal Spacetime Numerics 

- Objective: Solve the fractal Helmholtz equation at Planckian resolution.  

- Methods:  

- GPU-Accelerated PDE Solvers: Adaptive mesh refinement for \( \Delta_F \psi_n = \lambda_n \psi_n \) on Sierpiski-like 3-manifolds.  

- Lattice QFT: Discretize spacetime with Hausdorff measure \( d\mu \propto r^{D-3} dr \).