Visual Evidence of Geometric Phonons and Inertial Ricci Flow on 10D Discrete Compact Manifolds (L=32)
Abstract
This dataset provides the foundational visual evidence and spatial heatmaps documenting the discovery of lattice resonance (geometric phonons) and the "discrete Ricci floor" within 10-dimensional compact manifolds. The figures are derived from a custom C++ high-performance implementation of Inertial Geometric Flow, utilizing an adaptive Heavy Ball integrator and Multigrid prolongation operators (L=16 to L=32). The collection includes: Temporal Oscillation & FFT Spectrum: Demonstrating sustained harmonic oscillation (ringing) of the metric tensor at the discrete Regge curvature limit, featuring a perfect period of 80 steps. Spatial 2D FFT (The Bragg Cross): A macroscopic crystallographic view of the discrete spacetime tissue, revealing a distinct cross-shaped interference pattern where wave vectors align strictly with the principal axes of the periodic torus (T^4). Multigrid Convergence Scaling: Showcasing the drastic computational reduction achieved via nested lattice interpolation (warm start) and the physical barrier of numerical discretization. Español: Este conjunto de datos proporciona la evidencia visual fundamental y los mapas de calor espaciales que documentan el descubrimiento de la resonancia de red (fonones geométricos) y el "piso discreto de Ricci" en variedades compactas de 10 dimensiones. Las figuras provienen de una simulación de alto rendimiento en C++ de Flujo Geométrico Inercial, utilizando métodos Multigrid (escalado de L=16 a L=32). Incluye el patrón de interferencia espacial 2D (Cruz de Bragg) que confirma la alineación de los vectores de onda de perturbación métrica con los ejes principales del toroide discreto.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Noncommutative and Quantum Gravity Theories
Publication details
- Journal / source
- Figshare
- Publication date
- 8 March 2026
- Language
- EN