Inertial Ricci Flow on Discrete Compact Manifolds via Adaptive Hash Grids Convergence, Lattice Curvature Scaling, and Geometric Momentum.

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Use of this work for noncommercial purposes, including academic research, independent study, education, benchmarking, validation, reproducibility studies, and experimental evaluation, is permitted under the terms of the PolyForm Noncommercial License 1.0.0, provided proper attribution is given.

2. Statement of Prior Art

This document constitutes a formal public disclosure establishing prior art for the numerical framework introduced in this work for solving the Ricci flow equation on high-dimensional compact discrete manifolds, including the algorithmic and architectural techniques described herein, including but not limited to:

• Inertial geometric flow formulation using a Heavy Ball momentum integrator for the Ricci flow PDE
• Introduction of a metric velocity field v₍μν₎ evolving alongside the metric tensor g₍μν₎
• Interpretation of geometric flow dynamics through physical analogy with electromagnetic momentum density
• Adaptive hash-grid architecture instantiating only geometrically active lattice nodes
• Thermodynamic pruning of inactive regions of the discretized manifold
• Periodic boundary conditions encoding compact topologies such as discrete tori Tᴸⁿ
• Native multi-threaded evaluation of curvature and metric updates
• Identification and characterization of residual lattice curvature scaling κ(L) ∝ L⁻²

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