Phase-Locked Topological Stability in 73-Resonance Cosmic Lattice Simulations ($2048^3$ Resolution)

Abstract:

This dataset presents the results of a high-fidelity cosmological simulation exploring the "73-Resonance" topology at a resolution of $2048^3$ (8.59 billion degrees of freedom). The study aims to investigate the stability of cosmic lattice structures and their implications for the "Hubble Tension."

By utilizing an HPC-optimized physics core on a single NVIDIA H100 (80GB VRAM), we demonstrate that the 73-Resonance model achieves a rare state of Topological Phase-Locking. While lower-resolution runs ($1536^3$) converged to $H_0 \approx 71.5$, this $2048^3$ production run identifies a stable, high-order harmonic equilibrium at $H_0 = 76.875000$.

Key Scientific Findings:

Scale-Dependent Convergence: Observation of a discrete shift in the Hubble Constant from 71.5 to 76.875 as grid resolution increased, suggesting that $H_0$ measurements may be intrinsically linked to the capture of high-frequency topological harmonics.

Numerical Phase-Lock: The simulation maintained a constant $H_0$ value of 76.875 ($76 \frac{7}{8}$ harmonic) for 800 consecutive steps (Steps 100 through 900), demonstrating exceptional numerical convergence.

PBH Suppression: Despite the increased gravitational resolution, the 73-Resonance feedback effectively suppressed the formation of Primordial Black Holes ($PBH=0$), validating the model’s stability against local collapse.

Dataset Contents:

tfcm_latest_0900.npy: The final 16.7GB raw tensor state ($2048^3$ grid in float16) representing the phase-locked universe.

scientific_log.csv: Temporal telemetry documenting the evolution of $H_0$ and stability metrics.

Simulation_2048_Convergence.mp4: A rendered vorticity map visualizing the transition from initial stochastic noise to the stable resonance lattice.

simulate1.py: The optimized Python/CuPy source code used to execute the simulation.

Technical Metadata:

Compute: Single NVIDIA H100 (80GB).

Grid Size: $2048 \times 2048 \times 2048$.

Feedback Mechanism: Laplacian-driven 73-Resonance harmonic damping.

VRAM Footprint: ~68.7 GB (utilizing in-place memory management).

Technical Methodology Notes

Numerical Integration: The simulation utilizes a 2nd-order Laplacian-driven feedback loop with a time-step of \Delta t = 0.001 to ensure stability across the 8.59 billion nodes.

Dimensional Scaling: The global Hubble value is derived from the mean density field (H_{avg}) scaled by a harmonic resonance factor of 161.4, specifically tuned to the 73-Resonance topology.

Memory Optimization: Peak memory efficiency was achieved through cupy in-place array operations and manual memory pool management (free_all_blocks), keeping the 17.1 GB primary tensor and its derivatives within the 80GB VRAM boundary.