Numerical Verification of the 73.04 km/s/Mpc Resonant Lock in the Topological-Fluid Cosmological Model (TFCM)

Description This repository provides the theoretical foundation and computational proof for the Topological-Fluid Cosmological Model (TFCM), a visco-elastic successor to the standard $\Lambda$CDM paradigm. The model addresses the current epistemological crisis in precision cosmology by treating the universe as a dynamic, visco-elastic fluid governed by non-equilibrium thermodynamics and quantized topological transitions. The provided datasets and source code demonstrate a stable numerical resolution to the Hubble Tension, achieving a consistent "Resonant Lock" of the expansion rate ($H_0$) at a centroid of 73.04 km/s/Mpc. The simulation, executed on consumer-grade CUDA hardware (NVIDIA RTX 3070), confirms the structural integrity of the manifold across 5,000 time steps without numerical divergence or boundary reflections. One-Click Verification (Peer Review Access): Primary 3D Simulation ($448^3$): [https://colab.research.google.com/drive/1S4ackhe417F0dVdXwuTW3YDIhC8HbqOs?usp=sharing] Direct cloud execution to replicate the $H_0$: 73.04 km/s/Mpc resonant lock. High-Resolution 2D Audit ($8192^2$): [https://colab.research.google.com/drive/12uJICb3FfiTgqQkZHQtcN8ImaoQySIMC?usp=sharing] Verifies algorithmic efficiency and the 73.04 km/s/Mpc "Resonant Lock" at ultra-fine grain (~67M voxels). Verification Note: The consistency of the 73.04 km/s/Mpc centroid across both 3D volumetric and 2D ultra-high-resolution (8K) environments confirms the scale-invariance and dimensional-robustness of the TFCM framework. Hardware Execution Audit (Video): [https://doi.org/10.5281/zenodo.19746455] A forensic video trace documenting the simulation running on an NVIDIA RTX 3070 with local CMD-level telemetry. High-Performance Computing (HPC) Validation: TFCM 1024³ Grand Challenge Simulation: [ TFCM 1024³ Computational Physics Engine & Reproducibility Lab ] Scale: 1.07 Billion active voxels. Hardware: Executed on NVIDIA H100 (80GB VRAM) infrastructure. Discovery: Confirms that the 73.04 km/s/Mpc "Resonant Lock" remains invariant at the billion-cell limit, demonstrating absolute numerical stability and the elimination of sub-grid dissipation artifacts. Full Theoretical & Empirical Validation For the exhaustive mathematical derivation of the TFCM framework and the cross-scale validation against 2026 HL-LHC/ALICE and DESI datasets, please refer to the primary repository: 👉 Full Theory & Data Validation: https://doi.org/10.5281/zenodo.19828308 Note to Researchers: This link contains the macroscopic evidence for the Hubble Tension resolution and the microscopic proof of topological tension in quark-gluon plasma, providing the "Theory of Everything" context for the $1024^3$ raw data. Key Scientific Contributions: Resolution of the $H_0$ Tension: Recalibration of the sound horizon via non-equilibrium thermodynamic turbulence and bulk viscosity ($\zeta$). DESI Phantom Crossing ($w < -1$): Mathematically derived as a hydrodynamic signature of metric-substrate surface tension, eliminating the requirement for ad-hoc ghost fields. Dark Matter Identity & $S_8$ Discrepancy: Dark matter is characterized as a granular phase-transition residue (primordial black hole seeds), providing a physical mechanism for the clustering amplitude observed in DES Y6 and NANOGrav data. Metric Continuity: Implementation of non-linear density-threshold surgery to circumvent classical singularities and preserve manifold rigidity during the quantum bounce. Dataset Manifest: 2026-04-04_TFCM_Preprint_Hamieh_v1.0.0.pdf: Primary theoretical framework and empirical synthesis. TFCM_Axiomatic_Computational_Framework.pdf: Formalized mathematical axioms and tensor mechanics. TFCM_Empirical_Data_Validation_Analysis.pdf: Comparative study against DESI, Euclid, and NANOGrav datasets. TFCM_Simulation_Architecture_Technical_Specs.pdf: Computational specifications and Israel-Stewart causal hydrodynamics implementation. TFCM_model.py: GPU-accelerated Eulerian fluid simulation (Python/CuPy). TFCM_Simulation_Telemetry_Log.txt: Raw audit trail documenting the 5,000-step resonant lock stability. TFCM_448_Manifold_Visualization.mp4: Volumetric projection of large-scale structure crystallization. Computational Efficiency & Scalability: Hardware-Agnostic Robustness: The TFCM architecture is optimized for high-performance execution on consumer-grade hardware. By achieving numerical convergence at a $448^3$ resolution (~90M voxels), the model demonstrates that the $H_0$ resonant lock is an inherent topological property of the visco-elastic equations, rather than an artifact of ultra-high-resolution dissipation. VRAM Optimization: The simulation utilizes aggressive memory management (toggling between Eulerian density grids and spectral transforms) to maintain a peak memory footprint under 8GB, making the discovery accessible for independent peer-audit without supercomputing resources. Linear Complexity: The algorithm exhibits $O(N \log N)$ scaling, ensuring that the theoretical framework is prepared for future $1024^3$ and $2048^3$ "Grand Challenge" simulations on A100/H100 cloud infrastructure. Technical Specifications: Grid Resolution: $448^3$ (approximately 90 million active voxels). Hardware: NVIDIA RTX 3070 (8GB VRAM). Software Requirements: Python 3.13, CuPy, NumPy, OpenCV, ImageIO.