*Resolving the Hubble Tension and Growth Dynamics via the TCU V9 Metric: Joint Analysis of SN Ia (Pantheon+) and eBOSS DR16 (BAO+RSD)*

📝 Work Summary (Description)This repository contains the numerical implementation and empirical validation of the ΛUTCU (Universal Cosmic Transfer Unit) model. This study presents a consistent solution to the "Hubble Tension" by introducing a dynamic phase-exchange metric, simultaneously validated against the most restrictive late-universe probes. ✅ What does this work do?Kinetic and Dynamic Unification: Unlike models that only fit expansion history, this work validates the TCU V9 metric in both the geometric sector (BAO) and the structure growth sector (RSD - fσ 8). High-Fidelity Data Integration: Pantheon+ (SN Ia): Integration of 1,701 supernovae using the Full Covariance Matrix (1701×1701), accounting for both systematic and statistical uncertainties. SDSS eBOSS DR16 (BAO+RSD): Utilization of the "Full Shape" likelihood (DMDHfs8) following the recommendations of Alam et al. (2020), including data from MGS, BOSS DR12, and eBOSS DR16 (LRG and QSO). Tension Resolution: Identifies a convergence value of H ∞ ≈65.23 km/s/Mpc, reconciling the discrepancy between local distance ladder measurements and Cosmic Microwave Background (CMB) global estimates. Robust Inference: Implements a Bayesian Inference (MCMC) engine and L-BFGS-B optimization to ensure that the obtained parameters (H ∞,ω,Ω m0,γ,A) represent a true global minimum. ❌ What does this work NOT do?It is not an empirical curve-fitting exercise; it is a formal resolution of Growth Differential Equations under a non-local metric. It does not modify General Relativity; instead, it proposes a dynamic energy source based on a fundamental phase frequency (ω=0.1594 Hz). It does not rely on simple linear growth approximations; it integrates the evolution of perturbations to compare them directly with RSD data. 📊 File ContentsUpon downloading this repository, researchers will find: Untitled415.ipynb: The Python source code (Jupyter Notebook) containing the full pipeline, from the loading of SDSS and Pantheon+ covariance matrices to the MCMC execution. README.md: Technical guide for installation and execution. Validation Images: Corner Plot: Visualization of the convergence and correlation of the model's 7 parameters. μ vs z Fit: Model comparison against the 1,701 SN from Pantheon+. Residual Analysis: Demonstration of stochastic consistency (white noise) in the fit. Structural Growth: fσ 8 plot showing congruence with eBOSS data. 🛠️ Technical Details for the ReviewerBackground Model: ΛUTCU with local mass coupling. Density Parameter: Ω m0 ≈0.366 (obtained via convergence). Critical Frequency: 0.1594 Hz (Universal parameter of the "Reality without Patches" project). Software Stack: Python 3.x, emcee, scipy.integrate, numpy.linalg. ⚖️ License and CitationThis work is distributed under the Creative Commons Attribution 4.0 International license. We kindly request that you cite this DOI when using the TCU V9 model in derivative research concerning the Hubble tension or dynamic dark energy.