Ψ-Time Metric Gravity (ΨTMG) Framework: A Unified Solution to the H₀ and S₈ Cosmological Tensions (v4.0.0)

ΨTMG v4. 0. 0: Unified Geometric Resolution to Cosmological Tensions — Verified Preprint The v4. 0. 0 release represents the definitive numerical and phenomenological validation of the Ψ-Time Metric Gravity (ΨTMG) framework. Moving beyond the exploratory phases of previous versions, this "Verified Preprint" edition provides a mathematically rigorous and reproducibility-audited solution to the H₀ and S₈ tensions. By implementing a purely geometric friction mechanism at late times, ΨTMG successfully reconciles the scale-dependent conflict between local gravitational-wave constraints (LIGO) and large-scale structure (LSS) requirements. This mechanism isolates the local regime—maintaining strict compatibility with General Relativity—from the cosmological regime, where metric modifications activate to bridge the gap between early-time (CMB) and late-time observations. Key Results and Statistical Validation The ΨTMG framework resolves the most persistent crises in modern cosmology by treating the gravitational coupling as a non-universal, scale-sensitive interaction. Hubble Tension (H₀): Marginalized median H₀ = 74. 18 ± 0. 82 km s⁻¹ Mpc⁻¹. Result: Natural convergence with local SH0ES measurements while strictly preserving the CMB acoustic scale anchor. Structure Growth (S₈): Marginalized median S₈ = 0. 748 ± 0. 021. The geometric friction suppresses growth at large scales, resolving the discrepancy with weak-lensing surveys (DES/KiDS). 5σ Exclusion of ΛCDM: Profile likelihood analysis demonstrates that the standard ΛCDM baseline is excluded at a confidence level exceeding 5σ. JWST Early Galaxy Formation: The framework predicts a specific "gravitational boost" (≈ 9. 05%) at z > 10 in the structure growth factor f (z), providing a physical explanation for the massive early galaxies observed by the James Webb Space Telescope. Bayesian Model Selection (The Statistical Verdict) The ΨTMG model overwhelmingly overcomes the complexity penalty (Occam's Razor) across the unified dataset. Bayesian Evidence: Δ ln 𝒵 = +40. 3 against standard ΛCDM. Interpretation: Classified as "Decisive Evidence" on the Jeffreys Scale, representing a definitive statistical preference for the ΨTMG framework. Methodological Robustness and Reproducibility Numerical Stability (Sentinel Engine): Audited at machine precision (ε < 10⁻¹⁶), ensuring zero numerical drift over 13. 8 billion years of cosmic evolution. LIGO Survival Envelope: 100, 000 Monte Carlo realizations establish a local constraint of |q₀| ≤ 10⁻⁶ for gravitational-wave phase consistency, ensuring the model's safety against multi-messenger observations. Full Reproducibility: The repository has been deep-cleansed of all local artifacts and verified for peer-cloning. All figures in the manuscript can be regenerated using the automated scripts in paper/scriptsgen/. Robustness and Falsifiability: Addressing Potential Counter-Arguments To ensure the long-term viability of the ΨTMG framework, this release explicitly addresses the most common challenges faced by modified gravity theories: Bayesian Occam’s Razor: Critics often argue that additional parameters naturally improve fits. ΨTMG addresses this by reporting Bayesian Evidence (Δ ln 𝒵 = +40. 3), which intrinsically penalizes model complexity. The preference for ΨTMG is not due to "overfitting" but to a genuine physical superior alignment with the data. The LIGO/Virgo Safety Wall: The model satisfies the strict cg = c constraints imposed by GW170817. By implementing a scale-dependent bifurcation, the local gravitational-wave phase consistency is preserved within |q₀| ≤ 10⁻⁶, while allowing for cosmological modifications. Theoretical Stability (No Ghosts): Unlike many dark energy alternatives, ΨTMG is verified to be free of ghost and Laplacian instabilities at the effective perturbative level. The geometric friction mechanism does not introduce new propagating degrees of freedom that could destabilize the vacuum. Concrete Falsifiability: The framework is not a "fit-all" theory. It makes a risky, testable prediction: a specific suppression of the growth rate fσ₈ (z) at low redshifts. Future surveys (Euclid, DESI) will either confirm this signature or falsify the model, providing a clear path for scientific verification. Installation & Execution git clone https: //github. com/JeanPhilipLalumiere/MCGT. git cd MCGT pip install -r requirements. txt python paper/scriptsgen/gen₀3ₜensionsₛummary. py Archive Contents MCGTPsiTMGᵥ4. 0. 0Preprint. pdf: The finalized 7-page research manuscript formatted for APS/RevTeX standards, featuring the 5σ resolution. MCGTPsiTMGᵥ4. 0. 0Source. zip: Audited source code, including the Sentinel perturbation engine, MCMC integration, and the /paper/scriptsgen directory. requirements. txt: Full dependency list for environment replication (camb, emcee, lalsuite, etc. ). ptmgₚredictionsᵦ0ₜoᵦ20. csv: Standardized theoretical curves detailing the 9. 05% JWST boost and density contrast evolution. Citation: Lalumière, J. -P. (2026). The ΨTMG Framework: A Unified Geometric Resolution to Cosmological Tensions (v4. 0. 0-verified). DOI: 10. 5281/zenodo. 18924465. Indexed on INSPIRE-HEP: https: //inspirehep. net/literature/3118046