BEYOND THE $\Lambda$CDM PARADOX: RESOLVING THE $H_0$ AND $S_8$ TENSIONS AND EARLY COSMIC MASS ASSEMBLY THROUGH GEOMETRIC PRESSURE GRADIENTS

The standard cosmological model ($\Lambda$CDM) is facing a critical crossroads marked by severe observational discrepancies: the persistent $5\sigma$ Hubble tension ($H_0$), the structure growth rate anomaly ($S_8$), and the unexpected presence of massive galaxies and supermassive black holes at high redshifts ($z > 10$) revealed by the James Webb Space Telescope (JWST). Conventional resolutions typically introduce additional unobservable degrees of freedom—such as early dark energy, sterile neutrinos, or decaying dark matter—adding theoretical constructs to an increasingly rigid framework. In this work, completing the four-part cosmological framework established in Papers 19, XX, and XXI, we demonstrate that these three anomalies are not independent physical crises, but the natural consequence of a single underlying oversight: the assumption of strict scale-invariance in the cosmic expansion background. By formulating the cosmic metric in terms of continuous geometric pressure gradients without non-baryonic dark matter particles ($T_{\mu\nu}^{\text{dark}} \equiv 0$), we show that the local vacuum expansion rate and the asymptotic early-universe horizon represent distinct hydrodynamic regimes of the same manifold. The measured $8.4\%$ local expansion offset strictly governs a $7.9\%$ suppression in late-time structure growth ($S_8$) without free fitting parameters, while simultaneously shortening the baryonic Jeans collapse timescale in the early epoch. The model fully reproduces current observational constraints from Planck, SH0ES, DES, and JWST from first principles.