Unifying the Hubble Expansion: The Manifold Scroll Hypothesis (MSH) v4.0 - A High-Precision Geometric Solution to the H₀ Tension with Peculiar Velocity Integration

The discrepancy between early-universe and late-universe measurements of the Hubble constant, known as the "Hubble Tension," has reached a significance of >5σ. This paper presents the definitive formulation of the Manifold Scroll Hypothesis (MSH) v4.0. We propose that the universe operates as a layered manifold unwinding anisotropically. By introducing a position-dependent expansion metric H(z, RA, Dec) and integrating local peculiar velocity corrections (γ = 0.92), we eliminate the systemic residuals found in the ΛCDM model. Testing against a catalog of 200 galaxies, the MSH v4.0 achieves an unprecedented mean absolute error (MAE) of 0.68 km/s/Mpc, providing a seamless bridge from the Planck base (67.36) to the local SH0ES measurements (73.04).