Absolute Cosmic Geometry: First-Principles Derivation of 5D Topological Self-Acceleration and the Exact Resolution of the Hubble H0 Tension

### الملكية الفكرية وإشعار الأولوية العلمية © 2026 Saif M. Al-Muazzab. All Rights Reserved. This repository serves as an official timestamped deposition securing the Intellectual Property (IP), mathematical derivations, and 10 falsifiable observational predictions authored by Saif M. Al-Muazzab regarding the 5D Topological Self-Acceleration Framework (Absolute Cosmic Geometry). --- ### KEY MATHEMATICAL & THEORETICAL INNOVATIONS (Protected IP): 1. First-principles projection of the 5D Einstein-Gauss-Bonnet (EGB) bulk action onto a 4D FLRW brane via Gauss-Codazzi-Mainardi formalism and generalized Myers-Davis junction conditions. 2. Derivation of the exact non-linear modified Friedmann equation: H² (1 + 4/3 α̂ H²) ² = (κ₅² / 6 ρ +. . . ) ² 3. Analytical derivation of the late-time geometric boost factor δGB (z), resolving the 5σ Hubble tension (H0 = 73. 12 ± 0. 68 km/s/Mpc) without modifying the sound horizon (rs = 147. 09 Mpc). --- ### TEN FALSIFIABLE OBSERVATIONAL PREDICTIONS (Scientific Priority Claim): 1. Exact Local Hubble: Permanent convergence at H0 = 73. 12 ± 0. 68 km/s/Mpc. 2. Transition Redshift: Topological boost derivative zₜrans = 0. 85 ± 0. 05. 3. Invariant Sound Horizon: Strictly fixed at rs = 147. 09 ± 0. 26 Mpc. 4. Tensor Velocity: Local cT = c, with Weyl phase shift ΔcT/c 2. 5. Ghost-Free Phantom Crossing: Effective equation of state wₑff (z) dynamically crosses -1 via geometry. 6. Simultaneous S8 Resolution: Growth suppression yielding σ8 = 0. 762 ± 0. 008. 7. LSST+Euclid Constraints: Cosmic shear Cₗ^ (γγ) 4. 2σ geometric deviation at l > 1500. 8. JWST High-z Overdensities: Growth factor D (z) enhanced by 12–15% at z > 7. 9. Weyl Dark Radiation: Bulk integration bounds ΔNₑff ≤ 0. 035 (CMB-S4 target). 10. Fundamental Coupling: EGB coupling constant α̂ = 0. 0412 ± 0. 0035. Author: Saif M. Al-Muazzab (Independent Researcher, Cosmology and Astrophysics, Sana'a, Yemen). License: Creative Commons Attribution 4. 0 International (CC BY 4. 0) - Citation required upon use. The persistent 5σ tension between early-universe inferences of the Hubble constant (H0) and late-universe local measurements signifies a fundamental failure of the four-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) paradigm. In this comprehensive treatise, we demonstrate from first epistemological principles that the H0 discrepancy is a direct manifestation of 5D topological boundary dynamics. By projecting the 5D Riemann tensor via the complete Gauss-Codazzi-Mainardi formalism and applying exact generalized Myers-Davis junction conditions, we derive the exact, non-linear modified Friedmann equation from the Einstein-Gauss-Bonnet (EGB) action. The topological self-acceleration branch induces a late-time geometric deformation δGB (z) that elevates the local H0 to 73. 12 km s⁻¹ Mpc⁻¹ while strictly preserving the comoving sound horizon rs. A joint MCMC analysis of Planck 2018, DESI 2024 BAO, and local distance ladder data confirms the complete resolution of the tension. We formulate ten stringent observational predictions, including combined LSST+Euclid cosmic shear constraints, offering a definitive geometric solution to the H0 crisis.