A Geometric Resolution to the Hubble Tension: The Extended Stretched Singularity Framework (A Zero-Free-Parameter Unification Theory)

Description / Abstract: This monograph presents the Extended Stretched Singularity Framework (ESSF), a zero-free-parameter geometric unification theory that resolves the Hubble tension, the cosmological constant problem, and the origin of fundamental particle masses. While the framework is anchored by its precise resolution of the 5 Hubble tension—deriving a vacuum refractive index of n = 1. 0838 to seamlessly reconcile early-universe CMB and late-universe supernovae measurements—it is fundamentally a comprehensive unified field theory. The ESSF postulates that the vacuum is a physical, elastic, electromagnetic medium: a 12-arm Beltrami lattice organised into a dual-phase Weaire-Phelan geometry. By replacing abstract fields with discrete biphasic lattice gauge dynamics, the framework unites Quantum Field Theory (QFT) and General Relativity through a single deterministic structure, achieving strict consilience across 41 orders of magnitude. Key theoretical breakthroughs detailed in this full monograph include: Particle Physics & QFT: Exact topological derivations of the Higgs boson mass (125. 08 GeV), the fine structure constant (^-1 = 137. 036), the lepton mass hierarchy, and the strong and weak coupling constants. It maps standard QFT renormalisation to finite geometric vacuum polarisation limits. Cosmology & Relativity: First-principles geometric derivations of the speed of light (c) and Newton's gravitational constant (G), identifying Dark Matter as the kinetic displacement of the vacuum and Dark Energy as its static compliant volume fraction. Quantum Foundations: A structural resolution to wave-particle duality and quantum non-locality, demonstrating how the arrow of time emerges as the discrete thermodynamic exhaust (neutrinos) of topological defects (baryons) rotating within the lattice. Ultimately, this framework demonstrates that the constants of nature are not arbitrary empirical inputs, but the conjugate, deterministic signatures of a single invariant lattice geometry, resolving major cosmological and quantum tensions without invoking new fundamental particles, dark fluids, or tuned parameters.