A Unified Geometric Theory from the Symmetry of GL(4,C)

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Abstract

We present a complete and self-consistent framework for the unification of all fundamental forces, matter, and the cosmological sectors of the universe derived from the symmetry of a 4-dimensional complex spacetime (GL(4,C)). To preserve unitarity and ensure the theory is entirely free of ghosts (negative-norm states), we enforce a physical stratification based on a Cartan decomposition. We demonstrate that the spontaneous symmetry breaking at the Big Bang (GL(4,C) -> U(4)) initiates a "Radiative Waterfall" that deterministically derives all physical constants—including the Higgs mass (125.190 +/- 0.032 GeV) and the top quark mass (172.68 +/- 0.22 GeV)—with sub-percent accuracy. Crucially, the framework provides a zero-parameter resolution to current cosmological tensions through first-principles predictions rather than phenomenological fits. The theory identifies the dark sector as a structural requirement of the GL(4,C) manifold, predicting the existence of Cosmic Threads as 1-dimensional topological solitons of shear that form the macroscopic scaffolding of the universe. These structures are mathematical necessities of the 10-5-1 partition of the coset GL(4,C)/U(4) and align with the structural ordering and "scaffolding" observed in the 2026 COSMOS-Webb high-resolution mapping. The dark sector is further resolved into a dual-natured system that is simultaneously attractive and repulsive, comprising an ultra-light dark scalar (m_phi approx 2.3 meV) and a massive dark vector (m_Omega approx 332 MeV). The scalar mediates long-range attraction for web formation, while the vector’s "geometric stiffness" generates short-range repulsion to resolve the galactic core-cusp problem. Finally, the model analytically derives an interaction constant beta = 3/(128pi) approx 0.00746 (corresponding to xi approx 0.0225) governing energy transfer between dark energy and dark matter. This prediction resolves the 5-sigma Hubble tension (H_0 approx 72.8 +/- 0.7 km/s/Mpc) and the S_8 structure tension (S_8 approx 0.764), providing a rigorous geometric foundation for the evolving dark energy signatures recently reported by the DESI collaboration.

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