DIMENSIONAL COSMOGENESIS: The Origin of the Universe as a Geometric Phase Transition

We present a comprehensive mathematical framework for the origin of the universe within Ferreyra Dimensional Mechanics (FDM), wherein the cosmos emerges not from a singular explosive event but through a geometric phase transition from a primordial two-dimensional state (Dₑff = 2.0) to the observed quasi-three-dimensional structure (Dₑff ≈ 2.414). This transition, driven by quantum vacuum fluctuations acting upon the intrinsic geometric tension characterized by the Ferreyra Constant (ΦF = √2 - 1 ≈ 0.414213562), produces an apparent "Big Bang" as a secondary phenomenological consequence rather than a fundamental mechanism. We derive the complete mathematical structure of this dimensional nucleation process, demonstrate its consistency with observational cosmology, eliminate the need for cosmic inflation, resolve the horizon and flatness problems through geometric necessity, and provide seventeen falsifiable predictions including novel CMB signatures, large-scale topological constraints, and distance-dependent violations of cosmological isotropy. This framework eliminates singularities, unifies the treatment of dark matter and dark energy as manifestations of dimensional gradients, and establishes the universe as fundamentally a deformed two-dimensional manifold embedded in higher-dimensional space. The theory is fully self-contained, mathematically rigorous, and immediately testable with existing and near-future observational facilities.