Effective Cosmic Acceleration from a Recursive Geometric Expansion: An Observational Formulation within the Unified Model of Creation and Reality (UMCR)

The observed acceleration of the Universe is one of the deepest open problems in modern cosmology. The standard answer, dark energy, works phenomenologically, but introduces more questions than it resolves: what is it, why does it have the value it has, and why now? This paper proposes a different path. Within the Unified Model of Creation and Reality (UMCR), cosmic acceleration is not something added to the equations, it emerges naturally from the recursive geometric structure of spacetime itself. No new fields, no exotic fluids, no cosmological constant. The geometry does the work. An effective expansion law is derived, from which the deceleration parameter follows directly. When the geometric parameter kβ exceeds 1, as the data independently confirm, the model predicts accelerated expansion as a pure geometric consequence. The best-fit value obtained from Type Ia supernova observations is kβ = 1.327, the same dimensionless constant that governs the recursive architecture of spacetime throughout the broader UMCR framework. The model is fully falsifiable and tested against real observational data, yielding excellent agreement with the Pantheon+SH0ES supernova compilation. This work establishes the observational foundation of the UMCR and opens the door to its application in structure formation and gravitational phenomenology.