Geometric Origin of Redshift and Hubble Acceleration in the Boukarroum Framework

This record introduces the Boukarroum Equation, a geometric framework for cosmic dynamics based on discrete energy points and an invariant temporal dimension. The core relation of the model is written explicitly as: T² = L² + V² where: T is the invariant temporal coordinate, L represents the geometric separation between energy points, V denotes orbital motion. In this framework, time does not expand and the global size of the universe remains fixed. Apparent cosmic expansion, redshift, and accelerated Hubble flow emerge from geometric redistribution (repulsion) of energy points relative to a fixed background, not from metric expansion of spacetime. The attached figure illustrates: A fixed cosmic radius acting as a stable background, Radial flow of energy points from a central origin, Redshift arising from changing geometric positions relative to the background, Linear Hubble behavior followed by apparent acceleration generated purely by geometric repulsion. The accompanying LaTeX source formalizes the theory, including Corollary 137, which defines photon dynamical stability and its role in cosmic structure formation, offering an alternative interpretation to ΛCDM without invoking dark matter or vacuum energy. Included files: Boukarroum_Geometric_Cosmic_Flow.png — high-resolution conceptual diagram. Geometric_Energy_Dynamics_Boukarroum.tex — complete LaTeX source of the model.