suplementary_black_hole_singularity

This article presents a novel framework for cosmic acceleration based on the Theory of Unified Relational Emergence (TURE). It proposes that dark energy is not a fundamental field, but an emergent consequence of structural coherence gradients in a dynamic nodal network. The paper introduces the relational parameter Λ_rel, derived from the divergence of a structural tension tensor, and shows how it drives self-sustaining expansion in a background-free network. Through a 2D simulation, the relational Hubble function H_rel(z) and dynamic equation-of-state w_rel(z) are computed and compared to real cosmological data. The results align closely with current observations, offering a falsifiable and geometrically-free explanation for dark energy within a unified relational model of the universe.