Statistical Evidence for a Fifth Functional Dimension in Cosmology: Analysis of 21 Independent Euclid Regions (N>200,000 Objects) and Validation of the DEBA Model

This study presents a systematic analysis of Euclid public data (ESA Sky portal, 21 independent regions, >200,000 objects), revealing empirical evidence for a fifth functional dimension—coherence—as the physical basis for dark matter and dark energy. Dark matter is interpreted as spatial coherence patterns (s(x)s(x)s(x)), while dark energy acts as the counterbalancing tension maintaining coherence against cosmic expansion. Key findings include: Dimensional reduction (covariance matrix rank