BECU–OLON V21: A Hidden Structural Order Governs Galaxy Populations — Evidence from Euclid

This work presents an independent observational test of the structural-manifold framework introduced in BECU–OLON V20 using the Euclid Q1 physical-parameter catalogue. A principal-component analysis of approximately 4 × 10⁵ galaxies reveals that the Euclid galaxy population occupies a low-dimensional structural organization space dominated by a compactness axis (PC1) and a disturbance axis (PC2). The dominant coordinate is strongly associated with concentration, Sérsic structure, stellar mass, and centralization, defining a continuous sequence extending from diffuse to compact systems. A second independent coordinate traces morphological disturbance through asymmetry, smoothness, and structural irregularity. Together, these coordinates define a two-dimensional structural state space capturing the majority of the observed organization. Cross-matching with the Euclid merger catalogue demonstrates that merger activity increases monotonically along the dominant structural axis, with receiver-operating-characteristic analysis yielding AUC ≈ 0. 841. Ten-fold cross-validation confirms the stability of the relation. The results provide independent observational evidence that morphology, compactness, stellar-mass assembly, merger activity, and structural disturbance are organized within a common low-dimensional framework. This work extends the structural-manifold interpretation of galaxy populations and supports the broader interpretation of the structural-gradient formalism as a generalized information-gradient framework. ``