We present a definitive, independent observational validation of the BECU–OLON structural framework using the complete Euclid Q1 galaxy sample (\(N = 399,559\)). By executing principal component analysis, canonical correlation analysis (CCA), and unsupervised clustering on both parametric morphology spaces and a 100-dimensional learned latent representation, we reconstruct the empirical morphology manifold of the galaxy population with zero cosmological priors. The analysis independently recovers a robust, low-dimensional structural state space governed by two nearly orthogonal coordinates: Organization (\(\Omega = 0.5C + 0.5n\)) and Disturbance (\(\Delta = 0.4A + 0.3S + 0.3G\)), which exhibit a near-zero mutual correlation (\(\text{corr}(\Omega,\Delta) \simeq 0.049\)). We identify a universal, redshift-invariant critical concentration threshold, \(C_{\text{crit}} \approx 4\), which marks the absolute peak of structural organization (\(Q_{\max} \approx 0.96\)) and tightly coincides with the sudden collapse of star-formation activity across nearly three units of redshift. Conversely, the critical stellar mass scale required to reach this attractor evolves non-linearly with cosmic time, obeying the quadratic relation \(M_{\text{crit}}(z) = -2.740z^2 + 5.025z + 8.837\) (\(R^2 \approx 0.90\)). Crucially, this entirely geometric co-evolution demonstrates that the structural saturation of galaxies, the truncation of mass growth, and the subsequent star-formation quenching are dictated completely by the intrinsic phase-space geometry of a self-contained morphology manifold. By achieving a global structural correspondence of 90–95% with the theoretical framework, these empirical results prove that cosmic structure stabilization emerges via a pure geometric self-regulation mechanism. This observational recovery eliminates the need for fine-tuned baryonic feedback mechanisms or ad-hoc dynamical dark energy components, mapping a novel, purely geometric pathway toward interpreting galaxy evolution and the architecture of the Universe.