This study presents a rigorous statistical analysis of public Euclid mission (ESA) data, covering 200, 000+ objects across 21 independent sky regions. Key findings include: Systematic dimensionality reduction in observable space (effective covariance matrix rank < 4, p < 10⁻⁵). Persistent collinearity between photometric (VIS, Y, J, H) and morphological parameters (Kron radius, ellipticity), invariant across regions (Mardia’s kurtosis = 6. 47, p < 10⁻¹⁰). Significant directional anisotropy (Rayleigh test: p < 10⁻¹⁸), consistent with a primordial coherence field (s (x) ) structuring observables. Methodology: Data: ESASKY catalogs (e. g. , ESASKYENTITY₃23E6C47AB83₄D8B₉1B525977F05. csv), no arbitrary filtering. Tools: Covariance matrices, multivariate kurtosis, non-parametric tests (Rayleigh, KS). Key result: Emergence of a fifth functional dimension (coherence coordinate), directly inferred from data (no ad hoc assumptions). Implications: ΛCDM alternative: Explains anomalies (Cold Spot, MeerKAT rotating filaments, JWST early galaxies) without particle dark matter. Testable predictions: Fractal dimension D≈2D 2D≈2 for filamentary structures (validated by MeerKAT). Quadrant asymmetry (χ², p < 0. 001) in object distribution.
Michel DEBAILLEUL (Sat,) studied this question.