HGD 2.0: An Observational Hierarchy Measurement Framework

HGD 2.0 is a falsifiable observational framework designed to quantify hierarchical organization across astrophysical scales. The framework does not propose a new theory of gravity, a dark matter alternative, a dark energy model, or a unified cosmological mechanism. Instead, it investigates whether reproducible hierarchy signatures can be measured across galaxies, halos, large-scale structure, and cosmic void populations.The current implementation focuses on cosmic-void catalogues including VoidFinder (WMAP5 and Planck2018), VIDE, REVOLVER, and ΛCDM mock catalogues. Results support continuous hierarchy measures across independent catalogues and algorithms while rejecting discrete or quantized hierarchy states. The framework emphasizes operational definitions, null tests, catalogue independence, and predefined failure criteria.Current evidence supports HGD 2.0 as a conservative observational hierarchy framework and remains fully compatible with standard ΛCDM structure formation.