THE PHC GROUP
This project presents a scale‑dependent structural constant that appears consistently across multiple CMB analysis pipelines, GCC cold‑clump sampling, lensing reconstructions, and multipole‑range decompositions. The constant forms a smooth numerical family ranging from −1.75 to −1.96, with stable anchor values at −1.8889 (GCC), −1.9367 (CMB), and an asymptotic limit near −1.9593 (lensing). The work shows that this structural constant naturally defines the amplitude of a minimal ripple added to the standard GR expansion history. When this ripple is applied to the Hubble parameter, it produces a few‑percent shift in the inferred value of 𝐻 0 . This shift matches the observed Hubble tension without introducing new physics, tuned parameters, or additional degrees of freedom. The ripple model provides a direct link between CMB structural geometry and late‑time expansion measurements. It preserves CMB anisotropy constraints and early‑universe observables while producing the correct tension magnitude. This project includes the full preprint, supporting analysis, and references documenting the connection between the structural constant family and the Hubble tension.