Model H - Addendum V: Geometric Derivation of Cosmic Baryon Density matching Planck 2018 Data

This document presents a theoretical derivation of the cosmic baryon density parameter (Omega_b * h^2) based on the geometric principles of Model H. The paper proposes that the fundamental parameter delta (0.00947), originally derived from the universe-proton scale discrepancy, represents a linear tension at the cosmic boundary. By projecting this tension into the spherical volume of the universe using the geometric form factor 3*pi/4, the model derives the volumetric baryon density without introducing free parameters. Key Results: The derived value is Omega_b * h^2 = 0.02231. This result coincides with the Planck 2018 measurement (0.02237 +/- 0.00015) within 0.4 sigma. The findings suggest a potential unification between galactic dynamics (Rotation Curves) and cosmology (CMB) under a single geometric framework. Formula: Omega_b * h^2 = delta * (3 * pi / 4) "Disclaimer: This work represents an independent theoretical proposal and is intended for open discussion and peer review.”