Unified Geometric Theory Based on the Constant G = 4/3 : From Galactic Dynamics to the Y(715) Resonance and Resolution of Cosmological Tensions

10.5281/zenodo.18550484 Based on a statistical analysis of 175 spiral galaxies from the SPARCcatalog, we report the discovery of a fundamental dimensionless constant αG =Π = 4/3 with > 8σ significance (⟨Π⟩ = 1.332 ± 0.012, p = 0.436). InterpretingαG as a geometric projection coefficient from an 8-dimensional octonionicspace to 4-dimensional spacetime, we derive a unified formula for StandardModel particle masses: m = mP (αEM/αG)1/2 Q3 i=1 κni i exp(P aini + b) withκ1 = 8/9, κ2 = 1/3, κ3 = 1/7. The theory predicts a new tensor resonanceY(715) with mass MY = 714.7 GeV, width ΓY = 44.8 GeV, and specific decaychannels: t¯t (59.8%), ZH (24.9%), ZZ (15.3%). As a geometric consequence,the model resolves cosmological tensions: it predicts the BAO scale rBAO =105.0 Mpc (matching DESI 2024: 105.1 Mpc) and provides a scale-dependentHubble parameter H(R) that reconciles local (H0 = 72.8) and CMB (H0 =67.4) measurements. We present a complete falsifiable framework with 14testable predictions for LHC Run 3, Hyper-K, DESI/Euclid, and sub-millimetergravity experiments. Keywords: fundamental constants, physics beyond the Standard Model, cosmologicalparameters, modified gravity, octonions, LHC phenomenology.PACS: 12.60.-i, 14.80.-j, 95.35.+d, 98.62.Dm, 98.80.-k, 02.40.Yy