OCTONION-GEOMETRIC UNIFICATION THEORY: From αG = 4/3 to the Prediction of the Y (715) Resonance

10.5281/zenodo.18549923 This work presents the complete consolidation of two previously independentframeworks – the octonion projection mass theory and the phenomenology of fundamental constants – into a single geometric theory. The starting point is thediscovery of the universal gravitational constant αG = 4/3 from the analysis of 175 spiral galaxies in the SPARC catalog (Π = 1.332 ± 0.012, p = 0.436). Thisconstant arises naturally as the projection coefficient from 8D octonionic space to 4D spacetime: αG = V (S4)/V (S3) = (8π2/3)/(2π2) = 4/3. From the geometryof octonion projection, three fundamental ratios are derived: κ1 = 8/9 (synchronization), κ2 = 1/3 (structure), κ3 = 1/7 (cyclicity). The universal formula forthe mass of any particle is mx = MP (αEM /αG)1/2 ∏3 i=1 κni i exp(∑3i=1 aini + b, where ni ∈ Z are quantum numbers determined by group representations. Allspecific mass formulas of Model B are shown to be exact consequences of this general formula (Model A). The theory predicts a new tensor resonance Y (715) withmass MY = mt × (2π/αEM ) × α−1/2 G × ϕ = 714.7(35) GeV, decaying predominantly to t¯t (59.8%), ZH (24.9%), ZZ (15.3%) with a characteristic 4:3 azimuthalasymmetry. Cosmological consequences include the prediction of the BAO scalerBAO = 105.0(25) Mpc (aligned with DESI 2024) and a scale-dependent Hubble parameter that resolves the H0 tension. The work provides a complete falsifiable framework with 14 specific predictions for LHC Run 3, Hyper-K, DESI, and sub-millimetergravity experiments. Keywords: fundamental constants, octonions, physics beyond the Standard Model, resonances, cosmology, unification PACS: 12.60.-i, 14.80.-j, 95.35.+d, 98.62.Dm, 02.40.Yy