Geometric Theory of Particle Masses: From Galactic Dynamics to Quantum Numbers via Octonionic Synchronization

10.5281/zenodo.18507601 We present a unified geometric theory connecting galactic dynamics, octonionic synchronization, and elementary particle masses. Analysis of 175 SPARC galaxies reveals universal dimensionless constants Π = 4/3 and α = √3/4 with 8.2σ significance. The ynchronization constant κ1 = 8/9 = 2Π/3 emerges naturally from octonionic algebra (8 synchronized oscillators of 9 total states). Projection from 8D Cayley-Dickson space yields a mass formula m(n1, n2, n3) = MP (αEM/αG)8(αG/2π)2(8/9)n1 (1/3)n2 (1/7)n that reproduces all known particle masses with average error 0.02\%. The theory resolves the ubble tension through scale-dependent gravity Geff(ρ) = G0/p1 + ρ∗/ρ, predicts new articles at 700 GeV and 5.35 GeV, and has combined statistical significance exceeding 10σ.