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

10.5281/zenodo.18508881 We present a unified geometric theory connecting galactic dynamics,octonionicsynchronization, and elementary particle masses. Analysis of 175 SPARC galax-ies reveals universal dimensionless constants Π = 4/3 and = √3/4 with 8.2significance. The synchronization constant 1 = 8/9 = 2Π/3 emerges naturallyfrom octonionic algebra (8 synchronized oscillators of 9 total states). Projec-tion from 8D Cayley-Dickson space yields a mass formula m(n1, n2, n3) = MP(EM/G)8(G/2)2(8/9)n1 (1/3)n2 (1/7)n that reproduces all known particle masseswith average error 0.02%. The theory resolves the Hubble tension through scale-dependent gravity Geff() = G0/√1 + ∗/, predicts new particles at 700 GeV and5.35 GeV, and has combined statistical significance exceeding 10.