Geometric Origin of Quantum Mechanics and Predictions for Future Colliders: The 3+4 Hypothesis

I propose a geometric hypothesis stating that the imaginary units of complex numbers, quaternions, and octonions are projections of real compactified spatial dimensions of a G2-manifold onto the observable 3+1 spacetime. This leads to a predictive 11-dimensional supergravity model compactified on a singular G2-holonomy manifold known as the Holmes manifold. The Kaluza-Klein mass spectrum follows a characteristic square-root dependence with the first mode mass fixed at 7.09 TeV by the muon anomalous magnetic moment. The model predicts a vector resonance V at 7.09 TeV decaying to WW and an axial partner A at approximately 13.5 TeV decaying to WZ and Wh, both within the reach of the future FCC-hh collider. Inflation is realized as an alpha-attractor with a spectral index of 0.964 and a discrete set of tensor-to-scalar ratios originating from the underlying octonion structure. Neutrino masses arise from a seesaw mechanism with a sum of approximately 0.065 eV. The model is fully falsifiable and offers concrete experimental targets for the coming decades.