Self-Consistent Accessibility and the Emergence of Three Spatial Dimensions

Abstract The dimensionality of spacetime is derived from a single principle: any consistent description of reality must be producible within reality. This forces a 34‑dimensional information geometry with a golden‑ratio hierarchy, projecting to 4 observable dimensions. Stable observers require 30 internal degrees of freedom, whose spectral analysis yields parameter‑free predictions: the electron mass me=MPϕ−108≈0.49 MeVme=MPϕ−108≈0.49MeV (experiment: 0.511 MeV0.511MeV), the muon mass mμ=me ϕ4ϕ≈105.8 MeVmμ=meϕ4ϕ≈105.8MeV (experiment: 105.66 MeV105.66MeV), and the tau mass mτ≈1.78 GeVmτ≈1.78GeV (experiment: 1.7769 GeV1.7769GeV). The theory also predicts the gauge coupling ratio g1/g3=ϕ3≈4.24g1/g3=ϕ3≈4.24 at unification and universal ϕϕ-scaling in MOSFET 1/f1/f noise. Quantum measurement is reinterpreted as observer‑relative updating, and physical laws emerge as conditions for observer existence. Keywords: foundations of physics, dimensionality, golden ratio, self-consistency, emergence