Derivation of the Fine-Structure Constant from the Topology of the Proton Vortex in PEW (Article 3)

Within the Primordial Energy Waves (PEW) framework, all physical entitiesare topological vortex configurations of a single complex scalar field Ψ = Ã exp(iθ). Theproton is modelled as a three-strand Hopf-fibration torus with aspect ratio R/r = φ(golden ratio). We derive the fine-structure constant in two steps. First, the idealclosed torus yields a topological coupling αtopo = 3/(16π² φ²) = 1/137.808. Second,the spiral of each strand never closes on the irrational torus: its free endpointconstitutes an open gate — geometrically analogous to the flared opening of acochlea or gastropod shell — whose exact cross-section contributes a correctionsin(1/φ)/(32π). The resulting prediction αem = (3 / (16π² φ²)) (1 + (sin(1/φ)) / (32π)) αem = 1 / 137.018agrees with the CODATA value 1/137.036 to 0.013%, with no free parameter beyondπ and φ both fixed by geometry and topology. We further show that the field Ψ = Ã exp(iθ) provides two topologically distinctcoupling mechanisms: the three gauge interactions (strong, electromagnetic, weak)arise from phase-mode exchange (θ sector) through inter-level gates, while gravityarises from amplitude gradients (Ã sector) acting within all levels simultaneously.Black holes possess the same flared gate geometry as the proton, but carry zeronet charge by topological inheritance of the neutrality of absorbed matter: theireffective electromagnetic coupling is zero not because the gate is absent, but becauseQ ≈ 0.