Gravitational Knots: Topological Origin of Matter and Lepton Unification in Imaginary Kaluza-Klein Spacetime

In this paper, I propose that fundamental fermions, specifically electrons, exist as stable topological solitons (knots) formed within a 5-dimensional Kaluza-Klein spacetime geometry. This model postulate a metric where the three macroscopic spatial dimensions and time remain real, while the fourth, compactified spatial dimension is imaginary. The assumption of an imaginary extra dimension enforces the cyclicity of the wavefunction and leads directly to strict electric charge quantization, interpreted here as momentum along the imaginary coordinate. In this framework, charge is not an intrinsic property of substance but an emergent property of global topology—a phase rotation on the complex plane. This model naturally unifies the lepton generations by interpreting the muon and tau as metastable, excited vibrational modes of the fundamental electron knot. Furthermore, neutrinos are identified as unknotted topological loops that, lacking charge anchoring, propagate freely through spacetime. This hypothesis resolves the infinite self-energy problem of point particles by postulating a finite knot structure at the Planck scale (10-33 m) and predicts a non-zero electron electric dipole moment (EDM).Update v2: Corrected editorial errors regarding L3 data interpretation and phrasing of ACME limits. Clarified unitarity and Koide relation interpretation.