Cosmic-Web Projection Dynamics and the Emergence of the Electron Soliton

The projection map Π is a metastructure intrinsic to the pregeometry, existing permanently and constant in time; what evolves is solely its image Π(��_pre) on the four-dimensional real manifold. Throughout this section, W_K specifically denotes the electromagnetic topological winding number, which must be strictly distinguished from the global geometric invariant Ŵ (see the chapter on notational conventions). W_K is a functional of the local configuration of the image set and does not characterize any intrinsic property of the projection map itself. In the early universe, the projection image exhibits a uniformly diffuse topological distribution; as the cosmic proper time elapses, it undergoes aging, contraction, and topological-residue concentration. This unidirectional evolution is driven by a topological monotonic quantity yet to be determined (see Open Problem OP1). The concentration process eventually gives rise to the large-scale filament–void dichotomy of the cosmic web and, through the repulsive topological pressure generated by the interference of positive and negative Euler spirals in the void regions, establishes an asymptotic large-scale transport balance, preventing a runaway accumulation catastrophe of topological structure.