The Dark Sector Topology: Cosmological Phase-Lag, Extremal Topological Solitons, and the Topological Origin of Baryogenesis

The standard ΛCDM model relies on phenomenological dark components and an inflationary epoch to bridge General Relativity with observational data. In this Letter, we extend the Z-Canvas framework—a pre-geometric causal graph governed by the non-Markovian Master Equation of Z—to resolve the dark sector through rigorous topological thermodynamics. We demonstrate that the Horizon Problem is natively resolved by pre-geometric informational fast-scrambling. Crucially, the subsequent percolation of the macroscopic metric drastically expands the geometric phase space, plummeting the relative macroscopic entropy and preserving the Second Law of Thermodynamics. We derive Baryogenesis via a time-asymmetric topological anomaly induced by non-Markovian flow, introducing a structural freeze-out mechanism that strictly preserves the Equivalence Principle. We identify Cold Dark Matter as extremal topological solitons; acting as marginal operators under the topological Renormalization Group (RG) flow, they allow the fundamental nodal limit to manifest macroscopically as topological exclusion pressure via a strict volumetric Jacobian, dynamically resolving the Core-Cusp problem. Finally, we account for late-time acceleration by replacing ad hoc vacuum energy with an IR-regulated structural memory phase-lag dictated by intrinsic fractional topological viscosity, explicitly predicting an irreducible, falsifiable topological Poisson shot-noise in the cosmological equation of state.