Two-Energy Theory (TDE) v12.0: Dark Matter Yield as a Topological Branching Efficiency

This chapter establishes an observationally anchored boundary condition for Two-Energy Theory (TDE) v12.0 using the cosmological dark-matter-to-baryon density ratio, Ωc/Ωb ≈ 5.36 (Planck 2018). In the TDE v12.0 interpretation, this ratio is not treated as a fit parameter but as the outcome of an early-Universe topological resonance of the Shadow Field χ into two channels: n = 1 (successful, baryonic topological knots) and n = 0 (unsuccessful, electromagnetically dark energy-localized configurations identified with dark matter). We introduce a minimal dimensionless “topological barrier” parameter, ΔStopo ≡ ln(Ωc/Ωb) ≈ 1.68, which directly maps the Planck ratio into a calibration target to be derived from χ microphysics in later work. The chapter specifies necessary conditions for the n = 0 sector to behave as cold dark matter (effective w ≈ 0 during structure formation), and provides explicit falsification criteria if such a regime cannot be realized or if ΔStopo cannot emerge from reasonable χ microphysics without ad hoc degrees of freedom. A reproducibility package (Python scripts and precomputed outputs) is included to independently verify all numerical anchors and plots.