Two-Energy Theory (TDE) v12.1 Neutrino–Dark-Matter Link via the Topological Barrier and Local Screening

This v12. 1 extension builds on the TDE v12. 0 cosmological anchor defined by the observed dark-matter-to-baryon density ratio (Planck 2018), expressed as a dimensionless topological barrier ΔSₜopo = ln (Ωc/Ωb) ≈ 1. 68. (H1) We introduce a conservative, falsifiable conjecture linking the baryonic mass scale to the cosmological neutrino mass sum through an exponential suppression: Σmν = mp · exp−k · ΔSₜopo, with k = (4π + 1). We provide arithmetic verification, uncertainty propagation from the Planck anchor, sensitivity analysis, and explicit falsification criteria as cosmological limits evolve. A brief geometric motivation is included for the k factor, relating it to angular/topological measures and spinor-phase structure rather than parameter fitting. (H2) We propose an environment-dependent extension ΔSₗocal = ΔSglobal + f (Φ), where Φ is the gravitational potential, enabling halo phenomenology via local screening of the Shadow Field χ. A minimal spherical toy model is included to illustrate how screening can generate halo-like profiles without introducing new particles. A reproducibility package (LaTeX sources, BibTeX references, Python scripts, and precomputed outputs/figures) is provided.