Two-Energy Theory (TDE) v13.0: A Resonant EFT with a 4D Topological Barrier Linking Neutrino Mass, Baryonic Mass, and Cosmology

Two-Energy Theory (TDE) v13.0 is presented as a compact, falsifiable resonance-based effective field theory that connects cosmological composition to particle-scale masses through a single topological control parameter. The model introduces a 4D geometric/topological barrier defined from the cosmological ratio of dark to baryonic density, expressed as a dimensionless entropy-like separation. This barrier governs a branching between a stable resonance channel (visible matter) and an incomplete resonance channel (shadow/dark sector). The core result is a closed-form link between the barrier and the summed neutrino mass scale, with the geometric factor (4π+1) interpreted as a 4D-sphere/volume ratio plus quantum corrections rather than a fitted parameter. To address dataset dependence and late-time geometry, the theory includes a controlled “renormalization” of the barrier using background cosmological geometry, benchmarked against public DESI DR1 BAO and Full-Shape parameter chains. This benchmark is a parametrization-level consistency check (the chains are prior-bounded in mν) and should not be interpreted as a direct measurement or validation of the neutrino-mass prediction. In addition, an EFT operator-level mapping is provided to classify precision anomalies as leakage into the shadow channel with exponentially suppressed amplitudes set by the same barrier. This Zenodo release contains the full formalism (Lagrangian structure, resonance mechanism, and parameter freeze), explicit falsification criteria, and reproducible supplementary calculations. The intent is not to claim endorsement by the community but to enable independent verification: the key relations can be checked directly against public cosmology chains and standard EFT normalizations. Readers are encouraged to download the source package and reproduce every numerical step.