Neutrino Physics within the GDUM Topological Framework and Full-Spectrum Falsifiable Predictions

Based on the three-layer topological architecture of GDUM (the programmatic layer ℤ₂ double-leaf conjugation, the computational layer of the 0-dimensional Euler-spiral operator and the Deck connection, and the phenomenological layer emergent from the topological residue ΔW), this chapter rebuilds neutrino physics from the bottom up. The chapter completes four core tasks in sequence: 1. Redefines the theoretical jurisdiction hierarchy of the particle-physics Standard Model (SM) and its neutrino extensions, distinguishing the phenomenological effective theory from the underlying ontology; 2. Establishes a unified topological mechanism for the full neutrino spectrum from meV to EeV, remaining compatible with standard oscillations at low energies while yielding unique beyond-SM predictions at high energies; 3. Establishes a topological phase-interference effect (OP-47 falsifiable prediction) between high-energy extragalactic neutrinos and the large-scale cosmic web (cosmic filaments/voids); 4. Provides a topological dichotomy criterion for neutrinoless double-beta decay, resolving the Dirac/Majorana ontological ambiguity at the fundamental level (OP-48). All conclusions of this chapter are 100% locked and self-consistent with the GDUM axiom system, the spiral-imprint mechanism, the dark-matter topological spacetime condensate, and the legitimacy of the Whitney-immersed representation. Throughout, the chapter remains compatible with all confirmed experimental results, and only at ultra-high energies and ultra-long baselines does it give falsifiable new signals beyond the Standard Model.