Topological Derivation of the Absolute Neutrino Mass a Computational Approach Based on Dodecahedral Symmetry

This article addresses one of the most profound analytical limitations of contemporary physics and the Standard Model: the inability to theoretically derive the rest mass of elementary particles, establishing the exact determination of the neutrino mass as the primary objective of the investigation. The study proposes a deterministic approach based on a quantized spatiotemporal infrastructure through the mathematical architecture of the dodecahedron.Abandoning the use of constants and free parameters, the model applies Ramanujan's modular forms to extract the fundamental geometric eigenvalues of the leptonic sector. The derived topological equation of state allows for the analytical calculation of the absolute masses of the three neutrino generations.The coherence of the theoretical architecture is validated on a macroscopic scale: the summation of the analytically derived masses falls rigorously below the most stringent upper cosmological limits, confirming both the historical measurements on background radiation and the most recent frontier observational data.Finally, the geometric identity of mass is corroborated by the analysis of subatomic state transitions, demonstrating that decay processes obey a deterministic dynamics of geometric deformation towards configurations of minimal spatial tension. In summary, this article demonstrates that the quantification of the neutrino mass and macroscopic cosmological constraints are direct expression of the same geometric architecture.