The Geometric Derivation of Hadronic Mass and Quantum Spin: Rest Mass and Angular Momentum from Tetrahedral Waveguides

In the Standard Model of particle physics, fundamental parameters such as hadronic rest mass and quantum spin are defined as intrinsic, axiomatic properties lacking a deterministic structural origin. This study introduces a geometric derivation of these constants based on the principles of dissipative information topology (DIT). The spatial fabric is modeled not as point-like entities, but as a network of dynamic tetrahedral waveguides. By applying strict geometric boundary conditions - specifically, the necessity of an inscribed momentum wave leaving the three vertices untouched to act as frictionless topological hinges - it is demonstrated that internal wave propagation is forced into discrete harmonic resonances, providing a pure mechanical basis for spin quantization. Furthermore, the maximum volumetric capacity of the tetrahedral node prior to geometric inversion is calculated and coupled with the critical energy density of the hadronic phase transition rho₂ₑ₈ₓ approx 500 MeV/fm³. This topological derivation yields a theoretical rest mass for the elementary dual-node configuration of132. 3 MeV, correlating with the empirically observed mass of the neutral pion pi⁰bwithin a < 2n% margin of error. The framework mathematically establishes that mass and spin emerge not as inherent mysteries, but as the absolute spatial consequences of asymmetric wave propagation within a converging, three-sided topological confinement.