TMDD: Oscillators, Invariants, Boundary. Part VI: Triadic Complexes

This sixth installment in the Tensor Model of Discrete Dynamics (TMDD) series investigates triadic complexes stable hierarchical structures formed by three interacting triads of θ-cells. The work establishes that three triads (nine θ-cells) constitute the minimal configuration capable of generating stable elementary particles, potentially providing a fundamental explanation for the discrete mass spectrum and quantum numbers observed in nature. We develop a stability analysis of triadic complexes, including topological contributions arising from cyclic connectivity. The model offers potential resolutions to several long-standing problems in fundamental physics: baryon asymmetry may emerge from topological CP violation in θ-networks; fermion mass hierarchies could follow from discrete topological configurations; and the Higgs mass hierarchy problem might be addressed through the finite-capacity principle inherent to TMDD. Furthermore, we reinterpret high-energy particles and radiation as specific excitations and topological defects of the θ-network, potentially offering a unified description of known particles and interactions. The theory suggests falsifiable predictions, including possible triadic resonances around 1 TeV and specific correlation patterns in particle collisions.