Intermediate results of numerical modeling of the collective mode spectrum in a coupled oscillator model

This preprint presents intermediate results from numerical simulations of a lattice model of quantized space. Each node of a 3D cubic lattice carries three internal modes with local harmonic and three-mode interactions, and neighboring nodes are coupled harmonically. Due to the huge Hilbert space dimension (∼1.6×10¹⁶ for an 8‑node lattice), a linearized approximation is employed, reducing each node to three independent oscillators. The collective frequency spectrum for a 2×2×2 lattice with periodic boundary conditions (ω₀ = 1.0, κ = 0.3) is computed. Twelve modes remain degenerate at ω = 1, while the other twelve split to ω ≈ 1.48. The absence of a hierarchy of three distinct low‑lying frequencies shows that linear dynamics cannot generate the three fermion generations; nonlinear corrections or a topological interpretation are required.