A discrete resonance lattice model for masses, dark energy and the vacuum catastrophe

We propose that spacetime is not a smooth continuum but a discrete, static lattice of exponentiallylocalized resonances. The energy-momentum tensor is constructed as a sum over these modes, witha spectral weight that naturally regulates the vacuum energy, solving the famous discrepancy of120 orders of magnitude. The first three modes are identified with the three generations of chargedleptons; their masses obey the Koide relation, which emerges as the Fourier decomposition of acirculant 3 × 3 matrix on a torus. For neutrinos we introduce a second, hexagonal lattice motivatedby their different mass generation mechanism (seesaw). This yields a modified Koide phase that,together with oscillation data, predicts absolute neutrino masses in the range accessible to upcomingexperiments. Quark masses are sketched from cubic lattice vibrations, giving a geometric origin forthe up/down ratio and the exceptional top mass. Dark matter is interpreted as the incoherent sumof higher modes (n > 3), which contribute gravitationally but do not couple to electromagnetism.Dark energy arises as residual lattice frustration under a fractal scale inversion connecting thePlanck scale with the cosmological constant scale. The Higgs boson appears as the elastic constantof the lattice itself. The model offers a unified geometric picture of several long-standing puzzlesand makes testable predictions, among them small violations of Lorentz invariance and a possiblespatial variation of lepton masses.