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 from the Fourier decomposition of a3×3 circulant matrix on a torus. For neutrinos we consider a separate, hexagonal lattice motivatedby their different mass generation mechanism (seesaw). This leads to a modified Koide phasewhich, together with the measured oscillation data, yields absolute neutrino masses in the rangeaccessible to upcoming experiments. Dark matter is interpreted as the incoherent sum of highermodes (n > 3), which contribute gravitationally but do not couple to electromagnetism. Darkenergy arises as the residual tension (frustration) of the lattice under a fractal scale inversion thatconnects the Planck scale with the cosmological constant scale. The model offers a unified geometricpicture of several long-standing puzzles and makes testable predictions, among them small violationsof Lorentz invariance and a possible spatial variation of lepton masses.
Daniel Speckmann (Thu,) studied this question.
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