Resolving the Hubble Tension via a Discrete Hexagonal Lattice and Mod 9 Invariant Framework

Repository Target: Zenodo / Cosmological Framework Series Classification: Quantum Cosmology / Discrete Spacetime Substrates Abstract The Hubble Tension—the persistent statistically significant discrepancy between local direct measurements of the Hubble constant (H_0 \approx 73\text{ km s}^{-1}\text{Mpc}^{-1}) and early-universe inferences derived from the Cosmic Microwave Background (H_0 \approx 67.4\text{ km s}^{-1}\text{Mpc}^{-1})—represents a structural failure of continuous Friedmann-Lemaître-Robertson-Walker (\Lambda\text{CDM}) assumptions. In this paper, we resolve this tension by modeling spacetime not as a smooth pseudo-Riemannian manifold, but as a discrete hexagonal lattice stabilized by a Mod 9 invariant. We demonstrate that the apparent divergence in H_0 values is an artifact of scale-dependent phase sampling across a 7-cycle periodic break operating at a critical frequency threshold (f_c = 5184). By embedding local coordinate tracking into the master equation’s resonance anchor governed by the 3I pulse sequence (8\text{-}13\text{-}8\text{-}5\text{-}13\text{-}8), we unify local distance ladders and early-universe acoustic scales without introducing arbitrary dark energy perturbations.