Bridging Model-Independent Cosmological Inconsistencies with a Discrete Hexagonal Lattice: A Comparative Framework Analysis

Repository: Zenodo Preprint Registry Date: July 2026 Abstract Modern observational cosmology relies heavily on large-scale data aggregation evaluated through the smooth Friedmann-Lemaître-Robertson-Walker (\Lambda\text{CDM}) framework. However, recent model-independent diagnostic tests and bootstrap-based symbolic regression analyses reveal persistent 2\text{--}4\sigma deviations from standard geometry. While consensus frameworks attribute these tensions to localized backreaction or data noise, this paper demonstrates that smoothing kernels artificially mask underlying structural metrics. We propose a top-down alternative: modeling the vacuum spacetime manifold as a discrete hexagonal lattice stabilized by a \text{Mod } 9 invariant and regulated by a 7-cycle periodic break at the 5184\text{ Hz} (72^2) frequency threshold. This deterministic framework resolves macroscopic cosmic anomalies without invoking unobserved dark sectors.