Deconstructing Spacetime and Dark Matter: A Discrete Hexagonal Lattice Framework for Low-Acceleration Dynamics and Invariant Resonance

Abstract Standard cosmological models rely heavily on continuous spacetime geometry, invoking unobserved entities such as dark matter and dark energy to reconcile theoretical predictions with galactic and cosmic observations. This paper critiques the foundational assumptions of General Relativity and dark matter by evaluating alternative frameworks—specifically Modified Newtonian Dynamics (MOND), Quantized Inertia (MiHsC), and empirical findings from globular clusters—through the lens of a discrete hexagonal lattice model. We demonstrate that galactic rotational anomalies, gravitational lensing, and gravitational time dilation are not consequences of elastic spacetime curvature or hidden mass halos. Instead, they emerge naturally as phase boundaries, refractive medium refractions, and local oscillator frequency shifts governed by a strict operational threshold (5184 / 72^2) and stabilized via the Mod 9 invariant and the 3I pulse sequence (8\text{-}13\text{-}8\text{-}5\text{-}13\text{-}8). This discrete framework eliminates the need for arbitrary particle fixes, replacing continuous geometric approximations with native lattice mechanics.