Deriving Dynamic Dark Energy and Resolving Hubble Tension from Planck-Scale Discrete Geometry Stability

Despite the immense success of the standard cosmological model (ΛCDM), it is currently facing severe challenges from a dual crisis: first, the Hubble Tension with a significance of up to 5σ between early and late universe observations; second, the strong preference for Dynamic Dark Energy (w ≠ -1) shown by recent DESI 2025 observational data. This paper proposes a theoretical framework based on first principles, positing that physical reality at the Planck scale is not a continuous manifold, but a condensed state of Planck Scale Discrete Vacuum adhering to the symmetry of the Binary Icosahedral Group (2I). To prevent the microscopic lattice from collapsing due to Geometric Frustration, intrinsic gauge charge conservation must spontaneously induce a centrifugal barrier. We demonstrate that this barrier macroscopicly projects precisely as a scalar field effective potential with an inverse power law form (V ~ |Ψ|⁻²), thereby emerging the Ratra-Peebles Quintessence model from the rigid constraints of microscopic geometry without introducing artificial parameters. The "Thawing" equation of state derived from this mechanism naturally leads to a higher Hubble constant in the late universe, thereby eliminating the observational tension. Simultaneously, this study proves the "Rank-5 Suppression" mechanism unique to icosahedral symmetry, which postpones light speed anisotropy effects to high-order terms of O(E⁴), remaining perfectly compatible with the stringent limits on Lorentz Invariance Violation (LIV) imposed by LHAASO. The conclusion suggests that dark energy is not an ad hoc scalar field, but an inevitable elastic cost paid by discrete spacetime to maintain geometric integrity. Keywords: Planck Scale Discrete Vacuum; Binary Icosahedral Group; Geometric Frustration; Hubble Tension; Dynamic Dark Energy; Emergence