DRAFT-SUPERSEDED-See GDHM: Quasicrystal Confinement, Viscoelastic Gravity, and the Baryonic Tully-Fisher Relation

The persistent mathematical crises in modern physics—the non-renormalizability of quantum gravity, the Hubble Tension, and the ad-hoc parameterization of the Standard Model—indicate a fundamental structural failure in the assumption of a continuous spacetime manifold. We propose a native departure from continuous R4 spacetime, introducing a rigorously discrete 7-dimensional manifold (6S+1T). In this framework, the observable universe is a positively curved 3-dimensional boundary, strictly tessellated by the Poincaré Dodecahedral Space (PDS) and holographically projected from an unprojected 6-dimensional continuous spatial bulk. By redefining fundamental particles as 1D topological sheers anchoring to the discrete 120◦ vertices of the PDS boundary, we organically derive the core pillars of both quantum mechanics and cosmology. This geometric formulation natively replaces the imaginary unit (i) of the Schrödinger equation with a physical orthogonal spatial rotor, analytically proves the existence of the SU(3)mass gap at ≈ 1.618 GeV, and bypasses the Nielsen-Ninomiya theorem via chiral isolation. On the macroscopic scale, gravity is derived as the volume-preserving elastic deformation of the lattice. By separating mass-anchored boundary expansion from photonic bulk refraction, we resolve the 5σ Hubble Tension as a topological optical artifact (72.26 km/s/Mpc vs. 69.8 km/s/Mpc). Furthermore, modeling the thermodynamic unzipping of the lattice (Bifurcation) yields a purely geometric, parameter-free equation of state for dynamical Dark Energy (w0 ≈ −0.809) that flawlessly aligns with 2024 DESI constraints. Finally, we demonstrate that mapping the uncountably infinite (ℵ1) continuous bulk onto the countably infinite (ℵ0) discrete boundary renders the universe locally deterministic yet globally non-computable, offering a rigorous mathematical mechanism for macroscopic information preservation and biological decoherence-free subspaces.