DRAFT-SUPERSEDED-See GDHM: Quasicrystal Confinement, Viscoelastic Gravity, and the Baryonic Tully-Fisher Relation

The unification of General Relativity (GR) and Quantum Mechanics remains hindered by the treatment of spacetime as a fundamental, continuous manifold. This paper proposes an emergent gravity framework where continuous spacetime is the macroscopic thermodynamic limit of a discrete, highly rigid microscopic lattice governed by the Poincaré Dodecahedral Space (PDS). We demonstrate that the microscopic topological strain (TPDS) exerted by quantum states upon the rigid dodecahedral vertices acts as an elastic deformation of the lattice basis vectors. By performing a statistical coarse-graining of these deformed vectors via Regge Calculus, we analytically recover the continuous metric tensor (gμν) and the Einstein-Hilbert action. Furthermore, we show that the inherent positive curvature of the PDS boundary rigorously derives the cosmological constant (Λ) not as vacuum energy, but as the baseline geometric torsion of the empty lattice. Finally, the strict fundamental edge length of the PDS mathematically forbids the formation of gravitational singularities, replacing them with topologically saturated cores.