DRAFT-SUPERSEDED-See GDHM: Quasicrystal Confinement, Viscoelastic Gravity, and the Baryonic Tully-Fisher Relation

The formulation of Quantum Chromodynamics (QCD) on a discrete spacetime lattice successfully demonstrates color confinement and the existence of a mass gap in the non-perturbative regime. However, rigorously proving that this mass gap survives the continuum limit (a → 0) remains a fundamental open problem in mathematical physics. This paper proposes an alternative geometric formulation: rather than approximating a continuous flat spacetime (R4) with an artificial hypercubic grid, we model the fundamental vacuum as a natively discrete, positively curved Poincaré Dodecahedral Space (PDS). By formalizing SU(3) gauge links over the rigid pentagonal faces of the PDS fundamental domain, we derive a geometric action (SPDS) where the fundamental lattice spacing possesses a strictly non-zero lower bound. Under this topology, the continuum limit is mathematically forbidden, inherently guaranteeing a strictly positive string tension (σ > 0) and a permanent mass gap. Furthermore, evaluating the geometric trace of this pentagonal action yields an exact theoretical mass for the 0++ scalar glueball at ≈ 1.618 GeV, in precise alignment with current algorithmic lattice estimations.