Topological Lattice Dispersion: A Causal Framework for Mass Emergence and Cosmological Dynamics

In this paper, we present a unified framework of topological lattice dispersion. Based on a causal, left-handed tetrahedral Planck lattice utilizing Causal Dynamical Triangulations (CDT) and Regge calculus, we model the vacuum not as an empty void, but as a discrete, geometrically frustrated structure. A fundamental angular deficit of inherent to the tetrahedral packing deterministically generates the curvature of space, while the chiral (left-handed) nature of the lattice naturally filters out antimatter, allowing only left-handed topological solitons to survive.At the quantum level, propagating waves must continuously adjust their phase to overcome the topological resistance of the Wilson links. If the residual kinetic energy drops below the depth of the local potential depression, a saddle-node bifurcation occurs and the wave freezes in place. The wave's continuous circulation within this localized depression manifests macroscopically as rest mass and quantum spin. Thus, the localization principle, the emergence of quantum fields, and the inverse-square law arise deterministically from lattice decoherence.On a cosmological scale, the continuous geometric frustration leads to an immense, permanent bending stress. To relieve this tension, the vacuum undergoes continuous microscopic quantum fluctuations (topological phase transitions), spontaneously inserting new spatial quanta. This discrete volumetric generation dictates the Hubble expansion, rendering ad-hoc parameters like "Dark Energy" unnecessary.Finally, the absolute rigidity of the Planck length necessitates a fundamental shift regarding the rotation curves of galaxies. As immense local mass concentrations push the spatial lattice to its elastic limit, the geometry cannot taper off smoothly. Instead, non-linear lattice elasticity forces the grid to stiffen into a steep topological potential barrier at the galactic edges, generating extreme inward-pulling radial forces. Consequently, the reliance on Cold Dark Matter (CDM) to explain these cosmological phenomena is rendered obsolete