Topological Theory of Discrete Space (TTDS) – Model Compendium

Abstract This Model Compendium introduces an extended and rigorous formulation of the Topological Theory of Discrete Space (TTDS)—a deterministic, discrete mechanical framework that unifies General Relativity and Quantum Mechanics through the wave kinematics of a 100% elastic, cellular vacuum. By modeling space as a discrete cellular graph anchored to a non-metric topological center (+1D) and governed by an absolute kinematic paradigm of invariant wave propagation speed (), TTDS treats mass as locked topological knots, forces as structural strain tensors, and photons as unclosed propagating waves. The framework reduces fundamental physics to baseline three material parameters of the medium: Planck length (), Planck time (), and the Lattice Elasticity Modulus (). Crucially, TTDS analytically derives that the gravitational constant () and Planck's constant () are not absolute universal laws, but environmental variables strictly dependent on local spatial strain. Furthermore, the model provides a purely geometric and mechanical resolution to cosmic expansion (Dark Energy via relaxation), galactic rotation curves (replacing Dark Matter with spatial hydrodynamic inflow), quantum non-locality, and the Hierarchy Problem, offering a concrete, testable path for empirical verification.