Theoretical Foundations of Relational Lattice Dynamics: Emergence of Inertia and Topological Coherence

This work presents the rigorous mathematical derivation and the analytical infrastructure of emergence processes within a discrete relational lattice, formalizingthe principles introduced in Unifying Informational Dynamics- Version v2 (DOI:10.5281/zenodo.18761132). By replacing the three-dimensional spacetime continuumwith a two-dimensional (d = 2) simplicial complex governed by the SU(2) gaugegroup, we demonstrate how inertial mass and fundamental interactions emergeas collective properties of informational dynamics. Through the Master Equationof vacuum saturation, the exact decoupling between linear inertia and quadratictopological stress in bound systems is derived. Calibration on the single nucleonallows us to geometrically determine, without ad hoc parameters or reliance on thePlanck constant ℏ, the topological coherence radius (ξ) and the vacuum relaxationtime, defining the exact geometric stability limit of baryonic matter. The resultsprovide a theoretical foundation for interpreting galactic kinematic anomalies aseffects of vacuum hysteresis, eliminating the need for exotic dark matter.