Quantitative Divergence and Non-Associative Drift in High-Dimensional State-Space Modeling A Center-System Approach to Octonionic Lattice Dynamics

Contemporary theoretical physics frequently encounters a "Crisis of Distinction" when reconciling continuous manifolds with discrete quantum excitations, often resulting in unresolvable singularities at localized limits. This paper proposes a structural shift from legacy boundary-measured ("Skin-System") ontologies to a deterministic, center-referenced computational substrate ("Center-System"). By analyzing the divergence between 4D quaternionic approximations and an 8D octonionic lattice across seven discrete iteration gates, we quantify the geometric friction inherent in lower-dimensional modeling. Our findings demonstrate that 4D associative models suffer from a predictable "associative drift"—a linear accumulation of error at a rate of ~0.066 per iteration—culminating in systemic model failure at the late-stage saturation threshold. Furthermore, we outline how an 8-dimensional non-associative framework allows for the first-principles derivation of critical physical constants, including the fine-structure constant (α⁻¹) and the Yang-Mills mass gap, presenting a zero-parameter foundation for high-order theoretical engineering.