Topological and Computational Origins of Fermionic Statistics and Inertia on Discrete Scalar Lattices

We propose a unified conceptual framework deriving the fundamental properties of matter— statistics and inertia—from the discrete dynamics of a 3D scalar lattice. Treating matter not as fundamental point particles but as Rank-2 topological defects, we demonstrate two key results. First, the configuration space of such defects admits a Braid Group (B𝑁 ) representation due to the non-trivial linking of phase-field discontinuities, where stability requirements enforce antisymmetry (Fermionic statistics) without prior quantum axioms. Second, we formalize inertial mass as the ‘‘Update Latency’’ (Δ𝜏) required for the vacuum to resolve these topological structures. We prove that a linear mapping between latency and mass is the unique solution compatible with the Casimir invariants of the Poincaré group in the continuum limit. These results suggest that quantum statistics and inertia are logically unavoidable consequences given the stated assumptions of a discrete, information-processing substrate.