Topological and Computational Origins of Fermionic Statistics and Inertia

We propose a rigorous unification of the two fundamental properties of matter— Fermi-Dirac statistics and inertial mass—deriving both from the ontological constraints of a discrete scalar lattice. Unlike standard formulations where statistics are axiomatic and mass is a coupling parameter, we show that these emerge as necessary consequences of topological stability and information processing limits. First, we define matter as Rank-2 topological defects (singularities with associated branch cuts). We demonstrate via topological analysis that the configuration space of such extended objects in 3D shares the fundamental group structure of the Braid Group B𝑁 , distinct from the Symmetric Group 𝑆𝑁 of point particles. We show that the stability of these defects identifies the projective representation 𝜎2 =−1 as the minimal stable unitary solution, effectively enforcing fermionic anticommutation without invoking quantum fields ab initio. Second, we identify inertial mass with the ‘‘Update Latency’’ (Δ𝜏)—the irreducible computational cost required to update the topological state of a defect. By analyzing the dispersion relations in the continuum limit, we prove the Latency-Mass Correspondence: strict linearity between latency and mass is the solution that preserves the Casimir invariants of the Poincaré group within an Effective Field Theory framework. This framework suggests that the ”weirdness” of quantum mechanics and the ”resistance” of inertia are dual manifestations of the same underlying discrete reality: the information processing constraints of the vacuum.