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.