Version 8.6.0 introduces an explicit topological definition of spacetime and matter, completing the ontological foundation of the EMU framework without modifying its underlying dynamics. Updated Abstract (EMU v8.6.0) In this updated version, the Excitation-based Model of the Universe (EMU) is reformulated with an explicit ontological definition of spacetime and matter. While earlier versions demonstrated that quantum and relativistic dynamics emerge from discrete scalar update rules, the underlying geometric meaning of these structures remained implicit. Version 8.6.0 resolves this by identifying spacetime not as a background manifold, but as a topological organization of information updates on an amorphous discrete substrate. Within this framework, particles are no longer treated as localized excitations, but are rigorously defined as topological defects characterized by nontrivial winding numbers in the phase field. Their stability, identity, and persistence arise from topological protection rather than dynamical confinement. Motion is reinterpreted as the reconfiguration of phase-topological patterns across the substrate, and the relativistic speed limit emerges naturally from the maximal propagation rate of update connectivity. Inertial mass is defined operationally as computational latency associated with maintaining nontrivial topological structures, providing a structural origin for inertia and the impossibility of superluminal motion. Gravitational interaction is reformulated as an induced geometric response of the substrate to local information-capacity depletion, linking lattice tension minimization to effective metric deformation in the continuum limit. This places general relativity within the class of induced gravity phenomena arising from discrete informational media. These clarifications do not introduce new dynamical postulates, but instead make explicit the ontological assumptions implicit in previous versions. As a result, EMU v8.6.0 constitutes a logically closed discrete-foundation framework in which quantum mechanics, inertial mass, and spacetime geometry emerge from a unified topological–computational substrate.

The unification of General Relativity (GR) and Quantum Mechanics (QM) remains the defining challenge of theoretical physics. The incompatibility between the smooth geometry of gravity and the discrete nature of quanta suggests that the ”continuum” is an effective approximation. This monograph presents EMU v8.5, a rigorous framework that derives physical laws from a Discrete Scalar Lattice (L) without assuming prior geometric or quantum axioms. Version 8.5 integrates a comprehensive Mathematical Reinforcement Package to address fundamental uniqueness and existence questions: 1. Group-Theoretic Origin of Statistics (Package A & B): We prove that fermionic statistics are not a postulate but a necessary consequence of the non-abelian exchange group G𝑅2 of Rank-2 defects. We demonstrate via representation theory that the stability of internal holonomy uniquely selects a Z2 structure, enforcing anticommutation. 2. Uniqueness of Inertial Measure (Package C): We prove the Latency-Mass Uniqueness Theorem, demonstrating that under requirements of additivity and relativistic consistency, the only viable measure of inertia on a discrete lattice is the topological update latency Δ𝜏. This eliminates mass as a free parameter. 3. Lattice Universality (Package D): We ground the 𝐸8 projection hypothesis in the theory of Meyer Sets, showing it is the minimal structure capable of supporting stable, local Clifford algebras in 3D. 4. Algorithmic Reproducibility (Package E): We provide explicit algorithms for the calculation of fundamental constants, including the fine-structure constant 𝛼−1 ≈ 137.036, ensuring the theory is computationally reproducible. This document unifies Ontology, Topology, and Dynamics into a single, mathematically robust ax- iomatic system.