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Several fundamental problems in software systems and AI remain without a unified formal solution. Deterministic reproducibility of execution, formal consistency between runtime state and historical record, and equivalence of governance and operational execution are unresolved across contemporary architectural paradigms. In AI systems, traceable decision processes and structurally enforced purpose-constrained autonomy remain open problems for the same reason. The common root is ontological: no formally defined execution substrate exists in which execution, governance, persistence, system evolution, and AI reasoning share a single causally ordered knowledge structure. This paper introduces the Zero Tier Execution Substrate (ZTES), an axiomatic execution model derived through formal synthesis of the Mesarović–Takahara system ontology, Lamport-consistent causal ordering, and the DEVS formalism. The Three-Phase execution kernel acts as semantic closure of this synthesis. The append-only historical knowledge base becomes the canonical computational medium in which governance and operational execution are formally equivalent transition processes over a single causally ordered structure. System execution is formally identified with the causal evolution of knowledge: Execution(Σ) ≡ Evolution(K). The scope of this work is foundational: the formal model establishes a stable foundation from which concrete realizations, empirical validations, and higher-level abstractions may be derived. The formal model establishes deterministic event serialization, projection-defined runtime state, and compensation-based correction without destructive mutation. Sixth Normal Form emerges as a natural ontological consequence of atomic event semantics rather than merely a storage design choice. A closure-based structural maturity model for execution architectures is introduced as a methodological contribution. These formal properties directly address the open problems identified above. ZTES therefore provides a formally grounded execution framework addressing several previously unresolved structural problems: deterministic reproducibility of distributed execution, structural consistency between runtime state and historical record, and governance–execution equivalence within a single operational model. In AI systems, it establishes a formally grounded substrate for historically consistent reasoning, traceable decision processes, and purpose-constrained autonomy as structural consequences of substrate closure. Software systems and AI infrastructures may thus be interpreted not as layered architectures but as causally evolving knowledge structures governed by formally defined execution semantics.