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 substrate is universal for discrete processes: any discrete process admits execution within ZTES without loss of process identity, event ordering, or executable semantics. 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. ZTES does not introduce new computational primitives; it defines the minimal semantic discipline under which existing mechanisms — append-only persistence, causal ordering, and discrete-event transition semantics — are interpreted and composed as a structurally closed execution substrate. The formal model establishes deterministic event serialization, projection-defined runtime state, and compensa-tion-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 and benchmark for execution architectures are introduced as methodological contributions. These formal properties directly address the open problems identified above. ZTES therefore addresses several pre-viously 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 substrate for historically consistent reasoning, traceable decision processes, and purpose-constrained autonomy as structural consequences of substrate closure. Software systems and AI infrastructures are therefore formally interpretable not as layered architectures but as causally evolving knowledge structures governed by formally defined execution semantics.