This paper develops a formal systems-theoretic account of persistence in economic systems. Its central claim is that four entity categories are both necessary and sufficient at the level of primitive structure: Individual, Firm, Governance, and Commons. Theorem 1 establishes irreducibility: no entity's function can be reproduced by any combination of the other three without loss of required informational or operational properties. Proposition 4.1 establishes closure of the entity set: no fifth primitive entity is required. Theorem 2 applies Ashby's Law of Requisite Variety to show that a regulator whose model omits any entity faces an irreducible variety deficit. Theorem 3 shows that entity-incomplete systems are non-persistent under extraction pressure, reaching at least one collapse condition in finite time. Theorem 4 gives a worked formalization of one derived rule, showing how a bounded productivity-gate mechanism prevents accumulation failure on cultivable land. Theorem 5 grounds the closure of the entity set in the cybernetic structure of feedback-controlled systems, putting Proposition 4.1 on the same foundation as Theorem 2's application of Ashby's Law. The framework provides a single structural diagnosis for a wide range of major economic failures previously analyzed as unrelated phenomena: each case examined — ecological commons collapse, financial confidence loss, agrarian abandonment, salinization-led productive failure, displaced pastoral commons, and the debt-driven dynamics of the contemporary global system — traces to a specific absence of one or more of the four entities or a specific violation of one or more of the eleven derived rules. Historical cases serve not as substitutes for proof but as external tests of the framework's explanatory reach. The paper's contribution is a compact formal architecture for analyzing persistence, non-persistence, and rule-derived failure in economic systems, with the implication that the trajectory of accumulating contemporary crises is a structural output of the dominant architecture rather than a coincidence of unrelated phenomena.