A Minimal Axiom of Traceability

Abstract Traceability is widely mandated across regulated supply chains and frequently cited as a prerequisite for effective recalls, inventory accuracy, and accountability. However, persistent failures observed during audits and operational incidents suggest that traceability is often asserted without a clear formal basis. This paper proposes a minimal axiomatic basis for traceability, defining it as a logically verifiable property rather than a feature of system implementation, regulatory compliance, or operational maturity. A single axiom (A₀) is introduced, accompanied by four definitions that establish the necessary and sufficient conditions under which traceability can be said to exist. The framework is deliberately system-oriented and independent of specific technologies or standards, enabling falsification, auditability, and cross-industry applicability. The paper argues that many contemporary systems commonly described as “traceable” fail to satisfy this minimal axiom and therefore possess records, but not traceability.