Use Exclusivity and the No-Cloning Theorem: A Conditional Implication in Structural Determination Theory

This paper proves that under a specified mapping from Structural Determination Theory (SDT) to quantum mechanics, the SDT axiom G5 (use exclusivity) implies the no-cloning theorem (Wootters and Zurek 1982; Dieks 1982). The implication is established by showing that any mapping image admitting a universal cloning operator violates G5: the output of cloning, containing two copies of a quantum state, corresponds under the mapping to a single realized structure entering two distinct structural layers. The reverse implication does not hold, for three independent reasons: SDT lacks unitary structure, G5 is more restrictive than no-cloning, and the SDT-to-QM mapping is not unique. The result upgrades the structural analogy "G5 ↔ no-cloning" recorded in the SDT-to-QM correspondence program to a conditional one-way formal implication, identifying G5 as a sufficient meta-structural condition for no-cloning. The paper does not derive quantum mechanics from SDT; it identifies the precise sense in which a meta-structural axiom about the role-instance structure of element membership translates, under mapping, into a quantum-mechanical no-go theorem about universal cloning.