Quantum Support and Classical Actuality: A Translation-Map Audit and Coupled Causal Test

This work examines a foundational question that precedes many debates about quantum superposition: what mathematical map is required to translate quantum support into definite classical actuality? Quantum states, Born probabilities for a fixed measurement, and Boolean truth valuations of classical events are treated as distinct structures. For a finite outcome space, the positive-support indicator Tₚ(E) = 1 iff p(E) > 0 preserves unions, but whenever two exclusive outcomes have nonzero probability it fails to preserve intersections. Hence it is not a Boolean truth valuation unless the support is a singleton. In particular, a superposition α|U⟩ + β|D⟩ with αβ ≠ 0 does not become the classical conjunction U ∧ D through the Born map alone. A deterministic single-outcome selector is also unavailable if it is required to respect the exchange symmetry of a balanced binary distribution. The analysis then grants the strongest charitable version of the disputed literal reading by moving to four-valued, non-explosive Belnap–Dunn semantics. In a correlated trigger–carrier–response model, a local glut propagates only when both positive and negative semantic support are explicitly transferred along the relevant causal links. This yields a precise signed-reachability criterion: the downstream contradiction is not a consequence of quantum dynamics alone, but of additional semantic transfer rules. Explicit countermodels show where the inference fails when one of these rules is removed. The result separates the physical channel from the semantic bridge and prevents classical explosion from hiding the actual logical structure of the argument. A complementary unitary dilation demonstrates that the required trigger–response correlations can be generated by ordinary quantum evolution without producing contradictory classical outcomes. Joint support is kept distinct from its marginals, coherent superpositions are distinguished from incoherent mixtures, and labelled-history models separate coarse causal order from microscopic history. The central diagnosis is therefore structural: any contradiction obtained under the tested assumptions originates in added translation and compositional postulates, not in an inconsistency of quantum mechanics itself. The framework provides a compact audit tool for claims that move from Hilbert-space superposition to classical co-actuality, and then from local semantic contradiction to causal propagation.