An AI benchmark result rarely reaches a consequential claim in one step. Evaluators generalize it to further cases, interpret it as evidence of capability, extrapolate it to new tasks, transport it to another system or site, and combine it with assumptions about human review and downstream consequences. Validity-centred approaches require evidence for each claim. This paper identifies a further epistemic problem: warranted links don't automatically make a warranted chain. The target of one study may not be the source of the next; system, population, outcome, or conditions may change at the interface; and shared data or model lineage may make apparently independent support dependent. Projectibility concerns whether a bounded extension from observed to unobserved cases is warranted. Goodman supplies the problem of rival extensions; argument-based validity supplies an architecture for testing them. The paper's distinctive claim is a non-composition principle: support for adjacent projections warrants their composition only when endpoints and assumptions align and dependence and uncertainty are carried through. A legal-research case shows how benchmark evidence and a deployment study can each be sound while remaining parallel. A reanalysis and simulation show why aggregate stability can erase distinctions a later projection requires. The resulting projectibility audit diagnoses unsupported joins in benchmark-to-use arguments.

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