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The ambiguous use of “falsifiability” in materials AI literature poses a significant challenge to the scientific status of AI-generated claims, as researchers frequently present predictive or generative outputs—such as “this perovskite structure is stable at room temperature” or “this inverse-designed alloy exhibits a target bandgap of 1.8 eV”—without clarifying whether these statements could, in principle, be contradicted by empirical observation. Rooted in Karl Popper's philosophy of science and extended through contemporary applications to machine learning, falsifiability serves as the demarcation criterion that distinguishes scientific claims from non-scientific ones by requiring that they logically forbid certain observations rather than merely accommodate data. This paper proposes precise definitions for falsifiable, verified, and testable AI-generated materials claims, tailored specifically to the challenges of data-driven discovery in solid-state systems, generative models, and inverse design. It further introduces a four-component framework for assessing the falsifiability of such claims, centering on claim specification, forbidden observation specification, test design, and falsification protocol. These conceptual foundations carry profound implications for materials AI practice, requiring authors to articulate disconfirming evidence explicitly, reviewers to demand falsifiability statements, and the broader community to adopt standards that elevate predictive modeling from statistical correlation to genuine scientific inquiry. By confronting the boundary between data-driven heuristics and empirically falsifiable science, the present work offers a definitional scaffold that can guide the field toward greater epistemic rigor amid the accelerating integration of artificial intelligence into materials discovery.