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Artificial intelligence (AI) is increasingly embedded across the materials design lifecycle. Yet, prevailing approaches to trustworthiness remain largely model-centric, emphasizing predictive accuracy while under-specifying how AI outputs translate into high-stakes material decisions. This limitation is particularly consequential in materials science, where decisions frequently commit resources to irreversible synthesis, deployment, and long-term societal or environmental impact. Here, we propose a novel decision-centric conceptual framework for trustworthy AI in materials design, defining trustworthiness as the justification of action recommendations under uncertainty—including decisions to select, reject, prioritize, stop, or redesign candidate materials—rather than as an intrinsic property of models alone. The framework structures the materials lifecycle as an iterative sequence of seven decision-bearing stages—from problem framing to revision—and introduces five validity gates—scope, domain, uncertainty, consequence, and sustainability—that serve as systematic filters between AI outputs and actionable commitments. Trust dimensions such as reliability, robustness, transparency, accountability, safety, and sustainability are conceptualized as emergent properties of gated lifecycle interactions rather than isolated criteria. By identifying where failures originate across the lifecycle and formalizing named failure modes with corresponding containment principles, the framework explicitly links uncertainty quantification, interpretability, and governance considerations to defensible decision-making in materials contexts. This work provides a unifying theoretical structure for understanding how trustworthy AI decisions can be operationalized in materials design, offering conceptual grounding for future methodological, institutional, and governance advances in applied artificial intelligence for materials science.