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The integration of artificial intelligence into materials science has accelerated property prediction, inverse design, and discovery pipelines. Yet, the reliability of resulting scientific claims remains vulnerable to distribution shifts—systematic differences between training and inference data distributions arising from variations in synthesis protocols, characterization instruments, environmental conditions, or sampling biases. This purely conceptual manuscript develops a novel theoretical framework for robust materials AI inference in the presence of such shifts. We posit that distribution shifts do not merely degrade predictive accuracy but fundamentally alter the epistemic status of scientific claims by introducing unaccounted covariances between material descriptors and latent generative processes. The framework reconceptualizes inference as a multi-layered epistemic process: (i) shift ontology delineation, (ii) value-laden alignment of data representations with domain invariants, and (iii) claim robustness via counterfactual stabilization. By synthesizing insights from materials informatics, machine learning theory on distribution shifts, and philosophical analyses of epistemic values in science, we argue that robust inference requires explicit modeling of shift-induced epistemic uncertainty rather than mitigation as a post hoc engineering concern. This theory provides a conceptual scaffold for evaluating the validity of AI-derived materials claims across heterogeneous datasets, advancing a shift from performance-centric to epistemically grounded AI deployment in materials science.