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Recognizing the physical states of objects and their transformations within videos is crucial for structured video understanding and enabling robust real-world applications, such as robotic manipulation. However, pretrained vision-language models often struggle to capture these nuanced dynamics and their temporal context, and specialized object state recognition frameworks may not generalize to unseen actions or objects. We introduce SAGE (State-Action Graph Embeddings), a novel framework that offers a unified model of physical state transitions by decomposing states into fine-grained, language-described visual concepts that are sharable across different objects and actions. SAGE initially leverages Large Language Models to construct a State-Action Graph, which is then multimodally refined using Vision-Language Models. Extensive experiments show that our method significantly outperforms baselines, generalizes effectively to unseen objects and actions in open-world settings. SAGE improves the prior state-of-the-art by as much as 14.6% on novel state recognition with less than 5% of its inference time.