The rapid rise of generative AI has intensified copyright and economic tensions in creative industries, particularly in music. Current approaches addressing this challenge often focus on preventing infringement or establishing one-time licensing, which fail to provide the sustainable, recurring economic incentives necessary to maintain creative ecosystems. To address this gap, we propose Generative Content ID, a framework for scalable and faithful royalty attribution in music generative AI. Adapting the idea of YouTube's Content ID, it attributes the value of AI-generated music back to the specific training content that causally influenced its generation, a process we term as causal attribution. However, naively quantifying the causal influence requires counterfactually retraining the model on subsets of training data, which is infeasible. We address this challenge using efficient Training Data Attribution (TDA) methods to approximate causal attribution at scale. We further conduct empirical analysis of the framework on public and proprietary datasets. First, we demonstrate that the scalable TDA methods provide a faithful approximation of the "gold-standard" but costly retraining-based causal attribution, showing the feasibility of the proposed royalty framework. Second, we investigate the relationship between the perceived similarity employed by legal practices and our causal attribution reflecting the true AI training mechanics. We find that while perceived similarity can capture the most influential samples, it fails to account for the broader data contribution that drives model utility, suggesting similarity-based legal proxies are ill-suited for royalty distribution. Overall, this work provides a principled and operational foundation for royalty-based economic governance of music generative AI.