The rise of open-source generative AI systems has sparked concerns about the true extent of their openness. While many systems claim to be open-source, many are only "open weight" and do not fully disclose training data or other critical details. This has led to the concept of "open-washing," where companies market their systems as open-source without providing sufficient transparency. The EU AI Act, which is set to be implemented in 2024, has the potential to redefine the term "open source" and create legal obligations for open-source systems. This paper argues that openness in generative AI is a composite and gradient concept, requiring multiple elements and varying degrees of openness. The authors propose an evidence-based framework for assessing openness, which includes 14 dimensions such as training data, documentation, and licensing. They survey 45 generative AI systems and find that while some are truly open, many are only partially open. The paper also highlights the risks of relying on single features like licensing to determine openness. The authors suggest that a more nuanced approach is needed to assess openness, which can help ensure that models are effectively regulated, providers are held accountable, and users can make informed decisions. The paper also discusses the challenges of assessing training data and the importance of transparency in AI systems. Overall, the paper calls for a more comprehensive and evidence-based approach to assessing openness in generative AI.The rise of open-source generative AI systems has sparked concerns about the true extent of their openness. While many systems claim to be open-source, many are only "open weight" and do not fully disclose training data or other critical details. This has led to the concept of "open-washing," where companies market their systems as open-source without providing sufficient transparency. The EU AI Act, which is set to be implemented in 2024, has the potential to redefine the term "open source" and create legal obligations for open-source systems. This paper argues that openness in generative AI is a composite and gradient concept, requiring multiple elements and varying degrees of openness. The authors propose an evidence-based framework for assessing openness, which includes 14 dimensions such as training data, documentation, and licensing. They survey 45 generative AI systems and find that while some are truly open, many are only partially open. The paper also highlights the risks of relying on single features like licensing to determine openness. The authors suggest that a more nuanced approach is needed to assess openness, which can help ensure that models are effectively regulated, providers are held accountable, and users can make informed decisions. The paper also discusses the challenges of assessing training data and the importance of transparency in AI systems. Overall, the paper calls for a more comprehensive and evidence-based approach to assessing openness in generative AI.