The text presents a solution to the Graded Agreement (GA) problem in the context of Byzantine consensus with unknown and fluctuating participation, improving upon the previous work by Momose-Ren. The authors aim to achieve a higher tolerance for corruption, moving from a ⅓ threshold to an optimal ½ threshold, and focus on the GA problem within the "sleepy" model, where participation can change unpredictably. The proposed solution involves a modified protocol that operates over three discrete rounds, utilizing a time-shifted quorum technique to address the challenge of fluctuating participation without requiring stability. Key properties of the solution include graded consistency, validity, integrity, and uniqueness, ensuring that outputs adhere to the required constraints even amidst Byzantine failures. The protocol leverages median calculations to achieve robustness in message tallying, allowing for accurate consensus even with malicious nodes present. The authors demonstrate how their approach maintains correctness by ensuring that all honest nodes can reach agreement under varying conditions, thereby contributing to the broader field of Byzantine fault-tolerant systems.