In a detailed exploration of Byzantine atomic broadcast (BAB) protocols, the authors present an innovative solution that builds upon previous work on binary Byzantine agreement, extending it to multi-valued consensus. The protocol features a deterministic and unconditional safety mechanism, maintaining a low latency of three rounds while allowing for unknown and dynamic participation of nodes, including the fluctuating presence of faulty nodes. The approach employs block chaining and graded agreement, ensuring that honest nodes achieve consensus without conflicts, and supports the decision on a growing sequence of input values. Notably, the protocol improves upon existing methods by reducing the number of graded agreement invocations, thereby enhancing efficiency and practicality in environments where node participation can vary widely over time. This solution addresses significant limitations in previous models, particularly by allowing for the dynamic involvement of faulty nodes, which existing solutions without proof-of-work struggled to accommodate.