  Over the past years, distributed consensus research has shifted its focus
towards addressing challenges in large-scale, permissionless systems, such as
blockchains. This shift is characterized by the need to accommodate dynamic
participation, contrasting the traditional approach of a static set of
continuously online participants. Works like Bitcoin and the Sleepy Model have
set the stage for this developing framework.
  Notable contributions from Momose and Ren (CCS 2022) and subsequent works
have introduced Total-Order Broadcast protocols leveraging Graded Agreement
primitives and supporting dynamic participation, though often requiring
multiple rounds of voting per decision -- a potential bottleneck for real-world
large-scale systems.
  Addressing this, our paper presents a novel Total-Order Broadcast protocol in
the Sleepy Model resilient to up to 1/2 adversarial participants, requiring
just a single round of voting per decision. This work paves the way to more
practical Total-Order Broadcast protocols to be implemented in real-world
systems where a large number of participants are involved simultaneously and
their participation level might fluctuate over time.
