In the context of Byzantine consensus problems such as Byzantine broadcast (BB) and Byzantine agreement (BA), the good-case setting aims to study the minimal possible latency of a BB or BA protocol under certain favorable conditions, namely the designated leader being correct (for BB), or all parties having the same input value (for BA). We provide a full characterization of the feasibility and impossibility of good-case latency, for both BA and BB, in the synchronous sleepy model. Surprisingly to us, we find irrational resilience thresholds emerging: 2-round good-case BB is possible if and only if at all times, at least φ1≈0.618 fraction of the active parties are correct, where φ=21+5≈1.618 is the golden ratio; 1-round good-case BA is possible if and only if at least 21≈0.707 fraction of the active parties are correct.
@article{arxiv.2510.06023,
title = {Optimal Good-Case Latency for Sleepy Consensus},
author = {Yuval Efron and Joachim Neu and Ling Ren and Ertem Nusret Tas},
journal= {arXiv preprint arXiv:2510.06023},
year = {2025}
}