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This paper introduces a new family of consensus protocols, namely\emph{Lachesis-class} denoted by $\mathcal{L}$, for distributed networks withguaranteed Byzantine fault tolerance. Each Lachesis protocol $L$ in$\mathcal{L}$ has complete asynchrony, is leaderless, has no round robin, noproof-of-work, and has eventual consensus.  The core concept of our technology is the \emph{OPERA chain}, generated bythe Lachesis protocol. In the most general form, each node in Lachesis has aset of $k$ neighbours of most preference. When receiving transactions a nodecreates and shares an event block with all neighbours. Each event block issigned by the hashes of the creating node and its $k$ peers. The OPERA chain ofthe event blocks is a Directed Acyclic Graph (DAG); it guarantees practicalByzantine fault tolerance (pBFT). Our framework is then presented using Lamporttimestamps and concurrent common knowledge.  Further, we present an example of Lachesis consensus protocol $L_0$ of ourframework. Our $L_0$ protocol can reach consensus upon 2/3 of all participants'agreement to an event block without any additional communication overhead.$L_0$ protocol relies on a cost function to identify $k$ peers and to generatethe DAG-based OPERA chain. By creating a binary flag table that storesconnection information and share information between blocks, Lachesis achievesconsensus in fewer steps than pBFT protocol for consensus.

OPERA: Reasoning about continuous common knowledge in asynchronous distributed systems