  This paper consolidates the core technologies and key concepts of our novel
Lachesis consensus protocol and Fantom Opera platform, which is permissionless,
leaderless and EVM compatible.
  We introduce our new protocol, so-called Lachesis, for distributed networks
achieving Byzantine fault tolerance (BFT)~\cite{lachesis01}. Each node in
Lachesis protocol operates on a local block DAG, namely \emph{OPERA DAG}.
Aiming for a low time to finality (TTF) for transactions, our general model
considers DAG streams of high speed but asynchronous events. We integrate
Proof-of-Stake (PoS) into a DAG model in Lachesis protocol to improve
performance and security. Our general model of trustless system leverages
participants' stake as their validating power~\cite{stakedag}. Lachesis's
consensus algorithm uses Lamport timestamps, graph layering and concurrent
common knowledge to guarantee a consistent total ordering of event blocks and
transactions. In addition, Lachesis protocol allows dynamic participation of
new nodes into Opera network. Lachesis optimizes DAG storage and processing
time by splitting local history into checkpoints (so-called epochs). We also
propose a model to improve stake decentralization, and network safety and
liveness ~\cite{stairdag}.
  Built on our novel Lachesis protocol, Fantom's Opera platform is a public,
leaderless, asynchronous BFT, layer-1 blockchain, with guaranteed deterministic
finality. Hence, Lachesis protocol is suitable for distributed ledgers by
leveraging asynchronous partially ordered sets with logical time ordering
instead of blockchains. We also present our proofs into a model that can be
applied to abstract asynchronous distributed system.
