RAFT and PAXOS are the main ones I know of. There are applications which can help you with this already, like Consul

https://www.hashicorp.com/resources/raft-consul-consensus-pr...

You might also look into the pBFT subject

Hyperledger Fabric, is a blockchain framework but not web3 / crypto that might be interesting too, if you are surveying widely

+1 for RAFT, Paxos is quite complex and easy to mess up.

If you're lazy, you can just throw Zookeeper at the problem (this is what many Big Data systems like Spark and Kafka often use for synchronization and consensus):

- https://zookeeper.apache.org/

- https://zookeeper.apache.org/doc/current/zookeeperInternals....

> If I want to architect a peer-to-peer application that needs to achieve consensus, what are some of the provably correct protocols/algorithms?

None. Ever.¹ Proof: https://groups.csail.mit.edu/tds/papers/Lynch/jacm85.pdf

[1] Assuming that peers in your application can crash.

Thanks. Interesting paper.

> THEOREM 2. There is a partially correct consensus protocol in which all nonfaulty processes always reach a decision, provided no processes die during its execution and a strict majority of the processes are alive initially.

This seems to be the silver lining from the paper for practitioners.

> This seems to be the silver lining from the paper for practitioners.

Indeed. Of course, the hard (impossible?) part is ensuring that no peers die.