This talk by radix CEO might help you understand the consensus architecture, much better than anything I could explain on a forum post.
https://youtu.be/t46NIbOsztgI want to bring into discussion the following paper, "On Stake and Consensus" link here:
https://download.wpsoftware.net/bitcoin/pos.pdfMore specifically, chapter 3.4 "No Universal Time":
[...] there is no well-defined clock time in a distributed system. Network latency gives a finite speed of information propagation, which we know from special relativity means different observers cannot agree on the time-ordering of events that occur closely in time [...]
With respect to the time-ordering mechanism that is mentioned in earlier posts to prevent double-spend attacks;
[...] Network latency is not something that can be bounded in an adversarial setting. An attacker may be able to slow systems by arbitrary amounts using denial-of-service measures, and may be able to physically partition the network by other means. In relativistic terms, this means that there is no amount of waiting that will assure somebody that they are no longer spacelike separated from other participants in the network [...]
How this can affect the finality of transactions and how does Radix address network partitioning?
[...] Users who are new to the network or have been offline recently need access to historical data. But there is no way to verify after-the-fact what order transactions occurred in, so they cannot be assured that the transactions they are receiving actually occurred before any conflicting ones [...]
This can impact the permissionless property of Radix as an open, public cryptocurrency.