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Theoretically, if all the nodes in the quorum participate only in disjoint slices, then there wouldn't ever be a single global state of the ledger. Does Stellar help identify such scenarios in the network (main or private)?

From the Stellar Consensus Protocol article, there is a universe of nodes of which a quorum of nodes is enough to arrive at a 'final' ledger state.

To tolerate Byzantine failure, SCP is designed not to require unanimous consent from the complete set of nodes for the system to reach agreement, and to tolerate nodes that lie or send incorrect messages.

Then, there is a quorum slice that is a collection of certain nodes within the quorum mentioned above.

Federated Byzantine agreement introduces the concept of a quorum slice, the subset of a quorum that can convince one particular node of agreement.

These quorum slices may or may not intersect. enter image description here

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