Finalized Blocks/Slots in PoS Ethereum. (theoretically) After how many Slots will an Epoch be finalized?

Question

What I'm trying to find out is: After how many Slots will an Epoch be finalized (theoretically)?

The first block in each epoch is a checkpoint and validators then vote on pairs of checkpoints that are considered valid [link]

Once a checkpoint gains a supermajority vote (2/3 of staked ETH), it becomes justified. When its child checkpoint gets justified, it is upgraded to finalized link

Let's have the following:

• 3 Epochs:

  • Epoch-A in stage justified, Checkpoint is A
  • Epoch-B in stage proposed, Checkpoint is B and B is a child checkpoint of A
  • Epoch-C in stage proposed, Checkpoint is C and C is a child checkpoint of B

• The Chain is processing Epoch-C

• When 2/3 of the validators vote on the pair checkpoint (B, C) then checkpoint B will be set as justified. Because checkpoint B is a child checkpoint of A then Checkpoint A will be finalized means Epoch-A is finalized.

Question: Is the following conclusion correct?

In a perfect world (no latency, no voting conflicts, no empty slots, and everyone votes) Epoch-A will be finalized after the 22nd Slot of Epoch-C. This means the last Block in Epoch-A will be finalized after about 54 Blocks and the first Block in Epoch-A after 85 Blocks. Is this correct or am I missing something :D?

Answer 1

To answer your question, I restate what is exactly justification and finalization:

All validators make one FFG vote per epoch. This vote contains a checkpoint source and a checkpoint target. If validators constituting more than 2/3 of the total stake make the same FFG vote (same source and target), the target gets justified, and we say there is a supermajority link between the source and the target. If a justified checkpoint is the source of a supermajority link having as target the checkpoint of the next epoch, the checkpoint source gets finalized¹.

So: After how many Slots will an Epoch be finalized (theoretically)?

It is important to remind here that a finalized epoch is an epoch where its checkpoint is finalized. You also rightfully precise the conditions:

no latency, no voting conflicts, no empty slots, and everyone votes

The answer is 54 slots.

We can see this with an example: Starting at epoch A, the checkpoint will be justified after 22 slots since 2/3 of the validators will have voted and made the same FFG vote. Then the epoch finishes, and epoch B starts. The checkpoint of epoch B gets justified after 22 slots since 2/3 of the validators will have voted and made the same FFG vote. This finalized the checkpoint of epoch A. The finalization has occurred in 54 slots.

This is true theoretically (as stated in the question). In practice however, validators wait for the end of an epoch to finalize new checkpoints. The response can thus be 64 slots.

---

1. I voluntarily omit one case of finalization for simplicity.

Answer 2

As far as I understood, an epoch, along with all the blocks of which it is composed, is only considered finalized after the progression of two more epochs after it. In other words, it takes two justified epochs (a “justified” epoch meaning the majority of validators agreed on it) for those epochs, and all the blocks inside of them, to be considered finalized.

In a perfect world (no latency, no voting conflicts, no empty slots, and everyone votes), this means Epoch-A will be finalized after all the slots of Epoch-C have been justified. That is to say, Epoch-A will be finalized after 64-95 slots have been justified.

See:

https://www.coindesk.com/tech/2021/01/08/ethereum-20-explained-in-4-easy-metrics/

https://notes.ethereum.org/@vbuterin/single_slot_finality