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Ethereum docs says:

However, occasionally validators might be offline when called to propose a block, meaning slots can sometimes go empty.

What happens when the randomly chosen validator is offline? Is the slot closed as empty, or is there a mechanism to choose a validator N number of times before the slot is considered empty?

Let's say there are 3 total validators(A, B and C), of which A is chosen to be the validator. But, A goes offline. Is the slot marked as empty, or is there an algorithm that chooses the next available validator(let's say B)?

Is there a heartbeat mechanism or a time-out mechanism when a validator is chosen? How does the network know the validator is alive? Let's say A was online when chosen by went offline right after it was chosen.

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When a validator selected for block production is offline, the network will not have a block in that slot (the slot is considered to be a missed block, or empty) and it simply progresses to the next slot. I don't think there is a mechanism to choose a validator N number of times before the slot is considered empty, but instead, further proposals or attestations are built on the last block available from a former slot.

A randomly chosen validator has 12 seconds of time to propose a block. In this case, the network knows the randomly chose validator is online when that validator successfully proposes a block within the 12 seconds interval.

See:

https://consensys.net/blog/codefi/rewards-and-penalties-on-ethereum-20-phase-0/

https://kb.beaconcha.in/glossary

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Each slot is every 12 seconds, and each slot has only 1 assigned block proposer: the lucky validator that creates the block for that slot.

If the block proposer is offline, the slot remains empty: the head of the blockchain should remain the same.

An epoch is 32 slots: 6.4 minutes. Along with the slot, the epoch is a heartbeat mechanism. An optimal validator will publish an attestation at every epoch. At every epoch, you can estimate which validators are online by seeing which ones have published an attestation. At every slot, you can estimate if a single validator is online by seeing if it proposes a block.

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