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I understand that the plan is to have shards with Ethereum PoS. I am trying to have a mental picture of how that will work. Basically when a wallet signs a transaction, what determines which shard of the block chain it would be added?

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With rollups, the focus has shifted to sharding data, rather than sharding execution:

https://ethereum-magicians.org/t/a-rollup-centric-ethereum-roadmap :

sharding data availability is much safer than sharding EVM computation

Rollups (which are on layer 2) need data availability (on layer 1) and data shards will provide them with much more capacity. Briefly, rollups need layer 1 because a key property of rollups is that even if the rollup sequencer is malicious, a user can always submit their transaction on layer 1 to secure their assets (and penalize the sequencer).

When a user signs a transaction on layer 1, it will go in a beacon block.

When a user signs a transaction on a rollup, the rollup sequencer determines which data shard to put the (compressed) transaction data on.

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