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Currently I think blocks look like [previous block hash + transactions + nonce], such that the hash of all that is less than the difficulty. After Casper what will it look like? I guess there is no point in the nonce and the hash of the block will be irrelevant.

After the switch to Casper is there anything stopping Ethereum being cloned and someone simulating it themselves and creating lots of valid blocks at no effort? With proof of work that couldn't have happened as they'd still have to mine to find the correct nonces.

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@atomh33ls references Block header structure change under Proof of Stake? as an answer to your first question. To answer the second, I interpreted your question as asking about attacking Casper with a sybil attack, as opposed to what your question seems to be more literally asking, which is to create your own private fork of Ethereum (if so, the answer to that is: no one is using that malicious fork).

Even with Casper, the rules of the protocol must be followed, so there still cannot be "cloning" of ether -- every ether must be in one place or another and can never be in two places at once. Also, to prevent a sybil attack, Casper requires validators to stake ether. Votes are effectively weighted by amount of ether held; since validators may, according to the Mauve Paper linked to, place finality bets across shards, an attacker must hold a large amount of ether to mount an attack -- the paper places an estimate of 40% of ether used for staking. Given the constants (32 minimum ether per validator, 80 shards, 100 validators per shard), at minimum, an attacker needs 102000 ether (~0.1% of the ether presently in existence) if every other validator is only staking the minimum amount of ether. If a bank were threatened by Ethereum, it could probably easily muster the ~$30M USD (at current exchange rates) required to mount such an attack, but would have to expect that amount to be lost when confidence in Ethereum were broken. This amount is out of reach of most individuals, though, and it wouldn't be a way to "get rich quick" as the price of Ethereum would likely drop in response and/or a patch would be made like when a bug allowed an excessive amount of Bitcoin to be paid as a miner reward.

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