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I was wondering about block import in particular about invalid blocks: What are the consequences of a block being deemed invalid/failing block import - except well for the block not being imported. Is there any punishment for the block author for example?

Related: The block producer will try to import its own block as far as I know, if that fails I would assume it won't distribute it over the network. So even if there were a punishment for invalid blocks an honest node should never get punished, because even if it produced an invalid block for some reason, it would not distribute it.

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Is there any punishment for the block author for example?

No there is no punishment. You can not really proof that a block is invalid to the runtime. Yeah, you could do similar to what Polkadot is doing with PVF validation, but you can also just rely on the fact that the block author is loosing its reward. The reward should be incentivization enough to not send invalid blocks. An author can also just send one block per slot as otherwise they can get slashed for equivocating (which can be proved to the runtime).

The block producer will try to import its own block as far as I know, if that fails I would assume it won't distribute it over the network.

No, block authors to not re-execute their own block. They just import the state changes directly to the db. So, they could potentially miss that their block is invalid, but as I said above they will not get punished for this.

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