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So in the first case, the statechain would act as a Layer 2, with Lightning as more of a Layer 3; And the second case, Lightning and the statechain are sort-of inter-operable Layer 2s?
Yes, king of. LN would still be as it is, but a channel would be opened on top of a statechain. Second case, yes - it is just part of the process of rebalancing without needing to go on-chain.
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