The plasma system defines a structure of interconnected blockchains arranged in a tree structure that promises scalable smart contracts. One of the key ideas there is that each of the blockchains regularly store their current block hash in their parent chain so that users can challenge potentially invalid child state transitions in the parent chain.
This model is secure not because of a difficult proof of work (the chains would use proof of stake or even a fixed validator set), but rather because users watch chains they have a stake in and thus will challenge invalid state transitions, potentially escalating as far up as the trusted main chain.
Here, the scalability does not come from the fact that blockchains are relieved from their load by creating a big number of smaller chains and moving the transactions there. Scalability is only achieved once a user does not have to verify every single transaction that is sent to the system.
If, for example, a user only cares about a single smart contract that resides in a single chain in a leaf of the system, it is sufficient for the user to verify this leaf and all nodes on the path to the root chain. If a transaction is committed by means of block hashes all the way up to the root chain and there is no invalid state transition in the chains on the way up to the root, the user can be reasonably sure that the transaction cannot be retroactively declared invalid.
This system still does not solve the scalability problem: As long as the smart contract only lives inside a single blockchain, it can merely process a limited amount of transactions. While this might be enough for some use-cases, a token contract can easily reach this limit. The system would scale, if the token contract exists on all of the blockchains, dividing the token transfer load and it is possible to move tokens up an...