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By design, they will always remain unable to directly affect the 1st layer. This is an important safety feature for the first layer. But it will always be possible to "port" proven, desirable functionality from the 2nd layer to the 1st layer. And a 1st and 2nd layer account can be "linked" via a common private key.

And a 1st and 2nd layer account can be "linked" via a common private key.

That sounds interesting. I tried to think if there would be a use case for the common private key, other than linking the two accounts together. Since L2 can't influence L1, but vice versa could potentially happen, if L2 allows it, I wonder how that can be used.