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Note that the tree being discussed here is not the one from Nash's orthogonal proposal where nodes in the tree track resources allocated to subtrees. Nash's proposal allows uniting multiple blockchains into a tree, but does not guarantee that any code executed on one chain did so properly. Therefore, the distributed purse design using zero-knowledge proofs that works in the models above would not work, because names can be forged and balances inflated in a low-security node; in order to move value from one node to another, a contract has to interact with a parent node to track the movement of that value.
Outcome of April 27th meeting:
Tree of arbitrary depth with a lattice on the leaves. Transactions at the top will be expensive, so there will be a tradeoff between wanting to be at the top (have to validate a lot) versus being lower in the chain (faster and tighter interactions).
Creating a lattice at the leaves implies that one will need to bring watchers or able to invite validators.
We provide an initial set of nodes - a frame to the tree.