Hi there! I was looking through some old research papers about merge-mining and came upon this thread. I'm very interested in your proposal as it seems like a great way to shard state without losing security via merge mining! I have a question for you though: If miners have to verify all the state that passes up to Prime, they have to run a full node so that they have the state of all the blockchains to properly verify everything. They are incentivized to do this so that they don't mine invalid blocks, but in doing so they might put a strain on the network because their zone and region nodes are not necessarily in the same geographic region as the rest of the zone and region nodes. (Of course, the zone that the miner is located in will be optimal, but I am talking about the rest of the zones and regions necessary for running a full state node).
For example, for n zones, n/2 regions, and m miners running a full state node, we have m - 1 latent nodes in each zone (or n*(m-1) latent zone nodes total) and m - 1 latent nodes in each region (or (n/2)*(m-1) latent region nodes total). Do you consider this an issue for network latency? Is there perhaps some way or incentive for a miner to run a full node and also run each sub-node (zone and region) in the proper geographic location? This might be physically difficult without the use of some cloud provider like AWS.

Looking forward to hearing more! Thanks.