Afaics, my point was unarguable. I already explained why. Strict partitions can coexist in a block with other transactions without causing the block to be invalid. The block becomes orthogonal to whether any of the partitions in it are valid or not. The key point is that the partition for which the block producer is guaranteeing is valid (i.e. has validated) has to be truth, else that block producer will lose his block reward if another subsequent block offers a proof-of-cheating on that partition. You can think of these proofs as equivalent to not mining on that chain in Bitcoin where Bitcoin has only one partition. Subsequent blocks can correct any deficiencies with proof-of-cheating, thus any cascade of lies is contained within the partition and can be corrected at any time by any proof-of-cheating. Same as for Bitcoin, the users of the currency have to trust full nodes but they should only trust a confirmation which was betting its block reward on that partition the user is relying on.

So in effect what this does is interleave a merge mining of separate "chains" into one block chain, one "chain" for each partition.

You made the assumption that the only way for block producers to veto a lie, is to not mine on the chain that contains the lie. But as you see, there are more flexible possibilities for a design.

I don't know if it is also very useful, yet it does stand as an exception to your desire to pigeon-hole the analysis. I try to have a flexible mind and consider all possible angles.