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.
Can you rephrase that statement? I'm having trouble parsing it; it sounds like you are saying opposite things one after the other.
The block producer makes sure his partition (the one he is validating) is valid. Thus he will never lose his block rewards. He marks the block as only guaranteeing the partition(s) he has validated, so any other partitions included are informational but not Nash equilibrium confirmations. Re-read my prior post with that in mind. Again this is only valid for strict partitions (no cross-partition) transactions system.
The partitions can be thought of as separate block chains, that have been interleaved into one block chain with orthogonality between them. It is a more granular generalization of merge mining, because each block producer can choose which partition(s) he is validating and risking his block reward on in terms of the Nash equilibrium. Since all partitions eventually get confirmed by a block producer, then the overall Nash equilibrium is sustained on the coin's external market value.