Yeah, we’ve discussed the possibility of relaying linearizations or other cluster/chunking information along with transactions.
It’s hard to make it a requirement however, because the sender’s cluster might not be the same as your cluster, and requiring that they’re identical would permit even worse attacks, by an attacker attaching different incompatible transactions to the same cluster for different peers.
Still, it is possible to do this as an independent improvement, because the linearization merging algorithm can always be applied between the linearization received over the network, and the linearization the receiver already had for a cluster, even when the clusters aren’t exactly identical.
Because of the above however, I don’t think it can remove the need for having a fast-but-good-enough from-scratch linearization algorithm that can run at relay/tx processing time.