Can blue sky control a session key and sign stuff?

This is super cool!

A local censorship fault will not be automatically by all the other chains. So it has to be long enough such that all the LPs detect it and exit.

Yea. That’s fine. Local amm code takes over the last valid root in exit mode. So all the LPs can exit

Nah, you need some timeout. If sequencer posts a different block on every chain, it could double spend and instant exit local coins.

I think you can guarantee instant finality by executing locally. But not 100% sure.

Sequencer signature must work on all chains, so once you have the data locally, you can always post it to the remote. All you need is a sequence number to prove it signed a different block for the same height.

Just a sequence number for each rollup block will work. The nodes can copy from local chain and post it to the remote at any time since the sequencer already signed it locally.

Sequencer would have signed conflicting blocks or roots.

If the data or roots on any of the chains diverge, that’s a fault and a local implementation takes over the last valid root and everyone exits.