Celestia does not support smart contract capabilities because it is designed to provide data and consensus for rollups, which will support them.
One advantage is that rollups will be able to explore new novel designs for settling proofs.
One approach is for rollups to distribute proofs directly on the p2p network.
In this case proofs aren’t posted on any settlement layer, they are verified locally by clients of the rollup. This is similar to how @MinaProtocol works.
Another model is for rollups to utilize a settlement layer for proof verification or dispute resolution.
The settlement layer is also helpful for cross-rollup communication and provides an exit mechanism for rollup users.
This is similar to how Ethereum rollups work today.
Both the rollup and the settlement layer submit their data to Celestia for availability and ordering which provides shared security to the entire stack.
This shared security extends to all the rollups that are deployed on Celestia.