Can You Build a Solana-like Rollup?

Would be theoretically possible to build a rollup / L2 platform that uses the Solana proof-of-history consensus?

In particular, how could this type of L2 inherit security guarantees from the Ethereum L1?

I am less interested in solutions like Polygon, which are more sidechain-like in nature.

Is this theoretically possible? If not, why not?