On Appchains vs Shared Rollups

The recent EpicWeb3 podcast episode (https://www.youtube.com/watch?v=jeuq12699aA), we talked a lot about the tradeoffs between these two "kinds" of rollups. I want to write more on why I'm in love with the appchain concept and why it's so powerful, but today I just wanted to bring this thought: You don't have to choose between Appchains and Shared Rollups! Isolation is great, but not everything should be fragmented. Sharing is great, but not all resources should be decided by an auction. There is a middle ground here; it is possible to have application-specific rollups with shared state, and I believe that is the best design. Imagine different app-chains with instant/atomic one-way composability. Imagine applications being able to fully customize themselves, enjoying all the benefits of being the sole owners of their blockspace, and simultaneously sharing a financial state layer with others. At @cartesiproject, we've been contemplating these designs for a while and call the one we like the most "Cascades." There are different ways to implement this design pattern; let's discuss the most naive one just to exemplify: Imagine a DEX, "A," with price information for every cool token out there. Now, consider application "B," which creates index products on top of those tokens. Application "B" can observe application "A," tracking all its inputs and replaying its state. Every input that arrives for "A" is also monitored by "B," ensuring that "B" always knows the state of "A." Picture another application, "C," also interested in token prices; it can perform the same process. Now, the state of "A" is available and shared between "B" and "C." In this setup, for "B" and "C" to communicate with "A," you'd still need to navigate the normal L2 <> L2 composability hurdles. However, the other way around is instant, atomic, and free. And Cascades naturally maps into the autonomous worlds thesis (a not-to-be-underestimated bonus). In summary, you have application-specific rollups that can CUSTOMIZE which percentage of their blockspace will be dedicated to shared state. I'm trying to think of a name for this concept; any suggestions? "Fusion Rollups" comes to mind because it's a fusion of shared and app-specific, but it's also different apps getting combined together.

I usually post my thoughts on X (twitter), but since there has been a lot of talk about fragmentation of liquidity and composability concerns, I thought about bring this discussion here as well :)