What kind of app could take advantage of this on Nostr?
Anything that requires computation. Picture a DVM that runs a filter to find the best posts for you. Today, even if you know the DVMs code, you need to trust the DVM to run it. With this, you can ask the DVM to run and check if the result was from the code you were expecting.
To verify your thread algorithm I see. Could be done on Twitter or any other platforms that open source their algorithm. Quite an heavy verification to run though given all the parameters and search results. There is a ton of unlocking potential on a platform with digital ownership like Nostr, verified computation is not the most obvious to me yet, but it will certainly happen, big time
Is this what is called zero-knowledge proof?
one of them, yes.
I think this only makes sense to use when it's very many users are interested in the output, because generating such a proof can be orders of magnitude costlier than just running the code.
Sending signed events is also orders of magnitude more expensive than just the data of each post and we do it anyway :)