Yep, that's a perfect minimal example of the kind of thing we could do. Exactly how to 'extend' the computation depends on how it's set up. What you describe is

Yep, that's a perfect minimal example of the kind of thing we could do. Exactly how to 'extend' the computation depends on how it's set up. What you describe is possible, as are more elaborate applications in which the 'result so far' includes a log of all previous results (basically a memoized table of the recursive computation so far). If you have a proof that the merkle root of this table is correct, then you can just look up any so-far-known value. Taken to its extreme, this could be used to produce a collective database reducing arbitrary deterministic functions to lookup — what I think of as 'compute-addressable' (riffing on content-addressable) data. Since Lurk can express arbitrary computation in its own data language, such a universal database wouldn't strictly require per-function circuits (though for performance, some customization will help).