Afaik there are basically two ways to solve this:

- run the algo on the client

- run it on a smart contract

A server can't prove that it hadn't changed iy

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yes, it has to be done on the client. that's what I'm developing at https://nostr.thecaptain.dev

I client like this can also run as a self hosted server app

Did you see the last post using STARK proofs on Nostr DVMs to verify computational execution?