bitcoin sv – Callback from compute thread to root UTXO without trusted third party signature

There are no Bitcoin experts. From what I understand, the loop can be done by storing the hash of the code needed to run the next iteration in a UTXO, then creating a new UTXO in the next iteration and running it from there. And this works for indefinitely long loops as long as someone pays for each step. It is assumed that anyone can be programmed to sign for each step (thus eliminating dependence on specific third parties).

What I’m interested in is if there is a way to return the result to the “root” UTXO in a way that doesn’t depend on the result and can authenticate that it came from a “thread” started by the root. A trusted third party signs the callback. I can’t think of a way to do that. This is similar to what I described previously. The thread itself can be stirred up without any specific third party signing it.