can you use zk snarks to prove an application binary is compiled from specific unmodified source
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AFAIU most implementations essentially have this property; that is, the validation procedure effectively checks the value of each step of the computation, and it would in general be intractable to manufacture a distinct program which nevertheless has the expected steps.
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The details depend on the specifics of the implementation, but see e.g. vitalik.ca/general/2019/0 for one representative scheme.

