What you're describing is decontextualization. A sufficiently powerful transformer would theoretically be able recontextualize a sufficiently descriptive natural language specification. Likewise, the same or an equivalently powerful transformer should be able to fully capture the logic of a complicated program. We just don't have sufficient transformers yet.

I don't see why a complete description of the program's design philosophy as well as complete descriptions of each system and module and interface wouldn't be enough. We already produce code according to project specification and logically fill in the gaps by using context.