I'm not saying the value of the returned information is equivalent, of course. But being "just a pointer" into a larger store isn't, in itself, the problem to me.
Because new books are written?
It feels to me that you are set on insisting that a prompt and an ISBN are the same, and no amount of logic will move you from there.
You are quite right that you're not convincing me of your original thesis that that a prompt contains the entire content of the reply in a way that some other reference to an entity in some other pool of information to doesn't. That's not the same as saying "ISBNs and LLM prompts are the same thing", which is a strawman. It's saying that they're both unambiguous (assuming determininism) pointers to information.
Of course no-one is disagreeing that a reply from a deterministic LLM would add no information to the global system (you, an LLM's model, a prompt) than just the prompt would. But I still think the same is true for the content of a book not adding to the system of (you, a book store, an ISBN).
In fact, since random numbers don't contain new information if you know the distribution, one can even extend it to non-deterministic LLMs: the reply still adds no information to the system. The analogy would then be that the book store gives you at random a book from the same Dewey code as the ISBN you asked for. Which still doesn't increase the information in the system.
Is it possible to get the same output, 1:1, from the same prompt, reliably?
And yeah I guess if you control the seed an llm would be deterministic.