Fixed input-to-output mapping is determinism. Prompt instability is not determinism by any definition of this word. Too many people confuse the two for some reason. Also, determinism is a pretty niche thing that is only necessary for reproducibility, and prompt instability/unpredictability is irrelevant for practical usage, for the same reason as in humans - if the model or human misunderstands the input, you keep correcting the result until it's right by your criteria. You never need to reroll the result, so you never see the stochastic side of the LLMs.

However, if you evaluate carefully the LLM core function, i.e. in a fixed order, you will obtain perfectly deterministic results (except on some consumer GPUs, where, due to memory overclocking, memory errors are frequent, which causes slightly erroneous results with non-deterministic errors).

So if you want deterministic LLM results, you must audit the programs that you are using and eliminate the causes of non-determinism, and you must use good hardware.

This may require some work, but it can be done, similarly to the work that must be done if you want to deterministically build a software package, instead of obtaining different executable files at each recompilation from the same sources.