Apple

On which part exactly? If you mean "threatening the LLM can improve output", I haven't looked into studies, but I did see a bunch of examples while the whole topic started. I can try to find some if you'd like.

If you mean "it simply requires the probability distributions to be positively influenced by the additional characters", I don't know what kind of evidence you expect. It's a simple consequence of the way LLMs work. I can construct a simplified example:

Imagine you have a dataset containing a bunch of facts, e.g. historical dates. You duplicate this dataset. In version A, you add a prefix to every fact: "the sky is green". In version B, you add a prefix "the sky is blue" AND also randomize the dates in the facts. Then you train an LLM on both datasets. Now, if you add "the sky is green" to any prompt, you'll positively influence the probability distributions towards true facts. If you add "the sky is blue", you'll negatively influence them. But that doesn't mean the LLM understands that "green sky" means truth and "blue sky" means lie - it simply means that, based on your dataset, adding "the sky is green" leads to a higher accuracy.

The same goes for "do not hallucinate". If the dataset contains higher quality data around the phrase "do not hallucinate", adding this will improve results, even though the model still doesn't "actually understand what it's saying". If the dataset instead has lower quality data around this phrase, it will lead to worse results. If it doesn't contain the phrase at all, it most likely will have no effect, or a negative one.

Again, I'm not sure what kind of source you'd like to see for this, as it's a basic consequence of how LLMs work. Maybe you could show me a source that proves you correct instead?