It's easy to know why they work. The magic invocation increases test-time compute (easy to verify yourself - try!). And an increase in test-time compute is demonstrated to increase answer correctness (see any benchmark).
It might surprise you to know that the only different between GPT 5.2-low and GPT 5.2-xhigh is one of these magic invocations. But that's not supposed to be public knowledge.
They never parsed your prompt. The magic word reduces the probability that the token corresponding to the end of chain-of-thought will be emitted, which increases test-time compute.
It's easy to know why they work. The magic invocation increases test-time compute (easy to verify yourself - try!). And an increase in test-time compute is demonstrated to increase answer correctness (see any benchmark).
It might surprise you to know that the only different between GPT 5.2-low and GPT 5.2-xhigh is one of these magic invocations. But that's not supposed to be public knowledge.