Which word means to acknowledge the existence or truth of something?

The term that means to acknowledge the existence or truth of something is "recognise." When you recognise something, you are admitting that it is real or valid, which involves a level of awareness and acceptance. This aligns perfectly with the concept of acknowledging existence or truth.

In contrast, other options present different actions: to manipulate generally means to handle or control something in a skillful way, often with a connotation of deceit or unfairness; to propose refers to putting forward an idea or suggestion for consideration; and to modify means to make changes to something. None of these terms convey the acknowledgment or acceptance of existence or truth in the same manner that "recognise" does.