What kind of contemplation constitutes direct perception (pratyakṣa)?

What kind of observation counts as direct perception/valid direct cognition? For example, when we observe the illusory nature of the aggregate of form (rūpa), birth, aging, sickness, and death, all of us can observe these directly in the present—this is direct perception. But the momentary arising and ceasing of the physical body is something ordinary beings cannot observe. If, based on the principle in physics that electrons arise and cease in an instant, one infers that the physical body arises and ceases moment by moment, does this kind of inference also count as direct perception? In fact, the momentary arising and ceasing of the physical body may be something that only the Buddha alone could observe directly; it requires extremely deep meditative concentration and profound, subtle wisdom—without extremely deep meditative concentration, it is absolutely impossible to observe. We can only know it through inference; if such inferential knowledge is correct and accords with the Buddha's authoritative teaching, then it can also provisionally be called direct perception.

For example, following the Buddha's teachings, we observe the arising-ceasing, illusory nature of the universe and the material world (the inanimate container-world). In reality, we cannot directly observe with the eye consciousness the arising-ceasing, illusory nature of the universe and material world before us, because our lifespan is too short—we do not have a sufficient span of time to observe the phenomena of arising and ceasing in the universe and material world; the universe is also too vast, and our range of vision too limited, to observe the material world as a whole. However, if through proper contemplation within our minds we can ultimately genuinely accept this principle, this too counts as directly realizing the arising-ceasing, illusory nature of the universe and material world. It is the result of contemplation that accords with the Dharma and with reason, and is not erroneous cognition/non-valid cognition.

Take another example: when criminal detectives solve a case, based on the evidence of the criminal gathered at the scene, they employ methods of inference and erroneous cognition/non-valid cognition—such as thinking, reasoning, and deliberation—and finally crack the case, bringing the truth to light. When the results of such inferential and non-valid observation are correct, this too is a realm of direct perception. In other words, any inference through inference or erroneous cognition that accords with the facts also counts as a realm of direct perception. Take another example: when students solve geometry problems, they likewise arrive at the proof of a problem's correctness through modes of thinking involving inference and erroneous cognition; this too is a realm of direct perception. Although we cannot directly observe the momentary arising and ceasing of the physical body in the present, we can ultimately verify this point through contemplation and contemplative practice (vipaśyanā-caryā) that accord with the Dharma and with reason; the result thus obtained is a realm of direct perception.