Thank you. Now I have a clearer view of it, although I dont know if I will have more doubts about it when I finally figure it out on my own.
Regards.

In an arithmetical sense, 3+5 results 8, for example, same as 1+7. I know it seems overly simplistic in this example but that is my intention, because it extrapolates to any possible extent. In this sense, is reality a cause or an effect? and, if two causes can result in the same effect, is "reality" objectively undetermined and determined only by our imagination, as how I imagined a subjective yet feasible cause?

juxtaposing object and subject leads to incoherence. — Banno

I perceive this is a prejudice. Understanding is not conceived without prior evaluation.

So perhaps more along the lines of willingness to process when talking about a concept? — Regretomancer

I think this is a good starting point; I will try to figure it out on my own. However, do you think of it as something immediate?
and specifically in that regard, how would you define willingness?

Consider the person who “accepts” a certain law, but nevertheless disagrees with it. — Pinprick

That depends on what one considers acceptance because, in that case, disagreeing is a direct opposite of believing, and in the most abstract sense, to accept is to believe.

note: not believe but to believe; and my confusion lies in what that distinction implies.

Or, if you want to think about it in different terms, it’s possible to accept something cognitively, or intellectually, but not emotionally. — Pinprick

I think what you mean by accept something cognitively and or intellectually is just recognition. I'm not sure what you precisely mean by emotionally... maybe to sublimate a suffering? because although I think of acceptance as a gradual process with several interrelated elements involved, it would be also not appropiate to infer its nature from the individual point of view of some of them.

Acceptance is the opposite of rejection

I really know about its opposite same as itself; only confusion.

the term acceptance implies more than factual acknowledgment

Not exactly an acknowledgement but rather a recognition, acceptance implies more than factual recognition. I think acknowledgement would be far beyond recognition in the way of acceptance; as I think of it as a process, rather than an immediate ability.

Part 2 means the same thing, but with ideas, such as accepting the truth of a statement or belief system.

In that sense, what does it precisely mean to "agree"? because even though an idea seem reasonable and often even evidently feasible, there is struggle including that particular idea or rationale in one's belief system. So my question would be better formulated as: "What does it psychologically implies to accept something?"

Also, you would agree that although many people boast of having accepted an idea, they sooner or later come back to their initial belief system status, so to speak, thus, the fact of accepting the reasonable quality of something does not directly implies accepting it itself.