Can it exist in a moral context?
As 2+2=4 is absolute, can we also consider that a certain action or way of doing things is absolutely the right and best thing to do? I think so, how about you?
The short answer is yes, but it is still an incomplete field of philosophy. That does not mean ethics are subjective, but rather we've yet to discover how it properly works.
One of the big reasons you can tell that it is not arbitrary is precisely the reason you asked the question. If it were arbitrary and subjective by its nature it would not occur to you or to anyone else that it should not be thus.
It suffices to say, if you take the rational egoist approach, you get into praxeology and psychology and (Aristotelian) virtue ethics; These are the branches of science that study action qua action, the motivation for action, and those actions which will make us happy in almost every case, and these are probably the branches which will develop the science of ethics into the future.
Here I will point out, although needlessly, that ultimately humans are the ones interacting -- ethics pertains to interpersonal standards of behaviour -- therefore any truth about ethics must come from either the human construct, or a physical construct that the human body follows.
Truth is so subjective. You'd be hard pressed to find an objective measure of this. Yes, theoretical math like 2+2 is absolute b/c we have all agreed to the rules and guidelines. Even simple real life math is not always absolute. For instance, if you want to add 2 apples, first you have to define apple. If one person says an apple is fully grown and ripe, and another says even the most immature apple on a tree is an apple, you may have two different outcomes while adding various apples.
Your proposition is that definitions are not well agreed upon. I disagree: given the amount of communication that takes place in the world, most definitions are well agreed upon. Further, the fact of poorly defined concepts does not preclude the fact of truth. If you have a bad telephone line to emergency services and are thereby unable to communicate effectively, then this does not change the fact that your building is on fire and you need a firetruck.
However, for something like beauty for instance, there is no textbook. We all have different gauges, wants, and tests. For the individual most everything is absolute if it is what you believe to be true. Girl 'X' is pretty for example.
This is also false. Firstly, there exists such a thing as a perfect female form, this much is scientifically demonstrable: even features, right height, 70% waist to hip ratio, etc etc, and we have the capacity to measure reactions in the brain to these various images. (I'm sure you can find those studies and look them up yourself.) But as to the subjective value structure that people walk around with in their heads, it isn't actually subjective, we just think of it that way.
The problem is a big one philosophically. It is the lack of knowledge, especially of the future, but also of the present. Each human lacks an incredible amount of knowledge about his environment. We have total tunnel vision: one small view point for a few short years.
What we choose is generally the best option open to us given the information we had. If all information traveled everywhere, instantaneously, all the time and for free, then it seems likely that everyone would arrive at the same conclusions about everything. That is: if you knew exactly what I know, and I knew exactly what you know, then debating is pointless. By sharing experiences we would no longer disagree.