But there are many valid systems of normative rules. If there is an absolute morality, that means that one such system must be identified as special in some way. The thing that makes correct physics special over other possible descriptive theories is that, in this universe, it accurately predicts events. What about absolute morality makes it special as compared to other systems of normative rules?

In the sense of "deny" as in "refuse to accept the truth of it", I did not deny the existence of absolute morality, I disproved it under a certain meaning of absolute. You have yet to show flaws in my reasoning or to counter with an alternate meaning of absolute where absolute morality is valid. Your original question "Is there anything absolute according to your defintion?". I need to rephrase this in terms of my definition of absolute; "Is there anything that has meaning in all contexts?". This is to avoid the confounding alternate senses of the word absolute. The answer is no. This is because I can always find or generate a specific context that does not provide meaning to anything proposed to have meaning in all contexts. For most cases I could simply use electrons as the context. For example, electrons don't have property X, or are not influenced by X. X is meaningless to electrons. For the few cases where this fails I could use algebra. Algebra doesn't contain a meaning for X. This allows us to get rid of the word absolute and to rephrase the problem as "Can the same morality be applied to all possible cases of level-3 intelligences.". For the common meaning of morality I think that this simply can't be done. As I've been saying, its all about context. Eliezer Yudkowsky's Baby Eating Aliens highlights clashing moralities. Ideally I don't hold beliefs about anything that happens outside of physical reality. If you notice beliefs of that nature point them out and I'll reconsider them. You should feel free to always assume that I don't believe that my claims apply outside the physical universe. I can't answer this question directly for several reasons. I don't know what would convince you. In your current context you may simply be unconvincible. Also, I've actually argued that nothing is absolute for a specific meaning of absolute, so I'm not inclined to now argue that physical reality is absolute. However, I will try to say something about the belief in

Relevance is the right question. When dealing with purely abstract concepts like mathematics, it's useless to ask whether they exist. It's extraordinarily unlikely that any empirical evidence could persuade me that 1+1 does not equal 2, but I can realistically doubt whether the addition of natural numbers is a good model for counting clouds. Similarly, the question should not be whether the absolute moral system you believe in is true or valid or genuinely universal, but rather whether it accurately and precisely models how you judge and desire. Since you could stop having desires and making judgments without damaging your belief in your absolute moral system, it seems reasonable that you could alter them as well, or even that you have already done so. How sure are you that what you believe to be fundamentally morally right matches what you actually want?

No, we have an absolute moral system per person. You can then take groups of those moral systems and combine them, in various different ways such as simulating what they would decide if they voted. However, you will get different results depending which combining procedure you use, and what sort of people you put into the combining procedure.