Honorable Rabbi, hello,
Regarding morality and mathematics, the Rabbi agrees that these are realities that exist outside the person, which a person can contemplate in some way and reach conclusions about. That is, in these areas too we are dealing with a process of at least observation. In light of this, I do not understand why the question whether the Holy One, blessed be He, prohibited or commanded something is not a factual question. After all, if there is a prohibition then it has legal force, and if the Sages derived it incorrectly then it has no force at all. As far as I understood, the Rabbi does not hold that the Sages create the word of God, and the Mishnahs in Horayot would prove this.

Norms are not facts in the physical sense. With regard to them, the concept of authority does apply. The norms that obligate us are not those that the Holy One, blessed be He, commanded, but those that interpretation extracted from the Torah. And this is “It is not in heaven.” The Mishnahs in Horayot deal with the question of which interpretation is binding, not with the question of interpretation versus the truth.
According to your approach, there is no such thing as norms. Everything is facts.

Honorable Rabbi, thank you for the quick reply, but I still did not understand the reasoning for why authority applies with regard to norms. Does the Rabbi hold that authority also applies with regard to moral norms? After all, just as the physical world is external to the person and the person observes it and infers the physical facts from it, so too the moral world is similar in exactly this sense. That is because a person does not create morality, but rather looks outside himself and infers in some way what the moral act or the correct moral law is. I am aware that with regard to morality the conclusions are not always as unequivocal as in physics, but it seems to me that we would not accept authority as deciding what the moral act is. In my humble opinion, the rules of logical inference function in the same way as well, that is, by contemplating objective rules that exist outside the person and deriving conclusions accordingly (and there, of course, the results are even more precise than physical results).
In light of this, if the Rabbi agrees that moral, logical, and physical truths are not to be accepted on the say-so of one authority or another, I do not understand the distinction between moral norms and halakhic norms.

There are two differences between the two contexts, which of course are connected to one another:
1. A factual claim reflects the fact it describes. Therefore there is a clear correlation between them. So an incorrect factual claim is incorrect because it does not fit reality, and authority is irrelevant to it. But a normative claim speaks about what obligates me, not about what exists in reality. True, I hold that the person deciding a moral question beholds the idea of the good, but the result is not a description of what he sees; rather it is a derivation (interpretation and application) of what he sees. And here there can be disputes.
2. A normative claim deals with the question of how one should behave, not what one sees. If you ask what the idea of the good says, then there is one truth about that and no authority. But when you ask how one ought to behave (halakhically, legally, or morally), there the concepts of authority do apply, since one can require a person to act in a certain way even if it is not correct. One cannot say that this is the correct thing, but one can require acting this way.
An example is the legal system. There too the question is what the law and/or the legislator says. And still, the interpretation of the courts is what is binding, even if in my opinion they are mistaken.