What is a core of the negative existential statement?

The third puzzle is concerning the negative existential statements, where we are going to use the example sentence of ‘the golden mountain does not exist’ while we outline this problem. ‘’Russell is able to give an account of how a speaker may be committed to the truth of a negative existential without also being committed to the belief that the subject term has a reference.’’. That is: the case that Scott does not exist is false since it is self-contradictory. In the end, if we were to explain this, there at least must be something that is identical to Scott as it is a logical truth that Scott (s) is identical to himself. On the other hand, the sentence about the ‘golden mountain’ may be true since there is nothing contradictory about it. He is confused as to how a sentence can make sense and can be talked about when the thing that is being talked about does not exist. According to his theory, for every meaningful sentence or its negation must be true and this creates a complication.  ‘Santa Claus does not exist’; if Santa Claus is a singular term and we accept ST2, (a sentence containing a singular term has no truth-value unless there is an object corresponding to that singular term) it is hard to see how ‘Santa Claus does not exist’ can be true. But what if we separated existent and non-existent objects from one another and allowed singular terms to refer to non-existent objects too? If we did that, then that means we could say that there are sentences containing singular terms which contain truth or falsity values even though there are no real objects corresponding to these singular terms. Therefore, with this, we would be able to say that Santa Claus, although is an object of some sort, it is not a real object.