Do your beliefs imply a Necessary being exists?

[Jackalope]

No, since logic is a subset of mathematics. Are there mathematical proofs that aren't logical arguments?

Not that I am aware of. However, there are logical arguments which are not mathematical proofs.

I expect that you do not think that math proofs require empirical evidence. Neither do I.

Let's look at the non-mathematical type. Suppose you had an argument that included the proposition "no swans are non-white". To assess the truth value of any conclusion which depended on said proposition, you need to demonstrate the truth of said proposition.

How would you propose to do so without depending on empiricism?

Now do you see the folly in conflating the two?

Perhaps you missed this in your absence.