Papers published during undergraduate degree: can they form the basis to a PhD?
I don't think this is impossible, but I doubt that many doctoral programs would permit it. Not zero, but not many. That is up to your university and an advisor.
You have published some papers which is good and will likely win you a slot at a good place, but there are &quot;papers&quot; and there are papers. If you have proof of some hundred year old conjecture that Erdős et al failed to prove then, sure.
But, since you seem to be good, I'd rather suggest that you spend the time it might take to earn a doctorate to do some even better work, ending up with a truly awesome CV and professors who will strongly support you in your career. I think that most places will still make you pass comprehensive exams, showing that your knowledge and skill isn't too narrow.
In the US, finances aren't a problem (unless you need to support a large family) as you will normally have a TA (or more likely an RA in your case) so that you get both a tuition waiver and a stipend.
But the early work you have done can certainly form the basis of what you will need to do for a dissertation. You might find the faculty of the right institution helpful in extending it, or not. But the experience would be a much more solid basis of a career than taking, what I think is a minimal path.
And, if you are as good as that then I'd think your path won't be all that long anyway. And the opportunity to get a bit of teaching experience as well will give you a better career base.
So, possible? Maybe. Advisable? Not so much.