What do PhD admission officers look for when evaluating an undergraduate thesis? (CS)
I think that significant research at the undergraduate level is pretty rare, especially if it can be completed and published.
The problem is that there is seldom time enough to get the needed background and also follow up to completion on a significant problem. Research is really open ended, especially in time. It is why some doctoral students take much longer than others to complete.
If you are diving into the unknown on a research question then it is impossible to foretell where or when you will wind up.
For that reason, I think that pretty much any research experience at the undergraduate level will impress a doctoral admissions committee in the US. This would even be true if there are no publication (yet) but perhaps many interesting questions still to be answered.
What is acceptable to your own institution is, of course, up to them, but I doubt, given what you say, that you are likely to leave too many admissions folks unimpressed.