The data on wart clearance are not precise. This has never been the subject of rigorous research, so the information is based on the clinical experience of providers like me. However, most experts would agree with me, that once visible genital warts are gone--either spontaneously or after treatment--if a few months go by without recurrence, most people have no further problem with them.
As I have said before, but perhaps not for a few months, the issue of HPV clearance is partly one of definition of 'cure'. Some experts believe that all HPV infections persist forever, at least in the sense that some HPV DNA persists at the cellular level. But even if that is true, in most persons the infection is kept in check by the immune system, and most people do not have recurrent symptoms any time in the future and do not continue to transmit the infection. So from a practical standpoint, they are cured, even if that's not quite true at a biological level. However, there definitely are exceptions; some infections do come back in the future in active form. Sometimes that occurs in people with immune deficiency (cancer, AIDS, etc)--but it can happen in completely healthy people. There is no way to predict who will and will not be in that inconvenient minority. But happily, such recurrent problems rarely represent serious health risks. All HPV infections should be viewed primarily as an inconvenience, not dangerous health problem.
I hope this helps. Best wishes-- HHH, MD
Thank you for the prompt response! Everything you said gives me a better understanding. I did have two acid treatments performed and the second time it took. My doc even commented on how it looked like it was receding after the first treatment so it may have been disappearing on its own at that point. Knowing my nature, I would want to be honest if I have any new partners in the near future. At least now I feel like I can explain it better!