Edit: While my comment came from caution due to historical human hubris, it appears I am wrong:
“According to the Centers for Disease Control and Prevention (CDC), a person with an undetectable viral load has “effectively no risk” of sexually transmitting HIV. In 2016, the Prevention Access Campaign launched the U=U, or Undetectable = Untransmittable, campaign.”
Here [1] is for instance an article referencing this claim, describing it as "based on strong scientific evidence" that was peer reviewed published by the journal of the American Medical Association. (EDIT: it's important to add the caveat, which is that this claim is about sexual transmission only, and does not cover pregnant-mother-to-child transmission or intravenous needle sharing).
Also your comment now refers to "HPV" which is the name of a different disease.
[1] https://jamanetwork.com/journals/jama/article-abstract/27209...
Too often we think we’re smarter than we are, and the consequences can be damning. Hence why I said its a bold claim that undetectable means it can’t be transmitted. Are we absolutely sure? Because if we’re not, someone could acquire a life long chronic disease that would otherwise have been preventable. But the CDC says undetectable says no transmission; I hope they’re right in 100% of transmission scenarios.
https://www.healthline.com/health/hiv-aids/undetectable-vira...