Hello,I will repeat part of what other people have mentioned, for a complete answer as I have gone through the process:Scenario 1: There is not enough left of the old passport for the State Department to ID it as a valid passport.-You fill out the form for reporting Lost/Stolen passports. I recommend doing this online as it will be processed faster.You will need to apply for a new passport and this can have three options:1a) You apply for a new passport, just as though you have never applied for a passport before.1b) You fill out another form, the Request File Search form and pay another $150 for the State Department to verify that the documents you need (and indicate on the form) for a new passport already exist with them (yes, I know, but that’s what they charge).1c) You submit ANY formerly valid but currently expired US passport with your new passport application (assuming you were smart enough to store an old passport somewhere safe, and not in your burned down home).Pretty much no Ifs-ands-or-Buts about having to apply for a new passport.Scenario 2: You have enough left of your old passport for the State Department to verify that it was a valid passport.This scenario I’m replying on based on what I read so you should probably consult with the State Department (they have a hotline that a live human answers, and can actually answer your question quickly) to verify but you go through a process similar to option 1c listed above for replacement. I don’t think I saw any specific form for this so you’d need to contact the State Department. I believe they consider the process similar to a renewal, which is much easier than a new application.Important for this scenario is that you do NOT fill out the Lost/Stolen report form because your passport immediately becomes invalid…I could be wrong about this part.As far as your question about proof, I don’t believe I saw on the Lost/Stolen report form any request for proof. I don’t think they care about proof because they immediately invalidate your old passport so even if it was re-used, it will be flagged as invalid.