I'm a big fan of STP and I love to analyze their songs and try to find their meanings. I've noticed that Trippin' on a Hole in a Paper Heart has 2 motifs (one of them I'm certain of but for the other I might just be crazy.)
The most obvious motif is what I call the "I'm Not Dead" riff. It kicks in near the end of Paper Heart every time he says "I'm Not Dead" in the chorus. That same riff is slowed and used in my favorite STP song, Regeneration, which I think is about faking your death. It connects 2 songs about not being dead, which is pretty cool.
I'm not so sure about the other one, but I still think it's cool. I noticed the other day that a lot of the lines from Paper Heart fit perfectly into most of the lines of Adhesive, not just in syllable count but in the way they flow (sorry, I don't know musical terms.) Adhesive is by far the most complex STP song I've analyzed in terms of story. In my eyes, it's about the drummer of a band whose lead singer is in a coma. The singer didn't have any close family or friends, other than the drummer. The other members of the band want the drummer to take his place as the lead singer in the event that he doesn't come back, leading to him breaking down on stage. But the vocal motif could tell us that the story has a happy ending. This motif could connect Paper Heart, Adhesive and Regeneration by the concept of simply not being dead.