For a little more context on the "pet theory" part, Wen (2006) (The commenter) looks at waves that reflected off the same spot at the surface of the inner core

For a little more context on the "pet theory" part, Wen (2006) (The commenter) looks at waves that reflected off the same spot at the surface of the inner core 10 years apart and proposes that the differences in reflections are because the core itself grew by ~1km in 10 years at that location. You can also explain these differences by spin (the boundary is moving) or a few other mechanisms, but you can't rule out "the radial location of the boundary changed". That's basically the point - spin can explain it, but we've measured inconsistent spins. The inner core boundary moving around vertically by a few km can explain it, but that is a little hard to stomach for geologic reasons. The issue is that it's _really_ hard to come up with a geologically plausible mechanism that would allow 1km of vertical solidification over a significant area in only 10 years that's also compatible with the liquid outer core existing at all. The paper proposes that it's constantly growing and eroding so the net gain/loss is essentially 0, but again, how do you explain that rate of 1km of solidification in 10 years geologically? That's what moves it into the "pet theory" camp. It's not crazy, but no one's been able to come up with a convincing mechanism for the proposed very rapid growth+erosion of the inner/outer core boundary and there are other explanations (like spin of the inner core relative to the rest of the Earth) that have gained broader acceptance. The comment of "Hey, we have an alternate explanation for this that wasn't mentioned" is also pretty fair, though.