I got into a conversation with somebody because I insisted that a mystery requires a solved crime and a caught perpetrator. (They tried to use The Lovely Bones, which is not marketed as a mystery, as a counter example. If you have a genuine one, I'd love to hear it).

Not every story that contains a crime is a mystery! Kyx has a dead body at the start, but its an instigating incident, not a driving force in the plot.

So, what makes something a mystery, as opposed to sparkling crime fiction? I'm going to go through what I think it is. I'm open to disagreement!