Bedrockgames
I post in the voice of Christopher Walken
I'd just like to note here that pre-authorship isn't required.
The only thing that is required is that there is some fact of the matter, within the fictional space. That fact-of-the-matter is most easily done by having it be pre-authored, e.g. by a GM or by an adventure writer, but it does not have to be done that way. Random determination is also possible, or (say) you could have a third party that doesn't know the context picking things out (so that it isn't random, but also isn't strictly "authorship" either.)
I've used the word "established" a lot here, and it's not for nothing. The order in which the truth is established matters. If the truth is pre-established--by whatever means, authorship being only one of them--then it is possible to solve for that truth by gathering evidence that points toward it (or which pushes you away from the false conclusions). If the truth is established by the investigation, if the establishment is causally downstream of the investigation, then I don't see how that investigation can be "solving" the mystery. It is, most certainly, still an investigation. But it is an investigation which creates a truth, rather than an investigation which discovers a truth.
If you're creating the truth, you aren't solving for it--you're building it with your own hands. Even if that creation is divided amongst multiple people and bound by strict and reliable rules and procedures, you are still creating that truth.
I cannot create the truth that 3+4=7, or at least I have no idea how I would create such a thing. But I most certainly can create a solution to X+Y=7 where X and Y are natural numbers, which does not have a solution as stated. I can create that solution by saying, "I declare that Y is 4, and thus X must be 3." Y could be any number of the set 1 through 6 (possibly 0 through 7, if you are like me and consider 0 a natural number); it is my choice to make Y=3 that creates the possibility of a solution in the first place.
I think the important thing is there be an objective mystery to solve. And ideally this mystery is set from the beginning so that your investigative efforts matter from the start. But a GM could easily use a random method for setting this up. Other methods could probably work too (as long as players can investigate it without knowing the solution and there is a way the steps of the investigation to make sense in terms of gathering clues, talking to suspects and that enabling them to try to solve the case in a way where they are genuinely solving something