This one's pretty new and very hand-wavy.

People build a machine to solve the universal system of equations. Essentially, the gist is that it derives a set of equations to describe every action in the universe, and then it collects enough information to solve out the constants, and therefore predict all of the past and future.

It does this, I see, by solving some parts of it, and using the information it gains from this to construct new components which will solve more, until it has everything. Kinda bullshit, but meh. Could happen...

So, we end up with a record, but since the machine can't predict paradoxes, it requires a fixed-point where no one takes actions based on the record, and thus no one may read it. Basically, if the record says "You will sit down" and you decide to not, then the record will say "You don't sit down", so you do, so it says "You will sit down" so you don't, etc.

I'm not really sure what happens after here... It's possible the work is just a description leading up until the machine gets to sufficient complexity to say "I know what will happen, but you cannot."

Or, the machine decides that if it only outputs the complete record of what happened after it has happened, that will be fine. In this case it operates as a universal log of all that's happened, down to infinite detail.

Or, it finds a fixed point involving an almost complete record of the future. A "keeper" is given an incomplete copy of the record that is everyone's path, with all of the keeper's actions omitted along with anything that is computed to get close enough as to influence the keeper. It omits just enough to know that the keeper won't know enough to screw with the system.

Oh, screw that, call the "keeper" "the fixed-point", which is the person who is allowed to read the record and direct people based on it, answer queries etc.

Really, The Fixed Point is allowed to know certain things about their own life, so long as the computer know that they will do as the record says rather than deviating, and the computer is definitely capable of knowing that.

I'm not really sure where I want to go after this. I think it's more of an exploration than any real plot.