Thank you for your interest. Your "TrueCoin" idea does seem similar in spirit. One difference is that you describe TrueCoin as relying on the "useful Proof of Work" of proving mathematical theorems while Qeditas is planned to be (primarily) Proof of Stake. However, in Qeditas someone can increase their stake by proving theorems with bounties or by proving theorems others find useful (by collecting royalties). Perhaps this process can be seen as a simulation of a "useful Proof of Work."

The Qeditas White Paper provides an overview only. If you are interested in the details of the underlying logic (simple type theory), you can find those details in Chapter 7 of the Technical Documentation. The logic is the framework and users will need to publish a "theory" (primitives and axioms) to act as a mathematical foundation. (By default, the empty theory can be used, but this will have limited expressive power.)

The details of Proof of Stake are not fully described yet. Chapter 12 of the Technical Documentation should contain this information at some point, but even the single paragraph that currently comprises Chapter 12 is out-of-date and misleading. The best information can be found in the first half of Chapter 10. Also, Section 1.1 of Chapter 9 describes how coin-age is computed.

Here is a link to the Technical Documentation:

http://qeditas.org/qeditastechdoc.pdf

I hope this answers your questions. Honestly, it was not completely clear to me what you were asking, so please feel free to ask again if I have misinterpreted.