At this point I'd like to know if it's possible to thread mathematically the N-bool problem and create a library for generic multidimensional bool that works with templates allowing to determine N at compile time. Because in the future we should have a 8-bool implementation, and so on...

Theoretically, it would (probably) be possible to provide N-valued logics. But that is beyond my knowledge. bool3/bool4(Belnap) are still manageable. For N-valued logics N>4, mathematicians would have to be consulted (as I said: I am not one). If you are asking about such things, perhaps temporal logics could also be provided https://en.wikipedia.org/wiki/Temporal_logic. But that's where I completely drop out.