Recently, I have asked a question and made sure that I provided enough details showing that I somewhat understand what I'm reading.
Overall, what details should be omitted that make the question easier to understand?
This is somewhat improvement, but please, take a step back with your attempts. Pick a book, read questions here, take some course and learn basics. It cannot be done in one or two days, human brain needs three days to acquire concept and a week to remember it, with exercise execution when you keep revising every day. Otherwise, it will be shallow concept lost from memory in less than month.
There is a quote from Wikipedia, a summary of your attempt, your algorithm and still you try to merge complex concepts with your idea, and it does not stick.
I fully understand why, it is easier to grasp concepts through something close and familiar, but here unfortunately you really need to let it go and learn differently.
You have given a summary here in the comments, but all the time your questions are in the terms of your generator.
Imagine that I like Kakuro and you do not know this game, I am using some odd bit counting method to solve it, we talk, I ask you all the time to express anything in the terms of Kakuro. After a while you realize, that my operation is addition, but works only for even numbers, so you try to ask about odd numbers. Well, it simply fails because my Kakuro is even. So you try to somewhat tune in and it suffices for some time, but then you realize, we simply cannot continue this way, when I ask you to express Chess in terms of Kakuro addition, then ask about Draughts, then Hex and then ask more and more unrelated questions, like car driving, wood cutting or more on-topic, whether my Kakuro addition is NEXP-Hard and built this on assumption that some people add numbers really slowly.
Here huge problem arises, your generator (or mine addition example) is not complex enough to allow describing concepts in terms of it. Unfortunately it does not even allow talking about Sudoku, because it is not fully operational yet.
We are not tutoring site, to go through step by step with your journey into complexity theory, so iterative posts doesn't work well. Commonly it takes at least one semester of studies learning complexity theory, but you realize soon enough that it was not full knowledge, but description of tools to start. Try to understand us, we simply cannot believe that you have outsmarted learning curve and now keep going into advanced terms.
Any further help without your real involvement into learning will be harmful as you will get shallow or erroneous understanding, but keep building.