Your posts are closed because are unclear, not self-contained, using non-standard definitions and mixing terminology. P = NP attempt in the background is not a problem in your posts, because you did not throw your attempt with peer review request, but it is easy to connect pieces together. You were given advises, learning path plans and background required to such attempt and rules that governs this site. Please reiterate through them once more.
At very first post you have indeed started to attempt P vs NP problem, with tags and comments indicating this and to be honest I do not think it is cranky or wrong, it is just a wrong place and I all the time insist that you need some proper tools (definitions, understanding) to start a journey or realize the attempt is not going into good direction. It took whole day for me and ryan to extract underneath question and drop heavy implications from it. Overall it was 29 times edited, so I have asked you to wait and do less editing. You did, so thank you for that.
Here was missing post, but it literally asked the first question once more with question whether it would work, in the comments we have come to conclusion that it is a very long journey from your solver to proving P = NP, and exchanged advises to read about definitions (P, NP, NP-Compete, Sudoku, solver etc.).
Then you asked second question and got definition of Sudoku generalization ($k^2 \times k^2$) and info about what is NP-Hard.
Take a moment to look at this post, it has one edit, it is self-contained, you have not been asked what is going on, posts should look like this.
Your third post has wrong construction, it links previous question and once more shows your permuting/shifting operator which takes half of your post.
Answer suggests reading the definitions. It was clear at this point that you haven't read them.
Another post got closed, it took 11 edits and you still ask if something that works will work. By the way, 12 x 12 is not $k^2 \times k^2$ grid, is it?
In the comments you have given me definition of NP, and it was wrong.
Please read my comment and definitions, this time for real.
The construction of your post is wrong, you have referenced previous question, shown some 12 x 12 grid, formatted it twice, which I have asked you several times to drop and then asked whether your idea generalizes. After edit there is hand-waving argument about checking your equation at Wolfram and it works. I cannot follow your attempt, but if you are convinced that it works (and it was shown at least twice to you earlier), the post is not needed. If it is, you cannot show formatted consecutive natural numbers, format them into matrix and ask whether it generates Sudoku grid, parts of posts clearly do not stick together.
Your last post still suggests that you are confused with 3SAT and grid generator.
You have used over 5 posts to show your grid generator, but people still cannot get your idea, please stick to one definition (created by ryan), drop all irrelevant steps, and read carefully What is the definition of $P$, $NP$, $NP$-complete and $NP$-hard? then Is there a system behind the magic of algorithm analysis? and then read all https://cs.stackexchange.com/search?tab=votes&q=sudoku
This links aim at helping you to sort out definitions, get grasp of what is important to you.
You need to create real Sudoku solver, not mapper to continue your attempts, an algorithm that solves any valid Sudoku 9 x 9 grid. Measure its complexity, then generalize to $k^2 \times k^2$ and then, with your knowledge after reading given posts you may continue.
What will be closed in the future
You cannot throw another grid cyclic creator, insist it is solver, use half space of the post to show it generates some numbers and connect it to DNF, 3SAT or any other thing asking us to connect dots for you in the way you did.
Please, once again, start using standard terminology.
Sudoku puzzle is uniquely (or pairwise not uniquely) solvable grid with hints/clues (more than 9 for 9 x 9 grid). (look at https://www.websudoku.com/ what you see is Sudoku instance), whole grid filled with numbers abiding Sudoku rules is solved instance. If you want to describe solver, it will get encoded instance and return solved grid.
Grids generated by your shifting are subset of all possible puzzles, so you literally cannot infer anything from this.
It doesn't make sense to try instances 50 x 50 or 100 x 100, since you get result that it will always work. It works, yet still nothing follows from this.
One box (3 x 3) is not solved, it is filled. It is not enough to provide solution.