You are mathematically correct that a fixed 9x9 grid is not NP-Complete; the NP-Complete problem is Generalized Sudoku (
n
2
×n
2).
However, the NLS framework is not limited to 3x3 or 9x9. The theory is inherently fractal and scalable. We have already defined the algebraic seeds for 4x4 and 5x5 NLS structures (which project to 16x16 and 25x25 Sudokus respectively).
The algorithmic mechanism is exactly the one I described: you take the base parametric block (e.g., 4x4), center it, and apply the same alternating vertical projection logic. Because the generation is parametric (
n±a,…
) and not combinatorial, the complexity does not explode exponentially when moving from 9x9 to 16x16 or 100x100. The "Lo-shuization" (fractal expansion) ensures the valid solution space is still generated structurally in constant time, without search.
The 9x9 in the paper is just the base proof-of-concept.