>>8380

Just to nitpick it would be O(sqrt) as we do compute the sqrt of c to get d. That is the upper limit in the case you're describing.

I see the bit trimming as a means to simplify. When we trim bits we simply remove 2 as a factor, leaving us with factors beyond 2. I'm not sure why, but the number 2 appears to be "special" in the grid. Several times I've seen patterns where I expect the result to contain 2x2x…, but instead contain 2x… (One less factor of 2 than I expected).

I've said it before, but I suspect that VQC has been giving us hints related to all the keys he knows. The recursive one I suspect is one method. The triangle one is another and I suspect the (n-1)naa is a third.

How factorizing d and e solves it, I'm not sure. We know that if gcd(d, e) != 1, then we have the d = kq (for some k and q) and e = ko (for some k, o) which gives us: kqkq + ko =k(qq + o). I wonder if, when solving d and e we will end up with something similar that we can then use to "figure it out". It's the figure it out part that's hard and recusing over d and e doesn't give me any good ideas about how to solve it.

As for the subject, metacognition, I'm wonder what do we have? We have a huge grid, that exists as a lookup and we know that column 0 (row 1?) is supposed to operate as the QFT (Quantum Fourier Transformation), but just writing this doesn't make me understand it.

The grid shows us how numbers can be grouped together as the difference of two squares, and how this two squares are related to the integer and the integers factors.

We have patterns inside the grid for knowing how a cell is related to other cells in different columns. We can move in many ways, by shrinking or increasing the largest square we remove from the number. By transforming the number, but so far we haven't actually gotten a solution.

>>8380

I'm ranting a bit I know, but I'm trying to think loud.

If we assume the recursive method is the solution, then I'm wondering more about the patterns we spend time on. Are they then irrelevant? Or are they irrelevant for the problem at hand, but useful once you understand the grid? As in, will the grid be used further to solve other problems?

Based on the description of the recursive method, we only need to care about d and e. We generate a tree where we branch out from d and e, but for each node we only store d and e (and c?). However, we know that doing so doesn't solve for all d and e. As in, gcd(d, e) doesn't solve much, we still have branches that aren't solved, and I think I've seen "trees" where none of the nodes are solved using just that method. Which means, we're missing something.

Assume we're building a tree, where each node contains three values, d, e and c. c is the input number of the node, d and e are the d and e-values of the c-value. This tree is what the recursive algorithm gives us, but we aren't done yet.

What then would be the next logical step? How would you connect this tree to the grid? We have an initial c, we have a tree. We can move recursively down the tree and then what?

To digress a bit, I remember in one of the first threads, VQC talked about multiplying our c number with other numbers. As a means to create a column that is predictable and that we "control". From this column we could coax out the factors of c, did we ever to much with this? Was it just something to get us interested? Knowing now what we know, is that a possibility?