Your “Solution Landscape” idea is intriguing, but I’d like more detail on how you select and vary your concrete x-values and define the dual-variance “Hyperforce” operators to ensure you adequately sample all relevant behaviors. Clarifying the formal guarantees e.g. coverage of all roots, stability criteria, and computational complexity—would make the methodology much stronger.

I have several papers on hyperforce, basically you have to think that a number, operator or even unknown number x in the equation is a root (like a tree root, or a DNA that modifies itself and transforms) it can be transformed based on (logarithm, radical, power factorial or others...) basically the values ​​remain the same because they are the root, then that root is transformed into a set for example 9^2 is S (9, 81) in equation 9 becomes 81 if we choose this route. Then we have to think of an equation as a kind of test for operations (addition, subtraction, multiplication, division...) We simulate the equation, we do not solve it, we create answers. The equation is the equivalent of a system that we simulate to see how it behaves. I have also added other things if you search in various papers, because I could not give so many details in a single paper. I have developed an arsenal of tools for simulating an equation, to see how it evolves. The ideas are new and original developed by me, it is normal that you do not know the details.

Think at the equation as a mother equation or root equation, after the transformation with hyper force it will be a new network of child equations.