Stacking these together because of inversions and etc. You are making a pattern. Then using the new scene to search for an expanded model. You have information that may lead to new information, but only through their functions/pattern. Finding anything outside those "terms" will likely involve some form of chainbreaking.
Where You will Use Chain breaking on the patterns you have to substitute an answer for the "expanded model" chart.
This would detail alot of things including:
Using that you would have
1.The Best-Guess Answer. The ones we know can work based off what we have. (It can be more than one depending on the length you want to go to with pattern strings)
2. The Unknown Answer (answers we don't have due to lack of information) but we can assume are possible.
3.The Rare Fit Answer (An answer that just exists elsewhere in math as some random polynomial/function)
4.Literally No answer.
5.Additionally an answer that may be considered "a nullset of situations in which things work out"
6.The Incredible Chaos Theory of there being some broken scenario in which it something broken makes it work.
7.A quantum cloud answer.
8:Your data might just be wrong and there is no such expansion. And the pattern is just a sequence.