This is a question to the mathematicians on the forum: when you're trying to solve an open problem in pure mathematics, what are the first things you do? Do you test the conjecture with a few example problems? Do you look up recent theorems related to the question, or do you just dive right in?

The first thing to do is be sure the open problem can be solved with math. The second thing to do is compose a list of all the features involved in the problem The third thing to do is to try and give the composed list some sort of order in event sequence. By doing this you have already composed directions etc, then just fill in the gaps with math. What open problem are you thinking of ? Gravity is a cool one. In example of gravity I already have my composed list and list order in my mind, I will break it down to my abstraction for you to show you what I mean. atom→←atom You can take that further down to (q1+q2)=N→←(q1+q2)=N Then even further En→←En En←→En Of course this is my personal abstraction so you may or may not understand this. I am just showing how to break something down before the extensive proper maths is involved.

I am not sure unless you specify you symbols. Are your >< less than and greater than ? or does it represent direction? What is E and e stating? What is N and n stating? En in the one I did represents electrical field neutral, I describe polarity as a point of attraction or repulsion.

There is no set of rules for problem solving. If you read the history of discoveries, in any field, it's lots of trial and error, with an occasional lightening strike of inspiration.