Yes, if Gurobi and my code run as intended and I did not mess up any thinking while simplifying my chess model, then what I did is proof that the maximum number of legal moves available in a chess position reachable by a sequence of legal moves from the starting position is 218 (upper and lower bound). Gurobi proved the entire search space as "at most as good" using bounds, basically.
Yes, if Gurobi and my code run as intended and I did not mess up any thinking while simplifying my chess model, then what I did is proof that the maximum number of legal moves available in a chess position reachable by a sequence of legal moves from the starting position is 218 (upper and lower bound). Gurobi proved the entire search space as "at most as good" using bounds, basically.