I have a theory.
Nomura = Nomura
Q.E.D.
In this proof, we wish to show that Cloud and Noctis are the same person.
We will proceed by strong induction. For our base case, we take n = 1 where n is a boot being worn by the protagonist. Because the boot prints are the same, the base case holds.
In the induction step, we will assume that for some k >= 2, that boots worn by protagonists means the protagonists are the same person for all identical boot treads i, where i is an integer between 1 and k, inclusive.
Then we wish to show that if there are k+1 boot identical boot treats, then the protagonists are the same.
Observe that k is the 11th digit in the alphabet. Then k = 7 + 4. Then k + 1 = 7 + 4 + 1 = 7 + 5. 7 is the FFVII, 5 is XV.
By the induction hypothesis, we assume that 7 and 5 are identical. Then by the linearity of addition over the closed set of natural numbers, k+1 boots are also worn by the protagonists.
Thus, by the principal of strong induction, FFVII and FFXV are the same game with the same protagonist.
Q.E.D.