Mathematically representing all possible universes as unique integers

Here is a way to represent all possible universes of the same set of laws via unique integer scalars. Works for universes with any number of dimensions.

Let a point P_i in an n-dimensional space be represented as . Let x_i = (a_i)/(b_i), such that

Let N(x)=0 if x≥0, and N(x)=1 if x<0

Let where p_n is the nth prime number.

Thus, s(P_i) will assign a unique scalar integer for every rational point P.

Let

Thus, U is a unique scalar integer that holds information about every point provided.

Now, if any given universe can be represented via a set of points (particles) at rational distances from an origin, it can be represented via a single (albeit large) integer, U. Likewise, every real number greater than one can be decoded to find a given universe, so long as the amount of dimensions is know. Properties of particles (such as velocity or charge) can also be represented as additional dimensions.

If our universe does consist of only particles, it can then be dissolved into a set of laws and an integer. We can then find all other possible multiverses with our set of laws by checking other integers.

Edit 6-4-2025: Fixed formatting and improved notation.