If we look at particles of spin 1/2, 1 and 2 we can use values of pi to represent them. With 4*pi for spin 1/2 (fermions), 2*pi for spin 1 (photons) and pi for spin 2 (gravitons).

So that

spin 1/2 is e^(i*4*pi) = 1

spin 1 is e^(i*2*pi) = 1

spin 2 is e^(i*pi) = -1

spin 2 is then distinguished by having the opposite sign. Since spin 1 photons have only polarity and no charge we could amend its definition as

spin 1 is e^(i*2*pi) - 1 = 0

This is now a modified Euler identity.

The field of the electron can be given by

e^(i*4*pi) -2 = -1

The proton is then given by

e^(i*4*pi) = 1

As with the masses of the proton and neutron there is an imbalance between the derivations of positive and negative involving the value of -2. Elsewhere I investigated this mass/charge discrepancy in a slightly different way but the results were similar in nature.

Does this indicate a dual nature of the gravitational field? It may have no bearing at all. I will leave that for others to judge.