Proof of Positivity of Mass for Maximally Sliced, Asymptotically Flat Spacetimes

There exists in General Relativity an unambiguous notion of Mass associated to asymptotically flat spacetimes known as the ADM mass. The standard expression for the same is a surface integral over spatial infinity of a linear combination of spatial deriatives of the three metric adapted to a constant time spatial hypersurface evaluated at infinity. In this form however the positivity of this mass formula is not apparent, so in the following an attempt shall be made to bring this functional into a form where it's positivity is evident.