The MT2 or "s-transverse mass", statistic was developed to cope with the difficulty of associating a parent mass scale with a missing transverse energy signature, given that models of new physics generally predict production of escaping particles in pairs, while collider experiments are sensitive to just a single vector sum over all sources of missing transverse momentum. This document focuses on the generalized extension of that statistic to asymmetric one- and two-step decay chains, with arbitrary child particle masses and upstream missing transverse momentum. It provides a unified theoretical formulation, complete solution classification, taxonomy of critical points, and technical algorithmic prescription for treatment of the MT2 event scale. An implementation of the described algorithm is available for download, and is also a deployable component of the author's fully-featured selection cut software package AEACuS (Algorithmic Event Arbiter and Cut Selector).