  A Gadget, more precisely a scalar Gadget, is defined as a mathematical
calculation acting over a domain of one or more adinkra graphs and whose range
is a real number. A 2010 work on the subject of automorphisms of adinkra
graphs, implied the existence of multiple numbers of Gadgets depending on the
number of colors under consideration. For four colors, this number is two. In
this work, we verify the existence of a second such Gadget and calculate (both
analytically and via explicit computer-enabled algorithms) its 1,358,954,496
matrix elements over 36,864 minimal valise adinkras related to the Coxeter
Group BC4.
