We propose the recently defined "Holoraumy Tensor" to play a critical role in defining a metric to establish a correspondence between 4D, [Formula: see text]-extended 0-brane-based valise supermultiplet representations and, correspondingly via "SUSY Holography," on the space of 1D, N-extended network-based adinkras. Using an analogy with the su(3) algebra, it is argued the 0-brane holoraumy tensors play the role of the " d -coefficients" and provide a newly established tool for investigating supersymmetric representation theory.

We present an expanded and detailed discussion of the mathematical tools required to cull and filter representations of the Coxeter Group BC 4 into providing bases for the construction of minimal off-shell representations of the 4D, N = 1 spacetime supersymmetry algebra.

We present evidence of the existence of a 1D, N = 16 SUSY hologram that can be used to understand representation theory aspects of a 4D, N = 4 supersymmetrical vector multiplet. In this context, the long-standing "off-shell SUSY" problem for the 4D, N = 4 Maxwell supermultiplet is precisely formulated as a problem in linear algebra.

Starting with valise supermultiplets obtained from 0-branes plus field redefinitions, valise adinkra networks, and the "Garden Algebra," we discuss an architecture for algorithms that (starting from on-shell theories and, through a well-defined computation procedure), search for off-shell completions. We show in one dimension how to directly attack the notorious "off-shell auxiliary field" problem of supersymmetry with algorithms in the adinkra network-world formulation.