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We present arguments to support the existence of weight spaces forsupersymmetric field theories and identify the calculations of informationabout supermultiplets to define such spaces via the concept of "holoraumy." Forthe first time this is extended to the complex linear supermultiplet by acalculation of the commutator of supercovariant derivatives on all of itscomponent fields.

On the Four Dimensional Holoraumy of the 4D, $\cal N$ = 1 Complex Linear Supermultiplet