The superfield realization conjecture for engineerable Adinkra topologies

An Adinkra is a colored graph encoding a one-dimensional supersymmetry representation, and its topology records the graph structure up to the relevant identifications. A topology is engineerable if it occurs for an Adinkra compatible with the engineering-dimension assignments of the component fields. For each positive integer $N$, consider the topologies of engineerable Adinkras for $N$-extended supersymmetry.

Superfield realization conjecture. For every $N$ and every topology of engineerable Adinkras, there exists a corresponding set of superderivative constraints such that the set of superfields satisfying these constraints has an Adinkra of that topology.

The claim would establish the existence of a superfield realization for every engineerable Adinkra topology. The source presents this as an assumption whose affirmation is tempting but notes that the required algorithm for generating all two-to-one identifications of higher-$N$ cubical Adinkras, together with the corresponding superfield constraints, had not yet been constructed.