Cumulative-XOR conjecture for dictionaries and subset generators

Let a dictionary represent a valid solution for one of the isomorphic graphs, and let $SG$ be a subset generator with the same number of variables. Substitute the dictionary variables into $SG$, and interpret cumulative XOR across all paths or dimensional components.

Cumulative-XOR conjecture. After substitution, the cumulative XOR yields a string of ones across all paths or dimensional components, regardless of the subset size or dimension.

The claim asserts a uniform algebraic property connecting valid dictionaries for isomorphic canonical graphs with their corresponding subset generators. No proof, counterexample, or resolution is supplied in the source.