The cardinal-inequality realization conjecture for $cotimes$ graphs

An algorithm is a procedure that takes an input and may terminate or run forever, and $x$ is an input to such an algorithm. A $\otimes$ graph with cardinal inequalities is a $\otimes$ graph $\mathcal{G}$ equipped with cardinal inequalities between its vertices; it is realizable when it has a model satisfying those constraints.

Cardinal-inequality realization conjecture. For every algorithm $\mathcal{A}$ and input $x$, there exists a $\otimes$ graph $\mathcal{G}$ with cardinal inequalities such that

$$\mathcal{A}\text{ terminates on }x \quad\Longleftrightarrow\quad \mathcal{G}\text{ is realizable}.$$

The surrounding discussion places this claim in the context of Hilbert's Tenth problem: realizability for $\otimes$ graphs with cardinal constraints of the form $|p|\leq |q|$ is stated to be undecidable because it is reducible to HTP. The proposed equivalence would give a direct realization of termination behavior by such graph instances; no resolution is supplied in the source.