Computable bound on the number of rational solutions of a Diophantine equation

Let $D(x_1,\ldots,x_p)=0$ be a Diophantine equation, and suppose its set of rational solutions is finite. Computable solution-count bound conjecture. There is an algorithm that takes $D(x_1,\ldots,x_p)=0$ as input and returns an integer $b\geq2$ such that $b$ is greater than the number of rational solutions whenever that solution set is finite. The source presents this as a conjectural consequence related to the height-bound conjectures; its status is not resolved there.