 Ordinal heuristic comparator

A comparison oracle revealing the ordering of remaining optimal costs without returning their magnitudes. It supplies enough information for greedy best-first search. Its ordering alone does not provide the numerical differences needed to compare sums with independently varying accumulated costs. For $g(n)=5$, $g(m)=1$, remaining costs $(1,2)$ and $(1,10)$ have the same pairwise order but give opposite orderings of $g+h^{\ast }$.