= Solution
\b[Yes. <Greedy best-first search> needs only the ordering of remaining-cost estimates.] Store generated but unexpanded <search nodes> in a <search frontier>. To choose the next <search node>, compare candidates with $\kappa$ and retain the one it returns; a linear scan suffices, or a <priority queue> can use the comparison rule. Remove that <search node>, apply the <goal test>, and otherwise generate its children.
This implements <best-first search> ordered by $h^*$ without ever evaluating $h^*$. If stable tie handling is wanted, comparing both argument orders distinguishes equality, after which insertion order can break ties. No estimate of accumulated-plus-remaining cost is required for this greedy ordering.
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