Resolve exact edit distances when no path is recovered

Determine the exact edit distance between a starting molecular isomer and the accepted target connectivity when exhaustive searches through the certified shorter depths and the verified three-step procedure recover no valid path, rather than leaving the distance unresolved.

Background

The paper distinguishes an observed recovery depth from a certified shortest-path distance in the molecular isomer graph. A finite-beam search may fail to recover a target even when a valid path exists, and the target-side filtering procedure may miss paths ending at other structures with the same accepted InChIKey14 connectivity.

Consequently, when no verified path is found, the authors can establish only a lower bound on the distance. The exact distance between the starting isomer and the target connectivity remains unresolved, leaving an open computational characterization problem for the isomer graph.