A paradox ghost imprint is the result of attempting to appearify something from the past that could theoretically lead to a time paradox. To prevent the paradox, the Appearifier seems to have a safety mechanism that instead creates a green "gelatinous ghost" of the object. This substance is initially in the shape of the appearifier's target but quickly loses shape and collapses to the ground. There is one known use for these imprints: the genetic code of the target can be determined and used in the creation of a paradox clone. The imprints can even be combined to create new codes and thus new beings.
It is not yet known what constitutes a paradoxical 'removal' of an object, but it is theorized to be any object that has already been interacted with in the present time line. The four humans could not be appearified because had they been, they could not have been around to raise their children. The rotten pumpkin had been eaten, and Jaspers was about to tell Rose a secret. However, with the frogs, unless the Space player is dead set on capturing the frogs afterwards at the time, the frog itself is appearified rather than the paradox imprint.