The (dis)continuism debate in the philosophy and cognitive science of memory concerns whether remembering is continuous with episodic future thought and episodic counterfactual thought in being a form of constructive imagining. I argue that settling that dispute will hinge on whether the memory traces (or “engrams”) that support remembering impose arational, perception-like constraints that are too strong for remembering to constitute a kind of constructive imagining. In exploring that question, I articulate two conceptions of memory traces—the replay theory and the prop theory—that return conflicting answers to whether remembering is constructive imagining. The prop theory’s vision of traces is suggestive of continuism, while the replay...