If episodic memory were logically sufficient for personal identity, fission would entail that one person is numerically identical to two distinct persons simultaneously, violating transitivity of identity.

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Logically sufficient(as used in logic and philosophy): If something is logically sufficient for a result, then that thing alone is enough to guarantee the result must be true.
Numerically identical(as used to describe whether two agents are the exact same person): Being literally the same thing, not just similar or alike—like how the person you are today is numerically identical to the person you were yesterday (one and the same individual).
episodic memory(Distinguished from semantic memory by its first-person experiential character and its logical entailment of personal identity): Memory of a specific past event that logically entails the rememberer's existence at the time of that event, governed by the Previous Awareness Condition
fission(Used as a test case against psychological continuity and narrative identity theories of personal identity.): A thought experiment in which a single person X divides into two distinct persons Y and Z, each psychologically continuous with X.

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