From Pluralpedia, the collaborative plurality dictionary
partial-core, partial core (n., adj.)
Synonymsbase (n.)
Applies toheadmates
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The Partial-Core is a headmate with a partial connection to the body's pre-plural self. If the core is the headmate with the most connection to the pre-plural self, the Partial-Core is the headmate with the second, third, (etc) most connection.

Like the core, not every system has one. The Partial-Core often inherits the personality, identity, and/or memories of the pre-plural self.