What is (re)born? Did the Buddha explicitly state that it is "the mental idea of the self" that is reborn?
From Milindapanha:

-- “What is it, Nàgasena, that is reborn?”
-- “Mind and matter (namarupa).”
-- “Is it this very mind and matter that is reborn?”
-- “No, it is not, but by this mind and matter deeds are done and because of those deeds another mind and matter is reborn; but that mind and matter is not thereby released from the results of its previous deeds.

Just like an adult &quot;inherits&quot; results of the choices made by the child - even though most of the original body cells are gone, similarly future existence &quot;inherits&quot; karma from the past existence.

--“Can there be any rebirth where there is no transmigration?”
--“Yes there can, just as a man can light one oil-lamp
from another but nothing moves from one lamp to the
other; or as a pupil can learn a verse by heart from a teacher
but the verse does not transmigrate from teacher to pupil.”

It is information and causation that is reborn, or is re-embodied. Or, as Chogyam Trungpa said, it is our neuroses that are reborn.