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

It's been asserted by some knowledgeable individuals that the Buddha explicitly identified "the mental idea of the self" as what is (re)born in samsara and has done so in suttas spelling out the doctrine of dependent origination. Is it true that the Buddha *explicitly* identified "the mental idea of the self" as what is (re)born in samsara? If not, is it true that the Buddha *implicitly intended* to identify "the mental idea of the self" as what is (re)born in samsara? Please provide sutta references. In the Prasangika Madhyamaka we say it is the "mere I" that is reborn and not the "mental idea of the self" and we say *how* it is reborn is through the doctrine of dependent origination which *involves* the mental idea of the self. I think this is a significant difference.