if that was true, then Bm naruto passing his chakra+kyubi would've had Sasuke awaken the rinnegan immediately during the fight with Obito.
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And Sasuke said that he was given the Six path shadow from Hagormoo that is meant for sealing "this being" (kaguya) with it, which is this seal here:
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Those are two VERY different situations. Mangekyou is triggered by emotions, Rinnegan on the other hand awakens from a combination of Indra's chakra, Senju DNA and Uchiha blood. Madara had all three as an adult, but the Rinnegan would only awaken the Rinnegan to him as an old man. Sasuke had all three in him too, but awoke it just after talking to Hagoromo rather than years afterward. The difference in time and the way his specific eye works says by itself that his eye is not like Madara's.
Well madara is not Sasuke and this bold part here is just a mere speculation. There is no such thing as directly talking to hagormoo decreasing the year to obtaining the rinnegan. The only reason why it took so long is because Hagormoo said that Madara at his old age had his chakra finally mix to awaken it.
Sasuke just had his ashura part given to him mix faster than Madara did.
The name is not the point though, what I'm trying to say is that Sasuke's Rinnegan, regardless of its name, is clearly different, and by that I mean superior, to Madara.
It is not superior and just because it looks different doesn't mean it is inferior or superior in any single way. The manga said that it is a rinnegan and it never said it was better than or less than any other rinnegan we've seen in the series. We've seen 4 rinnegan users in the series now and only two of them look the similar.
And the two that looks similar are not even the same. One's a kekkai genkai and the other is a kekkai mora.
The statement has nothing to do with awakening the Rinnegan though, the hell are you talking about? Even if it did, Sasuke had no Senju DNA on him at the time, he wouldn't awaken the Rinnegan from it either way.
And Sasuke said that he was given the Six path shadow from Hagormoo that is meant for sealing "this being" (kaguya) with it, which is this seal here:
Again, nothing to do with the Rinnegan. It just says that they have the seal. Not that Hagoromo gave them the seal. Not that Hagoromo gave them ONLY the seal. They just have the seal.
Well madara is not Sasuke and this bold part here is just a mere speculation. There is no such thing as directly talking to hagormoo decreasing the year to obtaining the rinnegan. The only reason why it took so long is because Hagormoo said that Madara at his old age had his chakra finally mix to awaken it.
Sasuke just had his ashura part given to him mix faster than Madara did.
Madara took that entire life to awaken the Rinnegan despite implanting Hashirama's face on his chest, Sasuke took at the best hours and got it just from being given a bit of Hashirama's chakra. And you're justifying that immense difference because "different people". Directly talking to Hagoromo did not decrease the "time it took to awaken it", it triggered the awakening. He gave Sasuke his chakra, after all, just like he did Naruto.
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It is not superior and just because it looks different doesn't mean it is inferior or superior in any single way. The manga said that it is a rinnegan and it never said it was better than or less than any other rinnegan we've seen in the series. We've seen 4 rinnegan users in the series now and only two of them look the similar.
And the two that looks similar are not even the same. One's a kekkai genkai and the other is a kekkai mora.