I have come to the conclusion that based on the subtle evidences presented in Ch. 626 that Madara used a specific type of Genjutsu to make Hashirama believe he killed him and escape certain death. There is also the possibility of him using something similar to Muu's Fission Jutsu if the former is not the case.Take a look at this:

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Don't you find it peculiar that Madara's EMS was activated after dislodging from Kurama?And that the image of the Moon appeared Immediately after that panel:

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It's possible that prior or during the one on one fight, Madara casted a genjutsu on Hashirama

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And after Hashirama "killed" him, this was shown:

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And did you notice Hashirama's peculiar upward glare:Why would Hashirama be looking upward if Madara was laying on the ground?

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And did you notice the peculiar "diamond shape" symbol?

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That is the manga/anime trope for optical illusion/mesmerization

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The same sparkle effect that appeared after Itachi's Genjutsu on Naruto ended

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And that is why the same image/symbol appeared on the moon and on the panel after Hashirama looked upward:Before the fight:

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After the fight:

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The genjutsu had just ended/ wore off that is why Hashirama fell to his feet:

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That is why Hashirama has no idea how Madara survived even though he was apparently sure he killed him:

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Because Hashirama was under a genjutsu at that time. Hashirama might have injured Madara but Madara was not killed because he used a genjutsu or a limited form of Tsukuyomi during that fight:A friend of mine AlphaScythian noticed something peculiar:

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The moment Hashirama stabbed Madara, the latter's Sharingan reactedThat is the same Sound FX used when the Sharingan is activated/deactivated:

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(Sasuke's Sharingan)Which adds credence to the fact that Genjutsu was involved.There's also the peculiarity of the sword that stabbed Madara.When Madara fell to the ground, the sword was lounged in his chest:

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But after Hashirama looked upward and fell on his feet:

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The sword was glaringly missing in Madara's body:

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Which further suggests the involvement of Genjutsu.