@SDO
Perhaps the connection between the tablet and the RDS lies within Hagoromo's ability to call back souls from the Pure World. Normally when the Shinigami is first summoned, we see the user's soul being dragged out of their body, so we can say that the soul is what allows the user to make a connection with the Death God. Maybe the Uzumakis created a similar ability to that of Hagoromo's in which souls could be returned to the Impure World through the use of the masks.
The way this is done could possibly be similar to the Edo-Tensei, that is, using a combination of a seal formula, the DNA/chakra of the soul being summoned, and a sacrifice. And who knows, perhaps Tobirama created the Edo-Tensei after studying the Uzumaki clan; we know he did so with the Uchiha.
Now since Hagoromo's tablet can only be deciphered with the Sharigan/Rinnegan, it is safe to assume that it at least has a small portion of his chakra. From Kabuto we know that Orochimaru had theorized how the Sharingan evolved into the Rinnegan. We also know that Kabuto had knowledge on the Six Paths abilities as seen when he was controlling Edo-Nagato. Orochimaru may have discovered that the Rinnegan or Hagoromo’s chakra could gain access to the Pure World via its innate properties (the Outer Path’s control over life and death).
So Hagoromo’s chakra inside the Tablet acted as the means to connect to the Pure World and summon the Death God. Notice that when Orochimaru does this, his soul is not shown being grasped by the Death God
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unlike with Minato and Hiruzen, who needed their souls to make that same connection
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Well that's all I could come up with...
