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Is Ion's Home Planet [Earth] the same [Earth] We Live in?

At Ra Ciela, Clacket found the outer universe [Earthes] from his own world [Ciel], and afterwards, thanks to the Tenmon researchers, he managed to summon a soul called [Nei] from that world.
That happened because a link was established with the planet [Earth] existing in [Earthes], however is that Earth the same planet we live in?

The answer is Yes.
However, if we change the question to whether if it's the Earth located in the same tridimensional space we live in right now, the answer would be No.

The Existence of Parallel Worlds

The world is configured similarly to an air cleaner filter, so the Third Dimension would be formed by folding and packing the First Dimension multiple times, while the Third Dimension is formed by the T-Axis and the I-Axis.
As the Qualia advances as a point in an unidimensional line, what you're feeling right now or your Qualia is a single point in that dimension.
Actually there's an exception to this: while there are several parallel worlds that diverged from the current one every time you made a choice and you may exist in several of them, the Qualia that forms your own self still exists as a single point in the Qualia Dimension.
Therefore, there may be a possibility in which Ion and the player both exist in the same tridimensional space, but even so, there is a probability of over a 99.999% of them existing as humans living in different tridimensional spaces (parallel worlds).
So even if Ion and the player have a common history, they will also have different histories.
And if Ion goes back to Earth, it would be extremely difficult for her to point her return coordinates to the TI point where the player's Qualia exists.
The reason for this is that the player's TI coordinates are constantly changing, even as she is aiming at them.
It would be next to impossible to aim at such a specific spot even for a person of Clacket's caliber.

The Vita and the DSS (Dimension Sync Stabilizer)

The Vita game is equipped with a space-time vibration control function called the [DSS], which serves to synchronize two different time-space zones.
Whenever the DSS is active, this world and the world over there will have their Time Axis completely linked, but said linkage isn't guaranteed if the DSS can't complete the connection.
In other words, if the DSS can't complete the connection, the space-time for Ion's side will be stopped.
But even if we say it's stopped, Ion can still move around, but that's only because she can still move even with the time-space stopped.
The world on the other side of the Cielnotron is inside Ion's dreams to begin with, and due to it, the concept of [time] doesn't really apply to it.
In fact, the DSS's role is giving the order of [now it's year A, month B, day C, hour D, minute E, so show me Ion's memories from after she woke up at around that time].

As for in which state the DSS works, we could describe it in a realistic way as it being the state [of being online and connected to the Internet].

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