Here's what we know:
1.) FATE states it has always been observing the two worlds.
2.) FATE states that after 1010, it cannot send data to Home World, which is listed as World 01.
3.) Chronopolis is basically geared towards watching more than one dimension at a time (hence the RD reference).
4.) The main split point that is heavily referenced is Serge's life or death situation in 1010.
5.) Miguel remembers being in the Sea of Eden for 14 years; 4 are the Sea of Eden, the other 10 in the Dead Sea.
6.) Kid travels to 1010 to save Serge.
7.) Miguel was stuck in the Sea of Eden at 1006, after Serge came into contact with the Frozen Flame. In Home World, the Sea becomes the Dead Sea; this prevents FATE from existing due to the timeline changes (the Day of Lavos occuring again negates Chronopolis' existence). In Another World, the Sea remains the Sea of Eden since the Day of Lavos does not occur. Since FATE in Another World is still able to keep an eye on the AW Frozen Flame, it sends AW Miguel (still alive since there was no Day of Lavos) to the Dead Sea to watch over the HW Frozen Flame.
8.) As a result of #7, when AW Miguel is killed in HW, FATE activates some sort of program which destroys HW Dead Sea from AW (i.e., across the dimensions due to the location of the three islands in the Sea of Eden).
9.) Miguel stuck in Chronopolis, at which point FATE kills him. When the dimension is split, the two worlds are different from that original one; in HW Miguel arrives in the future to find it destroyed (i.e., a TB following Serge's interaction with the timeline), but in AW he is kept alive due to FATE understanding what is going on. It proceeds to do #7 and #8 above.
10.) Kid can travel back and forth between dimensions, otherwise how would she get from Home World to Another World?
11.) Belthasar states the dimension split was due to a 50/50 chance of survival.
12.) The effects the characters are after do not occur until will is enforced. You cannot trigger the grandfather paradox by simply time traveling to the past and then returning. You have to act on it and kill your grandfather. Otherwise, the intended change does not occur.
13.) Chronopolis states that Home World is World 01. Technically, Serge is the alteration, therefore Chronopolis in AW should be World 01.
Okay, let's see if I can't give a good example of my thoughts.
1, 2, 3, and 13.)
Chronopolis is geared for watching more than one dimension at a time. In fact, it can watch at least three at one time: Another World, Home World, and the Radical Dreamers World. Now, if we go off the fact that Belthasar planned all of this in order to free Schala, we would have to assume that the most important world would be the one where Serge lives (i.e., Home World). This means Belthasar would probably have programmed FATE to recognize Home World as World 01 in its databanks; this relegates Another World as World 02.
Now, FATE can watch other worlds, but cannot directly interact with them. What if it could interact with its other version? For example, let's say that between 1006 and 1010 FATE wanted a certain person not to head to Termina on a certain day. Seems easy enough. But let's say that the two FATES (AW FATE and HW FATE) are aware of each other's existence, which they technically should be. Perhaps AW FATE wanted Person A to head to Termina in HW. Perhaps AW FATE made some sort of action which prompted HW FATE to tell that Person to head to Termina. It does state that AW FATE cannot send data to HW, most likely under this theory because HW FATE no longer exists (or perhaps the nature of the Dead Sea allows the two FATES to have constant contact, but no physical interaction with the other world's Records of Fate).
4, 6, 10, 11, and 12.)
The most evidence is placed on the dimensional split occuring in 1010. Serge died in AW, but lived in HW. Simple enough from that viewpoint. But let's take it a step further without going nuts.
Step 01: Serge dies.
Split: Nope.
Step 02: Kid is sent back in time from 1030 to 1010 to save Serge. (Yes, 1030, since Ghost Lucca in 1020 says Kid will travel back in 10 years.)
Split: Nope.
Step 03: Kid acts upon her instructions and saves Serge.
Split: Yes.
That's the point we have to remember: Free Will. Just because Kid has the opportunity to doesn't mean she does. Until Crono and company make the decision to go after Lavos and actually land the final blow, does the world change automatically? Does Crono go "I will defeat Lavos" and the world change around him? No. The physical manifestation of free will must occur for a time change to happen in the Chronoverse. We've pretty much beat this one to a pulp; until Kid traveled back in time, Serge was going to die 100% of the time. With Kid's actions, Serge was saved and Home World became the new focus world. However, since Home World and Another World are intertwined, the Serge from HW becomes the key which fits the void in AW (which is what is stated: Serge is able to travel back and forth because at any given time he is filling the void from the other world; likewise, when he gets Lynx's DNA and body, he can't because Lynx is still over in the other world, and not filling a void).
With that being stated, another possibility arises for this: Arbiter's have the ability to jump dimensions. This stems from the fact that there are likely two versions of Kid, one from HW and one from AW. However, Kid is Schala's clone, so it's quite likely that because Schala was at one time an Arbiter (she controlled the Mammon Machine, which had the Frozen Flame as its central power source), her DNA would be recognized (assuming Kid is an exact clone of Schala's DNA). Therefore, at weak points she can jump dimensions.
Now, with all of this being said, we have one big problem to discuss: How does the Split actually occur? Is it a Y, or is it an H?
Well, I think I've found a way to answer it. We all agree that a timeline without any changes looks like a straight line. We also agree that any defunct timelines are sent to the DBT. What if it starts like a Y but then becomes a | |. Almost like two parallel timelines. Here's what I mean:
Timeline 1: Serge becomes Arbiter. Serge drowns. Kid doesn't go back.
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Okay, that's the original plan. Of course, we want to start here, since Kid has to actually act in order to change things:
Timeline 1: Serge becomes Arbiter. Kid arrives from 1030. Serge drowns.
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Now, the difference is not whether Serge lives or not, it's whether she saves him that triggers the "split".
Timeline 1: Serge becomes Arbiter. Kid arrives from 1030. Serge drowns.
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\
Timeline 2: \ Serge survives.
\____________________
Okay, so there's out split (Kid saving Serge). But the current assumption is that Home World (Timeline 2 in the diagram) did not exist prior to 1010. The way to describe this is based on the statement that defunct timelines are sent to the DBT. What if the ENTIRE defunct timeline, not just the remainder of the timeline after the change occurs, is sent to the DBT? The portion of the timeline prior to the change is copied, and is sort of pasted to be the history of the new timeline, and therefore it matches up with what we know. This also goes a long way towards a possible explanation for Opassa Beach's dimensional weakness. After all, Serge was drowned there, and subsequently saved there, so that's where the split physically "occurred".
Simple explanation. Say we have an alphabet of ABCDEFG. However, let's say we go back in time and change D so that it becomes S. Our old defunct future is DEFG, our new future is STUV. However, according to the current viewpoint based on Chrono Cross, STUV doesn't have a past, since it fissioned off from ABCDEFG. What if the past of DEFG (i.e., ABC) is copied over to the new timeline, making the new timeline ABCSTUV, which is correct. The old timeline, which is ABCDEFG (not just DEFG) is kicked to the DBT. So, now there are two timelines: ABCDEFG and ABCSTUV, not ABCDEFG and ___STUV.
At that point, the two timelines exist independently of each other except for places like Opassa Beach where a common void/gate/whatever between the two exists. There is no H, it's two lines like this:
Timeline 1 (AW): Serge becomes Arbiter. Kid arrives from 1030. * Serge drowns.
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Timeline 2 (HW): Serge becomes Arbiter. Kid arrives from 1030. * Serge survives.
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The link between the two hasn't always existed, only from that point forward (1010 AD). I put a * in the diagram to show a break-point. Anything to the left of the * is what got copied into the new timeline as it's past. Simple enough. If there are any problems with that, please let me know.
5, 7, 8, and 9.)
Okay, we've answered this one, but I want to go over it real quick and concise.
1006 A.D. (Death by Poison Universe)
Serge, Wazuki, and Miguel enter Chronopolis, which means they are in 1006+12000+2400 or 15406 A.D. This is the universe where Serge dies because he did not get any help for the poison. I.e., he dies in 1006 from the poison. Serge is healed, becomes Arbiter; Miguel is stuck there, probably to be killed by FATE (if the timeline were to continue). Wazuki and Serge leave the future, and return to the past, and continue to live their lives.
When Serge and his father leave, the timeline changes to the newer universe of AW. Which means that the Death by Poison Universe Serge, Wazuki, and Miguel are sent to the DBT when they step through the gateway to the future. The "newer" versions of themselves are the AW versions. AW Serge is healed, AW Miguel is stuck there, and they return to the past, and continue to live their lives. In 1010, Serge is killed by Wazuki/Lynx, and FATE continues to exist, etc.
Kid travels back and saves Serge, fissioning AW to the DBT, and HW to the current timeline status. Kinda flip-flopped around from they way they place emphasis in the game (they generally try to force on the player that HW is an abnormality, when technically AW would be the one in DBT since it was overwritten by HW). Therefore, we now have three universes, but we don't worry about the Death by Poison one since we never go there in the game.
So, basically, the Miguel in the Death by Poison universe is killed by FATE.
The Miguel in HW is killed because Serge lives and the future is apocalyptic (he probably got there and was killed by something, since all three would enter the present, run around for a bit, then Wazuki and Serge would simply disappear due to TB and Miguel would probably have been killed by something anyways).
The Miguel in AW is sent over to HW, probably while sleeping or something, to watch over the Frozen Flame there since FATE is no longer existing in HW (and therefore can't keep an eye on it like it can in AW).
I think that's enough. Thoughts?