Now, fast-forward to Time Error C+13004. It's now 1004 AD, and Serge is bitten and being taken to Marbule by Wazuki and Miguel. Schala hears him and blows them to Chronopolis. Serge is made into an Arbiter, Miguel is trapped and Wazuki corrupted. Remembering also that FATE has temporal links to itself in other time periods, I'm theorizing that the presence of an Arbiter not only locks the present 1004 AD FATE out of the Flame, but ALL versions of FATE present during any time - even 12000 BC. So, what do we have now? Time is in chaos, because FATE has existed for 13000 years and now lacks the ability to keep people oblivious to it. That in itself could cause a dimensional split if you ask me - one dimension in which FATE keeps everything under control, and one in which it doesn't. But, then Serge is killed and it doesn't matter anymore - FATE regains access and can keep things cool again. Maybe Serge's death unified the dimensions?
Now, fast-forward again to Time Error C+13020. Kid travels back in time to save Serge and, instead of Another World going to the DBT, Home World is just created as an alternate dimension. Now we have the same situation as before, except that Serge isn't gonna die this time. FATE is locked out of the Flame all throughout time, so in 12000 BC, it is powerless to manipulate the happenings around it and shield its existence. So - two dimensions exist - one where Serge is dead and FATE has always been able to control the past, and one where Serge is alive and FATE can't do crap. That would actually make the histories of Home and Another World different, and thus allows for Crono to fail killing Lavos in 12000 BC only in one dimension. So, if Serge died, the dimensions would be unified once more, probably just resulting in Another World. But, the Chrono Cross is used to that Serge can live AND FATE can somehow preserve history. It's a crazy theory I know, but at least attempts to explain why there was a dimensional split and not just a new timeline.
OK you have worded this much more clearly now. However, I think there are some things wrong with this. The first thing would be the idea that the Arbiter locks out all versions of FATE from all time periods. It's a clever concept to be sure, but we know from Chronopolis that the Frozen Flame has had multiple Arbiters. If every Arbiter locked out all others across multiple time periods, then there could only be one possible Arbiter. And there were many, so I don't think this is what happened unfortunately.
Secondly, the histories in Home and Another World appear to only diverge after the time of the split in 1010 A.D. Due to circumstantial evidence from the game, every significant event that made the two dimensions different occurred after 1010 A.D., and events before 1010 A.D. are mentioned as having occurred the same in
both worlds (such as the Fall of Guardia and the Acacia Dragoons having some sort of involvement in that, for example).
This second point is supported and perhaps solidly confirmed by the fact that the Sea of Eden transforms into the Dead Sea only in 1010 A.D., and that Miguel remembers being in Chronopolis for 4 years before that. If the dimensions had been fully split before then (having separate and not shared pasts) then the Dead Sea would have existed all along in Home World's past.
Now on to this:Going off my original assumption that keeping TTI intact (Eske's idea) while doing away with TB after 1010 A.D (my idea that Eske agrees with) would create a duplication problem. We've already established that TB is likely not preserved in the Ideal Timeline after 1010 A.D. for time travel events that happened in one dimension but not the other. Eske proposed that TTI is still kept intact in the Ideal Timeline (see our discussion above). Now my example will attempt to prove why this produces a duplication problem.
Hypothetical example: Two dimensions, Home (X) and Another (Y) fuse to make one Ideal dimension (XY), and two time travellers, person X from Home World and person Y from Another World that are doppelgangers of each other fuse to create person XY in the Ideal timeline.
In Home World, person X first travels 5 years into the past to Time X-5, Time Error 0. Then he makes another time travel trip to time X-5-10 minutes, Time Error 1. Then he makes another time travel trip to time X-5-20 minutes, Time Error 2, ten minutes earlier.
In Another World, person Y (his doppelganger) never time travels at all.
At Time Error 3 the dimensions fuse to create the Ideal (XY) timeline and as per the script of Chrono Cross the individuals fuse in the two dimensions to create a new individual, person XY. We have already established in a prior post that TB would not be preserved for person XY in the new timeline.
If TTI is still preserved, then at Time X-5 person X will emerge due to TTI and he will not disappear due to TB. At Time X-5-10 minutes person X will emerge due to TTI and once again he will not disappear. At Time X-5-20 minutes person X will appear again and he will likewise not disappear. Now you have 3 copies of person X and one copy of person XY (whether or not he can be treated as the same individual is irrelevant).
So you see, TB and TTI are like two sides of the same coin. If you have one, you have to have both, and if you do away with one for whatever reason, you do away with both.
So I stand by my original assertion that after 1010 A.D. in the new timeline, time travel events that happened in one dimension but not the other will not be preserved by TB or TTI or DB or DBT (see reasoning from a previous post).
Your thoughts, Eske?
EDIT: On second thought I don't see a reason why Person X couldn't still be subject to TB (the reason why person XY isn't is obvious), so I'm not too sure about my conclusion now. I'll still leave my example up for discussion though. Regardless, if person X and person XY can be the same person speaking in terms of matter and energy, then this would still create a duplication problem even if person X only appears once.