Questions raised:
1. What is the nature of the Ideal Timeline?
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1. Ideal Timeline
Inquiry
The ending of Chrono Cross suggests that the dimensions were unified and the rift closed. Time, which has been divided, will be unified again now. Schala says time is unified but she doesn't say when it must be unified. This creates somewhat of a problem since Home and Another Worlds both had distinct histories that could not be simply merged due to differences; for instance, the Dragoons were alive in Another, and dead in Home. Which timeline is used in the Ideal Timeline, the world after the Chrono Cross unifies the dimensions?
Please note that the question of whether Chronopolis would still exist in the Sea of Eden is addressed at Salt for the Dead Sea.
Theories
Timeline Rewind
Bubblebobby2000
The dimensions weren't unified, but rather Schala never interfered with time in 1006 A.D., preempting the events that shaped Chrono Cross's history. Time then proceeded normally from 1006 A.D. on, resulting it a new timeline whose details are unknown (apart from the fact that Serge lived, and he and Leena still are friends). The new timeline would proceed like this:
1006AD
Serge bitten by panther demon. Wazuki, Miguel then brings Serge to Marbule and there Serge was healed by the witch doctor.
1010AD
Serge never drowns (since Lynx was never there). And the world never divides.
1020AD
Serge continues with his life, except he finds that one day he falls unconscious at the beach. And then he wakes to find that he has in his mind a set of memories from some other Serge in some other world. This other Serge is the Serge who once lived in Home World and defeated the Time Devourer. Note that under the Time Bastard theory, the Serge indigenous to the Ideal Timeline would be replaced by the one coming in from Home World / the Darkness Beyond Time. Everyone would have their memories erased following the unification, consistent with what Schala had predicted. The exception is Serge of course.
The worst problem with this idea is that Kid would have never been created as part of Project Kid. Even this stipulation is debatable; perhaps Kid might have still come in to the world. At any rate, these points are so far removed from the original idea that they are almost moot, as Chrono Cross leaves much to be desired in terms of explaining its resolution. While ideas like Time Traveler's Immunity and Time Bastard can be applied to these possibilities, it's tenuous to do so because so little is known.
Happy Ending
SubwoofersIcecream
Somehow, the Chrono Cross was able to rewrite history taking the most optimal elements from each dimension and combining them. In this scenario, the Acacia Dragoons would live, but so would the Hydra; Marbule would be restored, but Fargo would remain an independent, self-made pirate without regrets. This theory is troublesome, as who is to determine what is good or bad in each dimension? The Chrono Cross would have to have a complete awareness of history and human emotion from 1010 A.D. onward in El Nido. FATE could provide something like that, but FATE was destroyed by Serge prior to the resolution of the game. Additionally, the Records of FATE weren't working in Home World anyway.
Serge Default
Fyrekun
Since Serge is depicted as being alive at the end of the game, Home World's history could have been used as default. Serge only lived in that dimension, as he was absent from Another starting with the time of the dimensional split.