No prob
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, I'll explain. It was as simplistic as I could make it, using two static parts and one part that "time travels" and using a letter designation to demonstrate what would happen. Part C could refer to anything that time travels from before the split point to after it, be it Crono and co. or a time travelling rock, it doesn't matter.
So in short, the first part shows what happens when the dimensions split into two, with dimension "X" (Another World) becoming a continuation of the original dimension and dimension "Y" (Home World) becoming a new one altogether which technically begins at the split point which is 1010 A.D. in Chrono Cross.
The second part shows that when the dimensions are refused, the parts in each dimension merge into one as is stated in the script of Chrono Cross - Parts Axy, Bxy, Cxy.
Now, the next part of the explanation has to do with the question -
"but what happens if someone or something time travels from before the split point to after it?" Well, as simply as I can put it, every thing in the universe/timeline/whatever you want to call it is duplicated at the split point and
only at the split point. If something or someone time travels from before the split point to after it, it is basically removed from existence temporarily and reinstated into existence after the split point. They are
not duplicated because the duplication only occurs at the split point, when the time traveller effectively did not exist in the universe. Because dimension "X" (Another World) is a continuation of the original dimension, and because we have just shown that
there can only be one copy of them, the time travellers emerge in the future of dimension "X" but not in the future of dimension "Y" (Home World). So if the time travel event was Crono and co. saving the world from Lavos in 1999 A.D., the future would be saved in dimension X but not in dimension Y. Simple, right?
But look what happens in the last part when the dimensions are re-fused together. Chrono Cross suggests that the reunification point equals the split point in 1010 A.D. If this is so, then just like when the dimensions split and everything was divided at 1010 A.D., now everything that exists at 1010 A.D. will be reunified again. But just like in the previous example, the time travellers do not exist at 1010 A.D. so their time travel event is unaffected. They still appear in the future due to time traveller immunity and in the case of Crono and co. they still defeat Lavos in 1999 A.D. and save the world.
So you see, it was the nature of the dimensional split that caused the future of Home World to be destroyed, and it was Serge surviving that caused the dimensional split, so Serge can be said to be the direct cause of the ruined future. But he and he alone also has the power to save the future by reuniting the dimensions.