GrayLensman, I have a question about Lynx. Under the TTI Sea of Eden assumption, wouldn't a version of Lynx still emerge from the Sea of Eden after Wazuki's brainwashing with the imperative to kill Serge? The game never elaborates on whether FATE had an active link with Lynx's mind, or if Lynx was simply operating on his own twisted will when not interfacting with FATE directly (like in Chronopolis).
If the above is true, then it is still all right, as Kid would be protected by TTI too and would appear to save Serge in 1010 A.D. But I'd like to just iron these two points out. Then I'm going to guess at some ideal situations, and this outline can then be used in the theory entry on the unification and also the Chrono Cross Resolution article.