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The way I do it, is backup the entire disk. Look at all titles with the correct length of 2:26:14 and disregard the rest. They are making it hard for this one. There are 150 (!) titles with that length. I grabbed 00778.mpls to see if there was any difference from 00198.mpls. Doing a quick compariso...

I tried the file that Coolmac suggested and it is probably the one you want, not the one I did. So far I noticed a different edit of the train scene at around 14:30. Interesting... Source file name: 00198.mpls File name: The_Hunger_Games_Catching_Fire_t35.mkv

If you scroll down about 4/5's of the way there is one file with "(Primary title)" in the name. Not sure what that means but I took a chance and it looks like it works. Source file name: 00861.mpls File name: The_Hunger_Games_Catching_Fire_t143.mkv

Anybody else have an guess?