Now, wait a minute. Some of you may be wondering why I never posted a 31x45 Polyominous as one of my previous giants. Well, the answer is simple: in Nikoli's publications, a Polyominous the Giant is 23x37, and my arbitrary adherence to Nikoli's standards for puzzles in the numbered "puzzles" series (as opposed to Monday Mutants et al.) means I only post puzzle genres Nikoli's made, in sizes Nikoli's made. 23x37 is hardly an adequate size for a celebration on this blog, don't you think? However, Nikoli has published 64x50 Fillomino puzzles on at least three occasions, including in volumes 123 and 134 of Puzzle Communication Nikoli, and in a now out-of-print Puzzle the Giants volume, making that size completely fair game.
Special thanks to Thomas Snyder, who set aside 1 hour, 31 minutes, and 45 seconds of his time to make sure this puzzle had a unique solution before it was posted here. I am incredibly honored to have the respect of such an amazing constructor and solver. Not everyone has the privilege of being able to send Thomas Snyder a puzzle and getting the time of day from him, much less his opinion on it. (In fact, I believe some of the people who ended up being ripped to shreds on Grant's Review Corner contacted him first. . .)
Edit: Okay, apparently, Blogger and Picasa handle images taller or wider than 1600 pixels in ways I don't like for the purposes of this post. I was able to find a way to link to the full 1797x1405 version of the picture, but you might be asked to download it instead of being able to view it in your browser. A small sacrifice, but it works.
(click to enlarge)