That's a BIG bear. From den emergence to fall hibernation, it is not uncommon for a bear to increase it's spring weight 50-60%. A genuine 400lb fall bear probably came out of the den around 250. A genuine 300lb SPRING bear may go 500lbs in the fall, and is a rare bear.
Not trying to be difficult or "row upriver" but I don't subscribe to that theory 100%. I have seen a few spring bears with over 100 lbs of fat on them (2+ inches) and I don't buy the statement that that same bear will gain another 100 lbs or even 40% of it's weight.
My biggest was a spring bear that dressed at 380 lbs. He had a couple inches of fat from his rear to his head. Easily close to 100 lbs of fat. There is no way that he was going to gain another 100+ ( or 200lbs if 50%) by the fall.
Now he may regain 100 - 150 lbs after losing 100 or so during the spring and fall.