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I was trolling on around on dba.stackexchange.com when I got a notification on the StackExchange Banner from stackoverflow.com. Even though the badge was issued for Stack Overflow, the sprite was pulled from the site I was currently on:
This is not the behavior I would expect.
Since the Stack Exchange banner is universal to the Stack Exchange network experience, I would expect a standardized version to be used. A more robust solution might even to pull in the appropriate sprite from the site that is showing the notification, but that might require loading too many resources.
Here are the sprites in question: