Currently I've finished all Time Challenges and gotten all Emeralds and Sonic Medals, and so I've been replaying the levels and trying to hit as many special stages as possible to boost my score more, and along the way I noticed that after the ring bonus for the special stage is finished tallying and you return to the game proper, the game adds an extra 5000 points out of nowhere. I'm not quite sure if this happens when you haven't obtained the emerald yet, but I figured it was worth reporting.
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Before: https://cdn.discordapp.com/attachments/315258983399161866/383991208118059009/unknown.png
After: https://cdn.discordapp.com/attachments/315258983399161866/383991269233524746/unknown.png
5000 points are awarded when a life is obtained. This behavior is not a bug.