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A reverse lookup for finding all the shortened URLs associated with a given canonical URL.

Interesting... what would be the application of this? Any ideas you can share?

Lots of possibilities, but think backtweets.com as an example of something which would be much easier to accomplish if such an API existed.

We opened up an API for backtweets a while ago: http://backtweets.com/api

What would you build with it? Some people are using it in cool ways right now, e.g. hype machine uses it to power a twitter music chart.