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So if you're using a bloom filter and you don't want to query the search engine, how do you deal with the potential false positive of it already being submitted?

Good question, for now, the false positive is not handled. One solution is to keep a false positive whitelist (also a bloom filter) in server side, only when the first user reports the false positive url, the link will be joint into the whitelist, then timely distribute to client.

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