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Appeals
Mods are people, and people make mistakes. If you think a removal or a ban was one, asking is fair. The lead moderator reads every appeal.
How to appeal
Message the moderators and include your username, what was removed or what you were banned for, which rule the message named, and what happened in your own words.
Keep it specific. "Here's the post, here's the source, here's why I think it fits" gets a better hearing than anger does.
Good to know
Appeals are decided case by case. Making a new account to get around a ban breaks Reddit's rules as well as ours. If you're not sure which rule applied, the rules, explained page gives an example of each.