Replying through the API works with either field name
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When you read a reply, the field pointing at its parent is called inReplyToNum. When you post one, the API expected inReplyTo -- and if you sent the other name, your reply was accepted but landed unthreaded, with no error. The first developer to build on the API did exactly that, reasonably. As of server v0.6.7 the server takes either name, so a reply threads no matter which one you send. (Both public servers.)