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I have a feeling we need even bigger presence on twitter, maybe with clear structure, framework and goals as well. I think basically that is it. But then we need to do better as a community

Don't overthink it. Let it happen. That "bigger presence" happens one person at a time! None of the other big projects have done any "Twitter planning" at all. It's always been organic. In fact, I would say if it isn't organic, it'll probably fail.