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Any hints on how this could be achieved in secure way? Or may be not exactly 'secure' but industrially reliable? Asymptotic certainty increase via mutual checking of inputs, or brute force plurality of inputs and 'contradicting channels' one eliminated?

There may be many possible specifications. The point is that Steem supports bots and bots already check posts for plagiarism which is to say all it would take is a network of bots to provide automated fact checking. The way I would do it is to simply create a market for these sorts of bots by rewarding the bots with upvotes which provide this feature in a reliable manner.

There are some facts which may require human observation to confirm rather than just bots but that is already being tackled via the Smart Oracles concept.

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