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Slashes that prove that a validator equivocate should result in the validators weight in the current weight map to be turned to 0. Since since parent blocks are used for scoring, this doesn't break the "irrelevance of slashing" property as only scores of the children blocks after the slash are affected.
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Define "justification regression"
Let B1 and B2 be two blocks created by B such that the creator justification of B2 is B1. Let A be an arbitrary validator and let B1, B2 's justification (latest message) for A be A1, A2 respectively. A1 is not in the justification chain of A2.
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Slashing protocol
If you create a block with a justification regression, you must slash the validator(s) that forced you to create the justification regression or you are eligible to be slashed.