If you don't know which sides crota moves to after time then you shouldn't be running sword you set yourself up for failure by going that way
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I've run that side every single time I do the sword across all three characters and have never been killed by Crota. Boomers yes but not Crota. Also, he isn't supposed to run into the crystal room lol I have 120+ completions. Just to credit my previous statement.
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Still I always run to the right side on first sword so there's no chance of him killing me