They are including multiple corrections in this particular work. One of which involves evaluating the moments and identifying, if any, moments that may require correction. Then the moment that would result in the best solution is chosen and corrected with the goal of preventing unphysical results. The correction appears to occur after the iteration solving for the moments. I hope my explanation makes sense.
I take it from your previous answers that I may not need to consider this, but can track the moments throughout the solution as I go in case I have concerns.
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