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I think it's getting close. The summarize tool can identify what categories totals to zero, however I need all of the unsummarized data (all the other fields in the table) to process further in the workflow.
So my table contains >1M records. I only want to pass through all of the records where the sum total of the categories are not zero. So using your example only want all of the records for Categories A,C,D. to remain because the sum of all the records do not equal zero.