Is the phrase "You are divorced" considered a single pronouncement, and is it possible to reconcile after it was uttered as a result of an argument with the wife that began with her saying, "It doesn't matter even if you divorce me," to which the husband replied, "You got it"?

Your statement to your wife "jaatek" (you've got it/it has come to you) is a kinayah (allusion) of divorce that takes effect with intention, whereas "anti taliq" (you are divorced) is an explicit statement that takes effect without intention. If you intended divorce with "jaatek", then you have divorced your wife twice, and it is a revocable divorce if you had not divorced her before, and you can take her back during her 'iddah (waiting period). However, if you intended the second divorce to be a confirmation of the first, then only one divorce takes place, provided that a long time has not passed between them. For more information, please consult the specialized courts.