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Actually, the Atkins induction (first two weeks) stage typically provides closer to ten pounds of weight reduction. Again, we can get into what that weight consists of, but whatever. 5 pounds is actually a fairly shitty result.
Sure, which is exactly my point. The composition of that weight is important in the grand scheme of things. The Atkins era was mostly focused on weight loss, not total fat loss. Up until a few years ago with the advent of DEXA scans, it was cost prohibitive to accurately assess % body fat changes with diets (and even those methods have sources of errors and limitations), so I don't think the early Atkins adopters and researchers were paying attention to that. They were just happy to hear that people were losing 10 pounds in 2 weeks.
I tried ketogenic a few years ago and easily lost a pound a day for about 10 days, but gained most of it back when I returned to a normal carb intake. Therefore I would expect 5-10 pounds of total weight loss with a keto or atkins diet, but 5 pounds of pure fat loss in 2 weeks with no corresponding muscle or water loss would be an anomoly. Which doesn't make it impossible, because outliers do exist, but based on most research regarding how fast one can lose weight without losing muscle those results are not typical.