A lot has happened since Dr. Atkins put out his original DANDR in 1972, and subsequent updates (I have the 2009 paperback). So the new answer is caffeine is A-ok! - Per Eric C. Westman, Stephen D. Phinney, Jeff S. Volek:

The New Atkins for a New You

I limit coffee to my eating window - which for me is stacked from breakfast to maybe sometimes lunch - so caffeine never affects me getting to sleep.


New Atkins Diet is better than ever: Flexibilty in veggies, caffeine revamps popular regimen

"It's okay to have limited amounts of coffee," Westwood says, citing both caffeine's good and bad effects on blood sugar and weight.

^ they probably meant Westman lol

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