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"Real ketosis" is the presence of markers that demonstrate fat metabolism. This is most commonly done by measuring beta-hydroxybutyrate with the same device that diabetics use to measure blood glucose (using a different kind of test strip). It wouldn't be uncommon for any given person on any diet to show signs of fat metabolism if, for example they've fasted for 12 hours or more and have done any kind of exercise.

Nutritional ketosis as practiced by anyone doing "keto" is generally considered to be somewhere between 1.0 to 3.0 mmol/dL BHB. Getting there is not hard for anyone on a fat-adapted diet.

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For anyone following this, here I am 12 hours later after having dined on a relatively low-carb meal with some sweet potatoes and a couple of small bites of the wife's dessert of crème brûlée. I've yet to have breakfast and did some low to moderate intensity cycling this morning. My BHB is 1.6 mmol/dL, definitive signs of nutritional ketosis with very little effort on my part.