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All of the graphs in the literature suggest a positive second derivative. Why do you say negative? AIUI the model is that hormesis kicks in even for extremely small amounts of radiation, but has a limited effect and is overwhelmed by the negative effects of larger amounts.

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I say negative because that's what this study is suggesting -- the slope of the curve is higher at lower dose than at higher doses.

That doesn't mean negative. The curve could be flat, then steeply rises to match LNT at some point.

It means that somewhere the second derivative must be negative (proof: take the derivative, then apply the mean value theorem of calculus)

You're correct of course. I read that as first derivative for some reason.

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