Looking at the paper itself.. it rests entirely on an allegedly strong correlation between "annual growth anomaly" (which is the absolute deviation from a cubic spline fitted to the entire data set) and annual cosmic ray flux. So far so good although the choice of a cubic spline is "interesting" (it has a very good fit to the tree ring data, well no shit Sherlock that's the whole point of a cubic spline isn't it).
The resulting 45-year record has a superficial resemblance to cosmic ray data over the same period although I rather suspect that this is dependent on the degree of smoothing specified for the cubic spline.
But now the good bit - the fit between the growth anomaly and cosmic ray flux has a correlation coefficient of 0.39, or if you prefer an "r^2" of 0.15, from 45 points. Alternatively you can (and the authors do) specify it as a probability of fit,which gets a mighty 0.8% (i.e. there is a less than 1% chance that the cosmic rays explain the growth ring data).
Of course the usual suspects that complain the entire field of anthropogenic global change is "junk science" will doubtless be all over this one like a rash. Different standards apply to research claiming an extraterrestrial effect, you see..
My biggest gripe was the small incompatibilities between
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