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The aftershock productivity law, first described by Utsu in 1970, is anexponential function of the form K=K0.exp({\alpha}M) where K is the number ofaftershocks, M the mainshock magnitude, and {\alpha} the productivityparameter. The Utsu law remains empirical in nature although it has also beenretrieved in static stress simulations. Here, we explain this law based onSolid Seismicity, a geometrical theory of seismicity where seismicity patternsare described by mathematical expressions obtained from geometric operations ona permanent static stress field. We recover the exponential form but with abreak in scaling predicted between small and large magnitudes M, with{\alpha}=1.5ln(10) and ln(10), respectively, in agreement with results fromprevious static stress simulations. We suggest that the lack of break inscaling observed in seismicity catalogues (with {\alpha}=ln(10)) could be anartefact from existing aftershock selection methods, which assume a continuousbehavior over the full magnitude range. While the possibility for such anartefact is verified in simulations, the existence of the theoretical kinkremains to be proven.

Utsu aftershock productivity law explained from geometric operations on the permanent static stress field of mainshocks