What are the K numbers used for Domenico Scarlatti’s sonatas?

The "K" numbers used to identify the keyboard sonatas of Domenico Scarlatti refer to the numbering system established by the American musicologist Ralph Kirkpatrick.1

Because Scarlatti’s 555 sonatas were not published in an orderly fashion, several numbering systems were historically used to organize them. In his 1953 monograph, Domenico Scarlatti, Kirkpatrick provided a comprehensive list that renumbered the sonatas in the chronological order of their surviving printed and manuscript collections. This "K" numbering system has since become the standard, replacing earlier systems such as the one created by Alessandro Longo.123