«Dr. Conrad Founds KDKA» by Donald G. Little, American Heritage, August 1955, page 71 (americanheritage.com)
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Presumably Conrad had been given an informal authorization to operate pending the license reissuance. "Getting Your Licenses" (QST, November 1919, page 12) noted that «Radio Inspectors are authorized, however, to advise applicants what call letters they will eventually receive on their licenses and authorize them to commence operation at once, using their official call, without awaiting receipt of the actual license.»
«New Stations: Special Land Stations», Radio Service Bulletin, August 1, 1916, page 3. The leading «8» in 8XK's call sign indicated that the station was located in the eighth Radio Inspection district, while the «X» signified that the station was operating under an Experimental license.
