Karen kindly supplied us with a copy of this document, which she obtained from the Maryland Archives in Annapolis.
Since we don't know who Jesse Cox's parents are, we were hoping this information would be reported on his death certificate. Unfortunately, it is not. It shows that Jesse was born in Caroline County, Maryland on January 13, 1856, but his parents are listed as "Unknown". (The birthdate on his grave marker is January 15.) The informant on the death certificate is his oldest son, Thomas A. Cox.
We have recorded his name as "John L. or Jesse" Cox in our blog posts, because of popular family belief that his name was John. However, in all of the documentation we have found so far, his name is listed as "Jesse", not "John". In some brief social items from the Denton Journal, he is referred to as Mr. J. L. Cox.