Suffolk Probate docket 3015 includes a document Vol. 6 (new series), p. 246 where Andrew Lane says he married the oldest daughter of Capt. John Smith, which would preclude Mary from being the wife of Jeremiah Swain. However this petition (undated, but Jan 1706 based on when recorded) says Capt. Smith died about 12 years prior so this is a different John Smith and the petition is filed in the wrong probate file. Source:Chamberlain, Mellen. Documentary History of Chelsea : Including the Boston Precincts of Winnisimmet, Rumney Marsh, and Pullen Point, 1624-1824 refers to a Captain John Smith and a Lieutenant John Smith, both of Winnisimmet, i.e., different people. The father of Mary was Lieutenant John Smith, apparently Captain at the time of his death in Sep 1706. Source:Eaton, Lilley. Genealogical History of the Town of Reading, Mass, p. 111, says the Mary Smith who married Jeremiah Swayne was the daughter of Francis, but this is also refuted by Chamberlain's book, p. 319, saying that in 1707 "Francis Smith son of Captain John Smith, deceased, and Jeremiah Sweyne, in the right of his wife Mary" in suit to recover land of their grandfather Francis Smith, father of Lieutenant/Captain John Smith, identified Mary as the daughter of John, not his sister.
