What source proves the hyperlinked father – Ralph Paine – and mother – Dorothy Payne were Anthony's parents, and what proves his town and shire of birth? The overview well explains that these things are unknown. Unless someone has fantastically come upon a previously unknown, bona fide source, the parents and GEDCOM uploads that brought their names to Geni ought to be jettisoned.
A quick look at a FamilySerach query shows no birth indexed birth record to date with Anthony Paine as a father:— https://www.familysearch.org/search/record/results?count=20&q.a...
There are many FamilySearch indexed Anthony Paines as a father in a slew of other shires in England where records were better kept/maintain before 1540 than Lincolnshire:— https://www.familysearch.org/search/record/results?count=20&q.a...
