Technically speaking, no there is no proof of the parentage of William Older.Thomas Older left no records naming his children.William Older left no records naming his parents.The original family record was compiled by his great granddaughter Margaret A. Older, in the early 20th century.She is the one that stated that Thomas Older was the progenitor of the family and gave his background. She likely gained the information from her parents.So the lineage is oral tradition. Margaret named Thomas' sons as being William, Nathaniel and Benjamin. She attributes children only to William and Nathaniel. It is largely accepted as true that your William was the son of Thomas Older, but as to actual proof, no there is no proof of the parentage of William Older.