Should William Frost (abt. 1630 - 1719) remain PGM?

Question

Do we have a reliable historical records showing this William Frost was in the colonies during the Puritan Great Migration (ala, say by mid-1641)?

Josephine C. Frost in The Frost Genealogy ... (1912) writes that William Frost was in Southold, Long Island, as early as 1655. See HathiTrust.

This week, our Bobbie (Madison) Hall wrote, "The only entry [in Robert Charles Anderson's Directory] for a William gives us [the entry below ... which is.a different man ... see William Frost (abt. 1589 - 1644)]:

Frost, William: Nottingham, Nottinghamshire; 1638; Fairfield [Plain Dealing 98; Ackley-Bosworth 93-94; TAG 64:161-67, 208-13].

If we don't have a historical basis for the presence of William Frost (abt. 1630 - 1719) in the colonies before 1655, should we add a research note and remove the Puritan Great Migration/PGM Project Box?

Edited to add: Directory is otherwise Robert Charles Anderson, The Great Migration Directory: Immigrants to New England, 1620–1640: A Concise Compendium (Boston, Massachusetts : New England Historic Genealogical Society, 2015). 

Comments

It looks like he's included based on statements that his father John was in New England by 1635...but the Directory doesn't corroborate the presence of a John Frost by that time either.

---

Yes, and among the three--father and sons--I find no event mentioned in the colonies until well after the migration had ended.

The profile manager is looking into it. --Gene

---

What's a PGM?

---

It's the Puritan Great Migration Project.

---

My bad, Beth, and thank you, Bobbie. --Gene