What does Hawthorne claim are the similarities and differences in The Scarlet Letter and the historical artifacts he discovered?

In his introductory to The Scarlet
Letter, "The Custom House," Nathaniel Hawthorne alludes to his ancestors and
provides some background for his novel as well as rationale for his writing about Hester
Prynne, who suffered under the rigid laws of the Puritans.  When he writes of having
discovered the mysterious package that contained the "rag of scarlet cloth" that assumed
the shape of a letter along with "several fooscap sheets" that contained details of the
life and conversation of Hester Prynne, Hawthorne seems to wish to establish
verisimilitude for his narrative.  In his words, he has striven for "the authenticity of
the outline."  And, from this outline, Hawthorne constructs his intensely psychological
novel.

Perhaps because of his brooding ancestral guilt over
the uncle who was a judge in the Salem Witchcraft Trials,  Hawthorne wished to create a
certain realism so that readers would consider the problems of the strict Puritan code
and the Puritanical hypocrisy which yet loom over America. For, he declares that the
ghost of the Surveyor Pue exhorts him,

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"I charge you, in this matter of old Mistress
Prynne, give to you predessor's memory the credit which will be righfully its
due!"

And, Hawthorne replies
to the ghost as though he feels an obligation, "I will!"