To review: My great-grandfather Leo had an elder brother Hyman (sometimes Herman), one of whose children was born Kalman Wertheim on 29 Oct 1890, and adapted his name to Coleman. I have a paper trail for him until the 1910 Census; and I have a record of his death in 1975 on Staten Island. (The SSDI record links him based on his date of birth.)
Coleman 2 has a consistent paper trail from 1915 to 1948. He was an auto dealer and chauffer.
Here's the trail, starting with Coleman 2:
1920 US Census, from Ancestry.com at http://interactive.ancestry.com/6061/4313901-01029/85940933?, gives him residing at 477 West St., Brooklyn.
Brooklyn Standard Union, 1 Feb 1920, p. 9, has the notice of incorporation for Ace Motor Sales Company, one of whose founders is Coleman Wertheim, 477 West St., Brooklyn.
Brooklyn Standard Union, 5 Apr 1921, p. 1, "Convict Dr. Kranzer in Stolen Car Deal", is an article about the conviction of Dr. Leo Kranzer, age 30, residing at 65 Tomkins Ave., for grand larceny. "The complainant against him was his cousin, Coleman Wertheim, of 570 East Second St., who conducts the Ace Motor Sales Company, of 279 Flatbush Avenue."
Dr. Leo Kranzer was the son of Nellie Wertheim Kranzer, the sister of Leo and Hyman, and thus a first cousin to both Coleman (1) and my grandmother Rosalie Wertheim. He was the attending physician on the death certificate of Pearl Wertheim, the grandmother of all these cousins. And indeed, according to the 1920 Census, he lived at 65 Tomkins Ave. (See http://interactive.ancestry.com/6061/4313502-00725/32241995?)
So at this point, I am asserting that I have met the Genealogical Proof Standard: Coleman 1 is indeed the same person as Coleman 2.
(In fairness, I should note that although Dr. Kranzer was found guilty, the jury urged mercy because they felt he had been tricked into breaking the law, and he was given a suspended sentence.)