What about this though complete with serial numbers?:
Oswald had eight $1 bills in his wallet when he was arrested. None of the eight were torn in half. These eight bills were inventoried (according to serial number, see CE-1149). Armstrong himself has even backed off from that and now believes that the two halves were found at the rooming house on Saturday the 23rd.
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J. Edgar Hoover, "Masters of Deceit",1958: To join the Communist Party does not automatically mean life tenure. Memberships must be renewed every year or, in communist language, members are "reregistered. This represents another means of control. If a member is delinquent in dues or donations, he'll have to pay a penalty, perhaps contribute ten dollars, or be disciplined. These annual registration drives are important events in Party life. Each member is personally contacted. Clubs and sections compete for speed and percentage of successful registration. The drives usually start in October and often extend well past the December 31 deadline.
A member moves. His district organization will send details concerning him to his new area: name, Party history, whether dues are paid, along with any other remarks. A member may be given half of a dollar bill and the other half forwarded to the new district. When the member arrives, the halves are matched. Identity is thus established.
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There's a document in the Dallas Police records which mentions two torn halves of dollar bills. This document lists the serial numbers of both bills. However, it says nothing about Oswald and there's really no proof whatsoever that it is assassination related. But, that didn't stop Armstrong from taking it and running with it.