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Question: What is the Bat Creek Stone and is it related to Mormonism?
The Bat Creek Stone is an artifact excavated in 1889 by the Smithsonian Institution: It is considered to be a forgery
A forged item can tell us nothing about ancient America in general, or the Book of Mormon in particular. Any current source that uses the Bat Creek Stone as evidence should be treated with caution; its author(s) are not using the most up-to-date information. At the very least, it is premature to rely on the Bat Creek Stone as evidence of anything related to ancient America.
The Bat Creek Stone is an artifact excavated in 1889 by the Smithsonian Institution [see Figure 1], and was also found with brass bracelets.
The stone was described in a 1894 publication by the same group.  The author of the report, Cyrus Thomas, claimed that the marks were Cherokee. A review of Thomas' subsequent publications demonstrates that he likely concluded that the items were forged, but he did not make a more public point of this because he and the Smithsonian "had placed themselves in a position such that they really could not afford to pronounce the Bat Creek stone a forgery after publishing it." 
After Thomas, little attention was paid to the Bat Creek stone until 1970--as noted above, Thomas had probably recognized that it was fraudulent by 1898. In 1970, Cyrus Gordon of Brandeis university argued that the stone had been oriented improperly in the original publication.  If it was inverted, Gordon claimed, it became clear that the text was Paleo-Hebrew, and read "for the Jews."  Other scholars joined the debate, and the positions are well summarized by Mainfort and Kwas:
- As of 1993/94, the opinions of the principals in the debate may be summarized as follows. Cyrus Gordon was the earliest credible proponent of the Bat Creek stone as an authentic Paleo-Hebrew inscription, though he acknowledged “problems” with three of the inscribed characters. Frank Moore Cross and Kyle McCarter pointed out additional paleographic difficulties and argued that too many of the characters were problematic for the inscription to be authentic. Huston McCulloch considered all of the inscribed characters to be legitimate Paleo-Hebrew (but disagreeing with Gordon about three of them) and presented radiocarbon evidence supporting an age for the stone in the first several centuries A.D. Finally, Mainfort and Kwas(1991, 1993a,1 993b) questioned the veracity of the find itself and presented evidence suggesting that Cyrus Thomas and his contemporaries recognized the Bat Creek stone as a fraud by the end of the nineteenth century. 
The case for forgery was strengthened in 2004
Although there were questions about the Bat Creek stone's origins, these were strengthened by a 2004 paper by Mainfort and Kwas. In it, they demonstrate that the text for the stone was copied from an 1870 book on Freemasonry: Robert Macoy, General History, Cyclopedia, and Dictionary of Freemasonry (New York, Masonic Publishing Co., 1870), 169. [See Figure 2.] The Masonic use of the inscription comes from a Jewish coin, reading "Holiness to the Lord," or "Holy to Yahweh." 
The man who discovered the Bat Creek Stone did so alone, and was not a professional archaeologist in the modern sense. He also seems to have "discovered" other artifacts that are clearly forgeries.  His problems with alcohol led to him being fired for a period; political pressure was necessary for him to regain his job, and his forgery may have been motivated by a desire to ensure his continued employment.  Others have argued that the evidence is not as air-tight as these authors believe. 
The Bat Creek Stone was also found with two bracelets, but these were dated to the eighteenth or nineteenth century
The Bat Creek Stone was also found with two bracelets, but these were dated to the eighteenth or nineteenth century.  This heightens the evidence of fraud still further.
McCulloch has replied to this analysis, arguing that the characteristics of the stone itself suggest many years of weathering, and argues that the inscription is not identical to the Masonic encyclopedia. 
- Cyrus Thomas, Report on the Mound Explorations of the Bureau of Ethnology Twelfth Annual Report of the Bureau of Ethnology for the Secretary of the Smithsonian Institution 1890-‘91 (Government Printing Office, Washington, D.C.), 394.
- Robert C. Mainfort, Jr. and Mary L. Kwas, "The Bat Creek Stone Revisited: A Fraud Exposed," American Antiquity 69/4 (2004): 762-763.
- Cyrus H. Gordon, "New Directions in the Study of Ancient Middle Eastern Cultures," Bulletin of the Middle Eastern Cultural Center 5 (1991): 62. See Gordon's argument in an LDS publication: Cyrus H. Gordon, "A Hebrew Inscription Authenticated," in By Study and Also by Faith: Essays in Honor of Hugh W. Nibley on the Occasion of His Eightieth Birthday, 27 March 1990, ed. John M. Lundquist and Stephen D. Ricks (Salt Lake City: Deseret Book and FARMS, 1990), 1:67-80. ISBN 0875793398. Vol. 1 off-site Vol. 2 off-site
- Mainfort and Kwas, 762-763.
- Mainfort and Kwas, 764.
- Mainfort and Kwas, 765.
- Stephen Williams, "Fantastic Archaeology: Another Road Taken by Some," Paper presented to the American Association for the Advancement of Science, Boston, Massachusetts, 1993 as cited by Mainfort and Kwas, 765.
- Mainfort and Kwas, 765-766.
- His reply was rejected for publication in American Antiquity where the original debate took place. It is available on-line in PDF.
- Mainfort and Kwas, 766. The authors cite their own previous work, Robert C. Mainfort Jr. and Mary L. Kwas, "The Bat Creek Stone: Judeans in Tennessee?" Tennessee Anthropologist 16/1 (Spring 1991): 1-19. For the reply, see J. Huston McCulloch, "The Bat Creek Stone: A Reply to Mainfort and Kwas," Tennessee Anthropologist 18/1 (Spring 1993): 1-26.
- J. Huston McCulloch, "The Bat Creek Stone," on-line posting, December 2005. His reply was rejected for publication in American Antiquity where the original debate took place. It is available on-line in PDF.