Census, and she was my grandmother. She personally told me her father's name and all legal records I have found confirm it.
"United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MSN1-Q85 : accessed 11 January 2016), Frank Smith, Cazenovia Township Cazenovia village, Madison, New York, United States; citing sheet 5A, family 130, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,241,071.
"New York, County Marriages, 1847-1848; 1908-1936," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XVGT-CY3 : accessed 23 May 2016), Frank W. Smith in entry for Thomas Gougherty and Ruth M. Smith, 02 Apr 1913; citing county clerk’s office, , New York, United States; FHL microfilm 831,341.
Obituary - "Michigan Deaths and Burials, 1800-1995," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:FHHX-YYC : accessed 11 January 2016), Frank Smith in entry for Ruth M Gougherty, 04 Mar 1974; citing Riverview, Wayne, Michigan, reference 23; FHL microfilm 2,107,773.
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DNA Connections
It may be possible to confirm family relationships with Ruth by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Ruth: