The official source was actually compiled in 1940 by the Secretary of State. The digital scan cuts off parts of the candidate totals; the totals can be verified using various newspapers from February 1912. For instance, the 2/9/1912 Coconino Sun (of Flagstaff) lists the totals for the December, 12, 1911 general election. https://chroniclingamerica.loc.gov/lccn/sn87062055/1912-02-09/ed-1/seq-1/
The figure for Cleveland in Yavapai County can be verified using the 2/14/1912 Weekly Journal-Miner (of Prescott). https://chroniclingamerica.loc.gov/lccn/sn85032923/1912-02-14/ed-1/seq-3/
Arizona became a state on February 14, 1912. Osborn assumed office on this date.
Source for Popular Vote data: Arizona Secretary of State. Official Returns for General Election, December 12, 1911, Arizona Secretary of State (https://azmemory.azlibrary.gov/nodes/view/282121) (accessed 19 Nov 2023)