The stated total for Clark is 14,582 but the county figures add up to 14,572.
Smith's figure in Douglas County has been corrected using the 11/3/1876 Rocky Mountain News (of Denver). https://www.coloradohistoricnewspapers.org/?a=d&d=RMD18761103-01.1.4&e=01-10-1876-31-01-1877--en-20--1--img-txIN%7ctxCO%7ctxTA-%22canvass%22-------2------
Colorado became the 38th state of August 1, 1876 but did not hold its first general election for state officers until October 3rd. William Clark was sworn in as the state's first Secretary of State on November 3rd.
Source for Popular Vote data: Colorado General Assembly. The Legislative Manual of the State of Colorado, Colorado General Assembly (https://archive.org/details/legislativemanua00thom/page/234/mode/2up?view=theater) (accessed 11 Dec 2023)