The current ruling authorities of Mexico go through the colonial viceroyalty, the War of Independence, the First Empire, the Federal Republic, the Second Empire, and United Mexican States.
I propose that the Federal Republic and the United Mexican States are the same ruling authority.
Currently the Fed. Rep. spans the years 1823 to 1905 and the UMS is 1905 to today with the 2nd Empire in the middle of the Fed. Rep. period. There was no change of government in 1905. There was a monetary reform in 1905 where the coins changed their legends from “Republica Mexicana” to “Estados Unidos Mexicanos” (which is why I think the cutoff was initially made in 1905) but the president from 1884 to 1911 was the same man. The date of 1905 does not meet the threshold for different ruling authorities set out in the Guidelines. In fact, the 1824 constitution explicitly names Mexico as “Estados Unidos Mexicanos" so even the “United Mexican States” had been around for 81 years before 1905.
There is an argument to be made for separating the ruling authorities based on 1824, 1857, and 1917 constitutions since they marked major departures from what came before, but given the inertia of the coins pages, merging Federal Republic (1823–1905) and United Mexican States (1905–date) is the cleanest and easiest solution, viz. consolidation would be easier than recategorization.
I would also argue that like the Mexican War of Independence (1810–1821) ruling authority, there should be a ruling authority for the Mexican Revolution (1910–1920) since a number of armies, states, localities, and provisional governments emitted currency without the authority of a central government during this time. This would obviate the need for separate revolutionary issuing authorities in Mexico since all issuers from this time issued pesos and none did so seeking to create a political entity separate from the nation. Also, from the guidelines: “Only when the territory of an issuer suffers a sudden, significant, and long-term change, resulting in a discontinuity of its currency, then the change result in a different issuer” The Revolution was sudden and significant, but it was not long term.