The question is, what is the Alpha Centauri Concordium?
The Alpha Centauri state, which had started out as a colony of United Earth but had become independent some time prior to 2161.
...And what does it mean for Mars?
In the continuity of the novels, the implication seems to be that Mars actually declared independence
before United Earth was founded.
Articles of the Federation by Keith R.A. DeCandido established that United Earth was created by the Traité d'Unification in 2130 (which, combined with "Attached"'s reference to old nation-states joining the world government in 2150, implies that some countries were holdouts for twenty years). The ENT novel
The Romulan War: Beneath the Raptor's Wing established that the Martian colonies rebelled in 2105, beginning with the Gundersdottir's Dome Rebellion and a series of strikes that damaged Earth's economy, and resulting in the Fundamental Declarations of the Martian Colonies and Martian independence as the Confederated Martian Colonies.
It is not clear against
whom the Martian colonies were rebelling. I like to imagine they were rebelling against the remnants of large mega-corporations on Earth, and that the Martian rebellion played an important role in ending corporate power on Earth, enabling Earth to end capitalism and establish a democratic socialist system. But that's just me.
Either way, though, the implication is that the Confederated Martian Colonies, as a sovereign state, is actually older than United Earth. But, that same novel also establishes that Mars was very much the "cosmic Canada," perennially less powerful and wealthy than Earth and less influential in interstellar affairs.
So far, the only folks associated with Alpha Centauri have been humans, but is that humans originally from Earth who are now independent of Earth politically, or humans native to Alpha Centauri or other non-Earth location? That is, can a human colony have independence at this stage of the game, and if so, why is AC a special case?
The novels have established that both the Alpha Centauri Concordium and the Confederated Martian Colonies were sovereign states that originated as Earth colonies but became independent. The Alpha Centauri Concordium was one of the five founding Federation Member States in 2161; the Confederated Martian Colonies was the first new Federation Member State, joining shortly after its founding.
Other former Earth colonies that later became Federation Member State include Vega Colony (
Rise of the Federation: Tower of Babel) and Deneva (
TNG: Losing the Peace).
"United Earth" is nicely different from "the United Planets of Tellar" in semantically excluding other planets in Earth's sphere of influence. Is that because Earth doesn't want to politically control its colonies, or is incapable of doing so, or doesn't want to be seen doing so?
Neither. It's mostly just to emphasize Earth's status as a unified planet -- the equivalent of George Washington referring to "united America" in his
Second Inaugural Address.
I think the implication is that United Earth still maintains its own colonies, as established by the numerous canonical and non-canonical references to "Earth colonies" (that is, a colony falling under the political jurisdiction of United Earth, with representation in the Parliament of United Earth and whose citizens get to vote for the Federation Councillor for United Earth on the Federation Council).
I think Mars is also independent by the time of the COP, it should also have a seat at the table or maybe they did not want to join?
The
Romulan War duology establishes that the Confederated Martian Colonies had a permanent representative to the Coalition of Planets, but seemingly did not wish to join as a full member, IIRC.