Even later, there was the Gadsen Purchase, as well. It makes me wonder what these Americans today think of the usurpers who denigrate their heritage as Spaniards, and then as Americans by invading en masse as if they are somehow entitled to.
They are entitled. Possession by right of conquest is recognized by the Law of Nations.
Spain abandoned the territories at issue, in some cases under the application of force by Mexico. Mexico, therefore, occupied some of the territory abandoned by Spain but claimed it all. However, Mexico was unable to maintain control over all it had claimed. Hence, some of the territory at issue was seized and held by Mexico by right of conquest, and some remained beyond Mexico's effective control. This latter, then, became unclaimed territory despite Mexico's assertion otherwise (a claim that connot be enforced has no standing).
When we (the US) won the war with Mexico, we settled the boundry dispute Texas had with Mexico, we claimed the territory abandonded by Spain, and took the balance of the disputed territories from Mexico by right of conquest (Texas, an independent nation for ten years, applied for admittance into the US and was accepted).
We hold these territories by right of conquest. Aztlan can claim these territories by right of conquest. At some point, one of three things will happen.