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http://en.wikipedia.org/wiki/Baja_California#Nineteenth_and_twentieth_centuries
Apparently there was an offer from someone close to Mexican President Carranza to sell Baja California to the United States for $50 million in gold.
What if the U.S. under President Wilson had accepted this offer?
Carranza might have some public-relations problems for selling off chunks of
La Patria, but $50 million would help him shore up his position somewhat.
I think it would be plausible to have it named "Lower California" and be one complete state.