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Does anyone have evidence of whether or not Google's search algorithm recognizes abbreviations such as...
It depends on what you mean by "recognize". While Google probably makes the association between commonly used abbreviations and what they stand for, Google appears always to favor a literal match.
So, if you're asking: "If I use 'TX' on a page, will Google treat that the same as if I'd used 'Texas'?"... in my experience the answer is no. If I were targeting, say, a business in Somewhere, Texas, I'd strain to get both 'TX' and 'Texas' on the page. Ditto with 'LA' vs 'Los Angeles'.
Conceivably, if you got down to a choice among not-very-many pages, Google might allow, say, the page containing the abbreviation rather than the actual word (or vice versa, depending on what was searched) to rank instead of the precise search, but I've never seen that happen.
Heavy inbound linking for alternative terms could of course change this.