I have doubts that a “4k version” is anything more than a 2k upscale.
Wasn’t it “2k” that the “special” editions were scanned at? …hint: yes.
http://arstechnica.com/business/2010/05/star-wars/

If “2k” was the best they had at the time, we’re looking at either an upscaled version of whatever “2k” meant back then, or a full re-scan. Probably of the “special” edition.
I don’t have high hopes for a full re-scan of the actual original. It’s far more likely that they took whatever “2k” meant back then, which could be somewhere a little past that, and simply upscaled it using whatever means to make it look nice in that format.