[link to original on tumblr]
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It's the addition of the "there" in the last line of the second verse:
One of these mornings, you're gonna wake up singin'When I originally transcribed "Summertime," I wrote that line as "With your mommy and daddy; they're standing by." There's a slight caesura there, and I guess I thought that it signified the completion of "there ain’t nothin' gonna harm you / With your mommy and daddy," so that "they're standing by" stood by itself.
Then you're gonna spread your wings and take to the sky
But 'til that morning, there ain't nothin', nothin' gonna harm you
With your mommy and daddy, there standing by
It makes more sense as "there standing by," but I think "they're" could also be argued for. It's an interesting lyrical ambiguity, and that "there"/"they're" isn't present in any of the other versions of "Summertime" that I have, including versions by Anne Brown (and since Brown played Bess in the original production of Porgy & Bess, from which "Summertime" comes, her version is pretty much the original), Abbie Mitchell, Betty Roché (by whom I have a complete version and two reprises, although only one of those reprises contains the lines in question), Billie Holiday, The Platters, Sam & Dave, Booker T. & the MGs (which, as an instrumental version, doesn't include any lyrics), Sam Cooke (by whom I actually have two different versions), and Brian Wilson (from the Reimagines Gershwin album).
One of the Sam Cooke versions approaches the "there"/"they're" ambiguity. After completing the second verse ("With your daddy and mommy standin' by"), he goes into vocal riffs using some of the phrases from those first two verses, including "They're standin' by."