Correct me if I'm wrong but I think I read somewhere that if you don't have something specifically dated June 15th 2012, you may still prove presence by gathering documents from the day before June 14th, 2012 + the day after June 16th, 2012. Or anything you have that is a couple of days prior and after that date.
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Application Status: Self-filed on 8/18/12 to Chicago w/ Priority Mail and Delivered on 8/20/12 @ 2:47pm
Date of G-1145 Notification Received (email & text): 08/27/12 @ 3:48pm Routed to Vermont
Date of I-797C Notice of Action Letter Received: 08/31/12
Date of Biometrics: Received 08/31/12 and Scheduled for 09/17/12 in Cranston, RI.
Date of Approval: 10/23/12