I fly with a foreign passport with nothing on them, as long as your photo part is there you are good.
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Application sent:9/7/12-self (EAC-NYC)
I-797c notice: 9/20/12 | Biometrics: 10/18/12
Approval Notice: 12/10/12 | EAD: 12/17/12 | SSN: 1/2/12