Wait...I dont think this is the correct response. I called the admissions office yesterday and you need to be COMPLETE by the 15th. She actually said you should submit your application through LSAC 7-10 business days before the 15th, which is basically today. She also said that if you need more time with your PS/Resume you can mail that in separately. She was very nice and very clear so I would probably take this as the truth.
Upshot: Please DONT tell people it only needs to be submitted on the 15th, because according to my convo with the admissions office you need to be COMPLETE on the 15th!!!!! unless she is full of it.
I obviously can't say that she is wrong but here's my source:
CLS Early Decision Contract wrote:If you have chosen to apply as an Early Decision candidate, please complete this form, print, sign, and send it to the Office of Admissions, no later than November 15. You will be notified of Columbia's decision in December.
I suppose it's probably better to get it in sooner tho jic. :S