Proof? That's a "General Birth Index" according to Ladysforest, which doesn't prove anything about Obama being born in a Hawaiian hospital:
Here is what you are given when you request the General Index Data book for births at the Department of Health in Honolulu, this is an actual image of the book in the DoH.
And
"This trip was something I was determined to do because I wanted to see if the obama name was or was not in the index book. I wanted to know if the DoH would again claim that they only have a “General Birth Index”, and if they would refuse to make a copy of an index entry.
Most importantly I wanted real proof, and I doubted it would just be handed over. "
-end snip-
http://myveryownpointofview.wordpress.com/2010/07/27/ya-cant-always-get-what-ya-want/
That is it doesn’t “prove” or “confirms” a Obama hospital birth”.
Correct. The General Birth Index entry for “Barack Hussein Obama II” doesn’t, in and of itself, prove that Obama was born in a hospital.
However, the fact that Obama isn’t listed in the Certificate of Hawaiian Birth index indicates that he did not qualify for the type of birth certificate that was issued to those born at home or whose parent(s) personally registered their birth within a year of the event.
Since he didn’t qualify for a Certificate of Hawaiian Birth, he qualified for a standard birth certificate, which is usually generated by birth at a hospital. But to your point, yes, it’s speculation that he was born in a hospital in Hawaii.