[Mount Athos]

I think you’re messaging the wrong person, I explicit say in my comment that the document was generated 3 years after he was born.

[Mount Athos]

(corrected)
There are two places for signatures, one for Obama Sr. and one for an official. Both are blank.

There IS a signature from the official on the document. There isn't one for his father, but the official might have been satisifed that one wasn't necessary for this document to be generated. One possibility is that the court of hawaii requested it. The court had proof the father was not responding to the divorce proceedings, this proof is included in the final divorce decree available online.

There are no details regarding time of birth, weight, attending physician, etc...It's possible that Kenya never records these but it is a question.

Very possible they weren't in the habit of recording it on registered copies of birth certificates. Maybe it's available on another type of document.

The fact that there was no Republic of Kenya in 1961 is a deal killer.

Actually it's the fact that there was no Republic of Kenya in February 17th 1964 when this Document was generated, not in 1961 when he was born. This document was generated when Obama was almost 3 years old. But you have the right idea. Someone needs to find a similar document from 1964 (for a citizen born before 1963) and see if it has the same stamp saying republic of kenya.

[Royal Wulff]

Here is a document which references a "Trade Agreement between the Government of the Republic of Poland and the Government of the Republic of Kenya signed on 20th April, 1964"

However, the document is dated March, 1990, and may incorrectly refer to the name of the country in the prior agreement.

Otherwise, this suggests that the name "Republic of Kenya" was in use prior to December, 1964.