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I said: "Again, we know that something, fraudulent or not, was filed with the Hawaii Health Statistics Bureau within days of his birth"

ES responded: Actually, "we" don't know anything of the kind. Someone may know that, but they certainly have not provided any proof to that effect.

Ok. What we "know" (or can know by calling the two respective newspapers ourselves - which I did, doing my homework), is that:
1. In 1961, the "Health Statistics Bureau" was responsible for maintaining birth, marriage, and death registrations.
2. In 1961, the only way that the "Health Statistics Bureau" would have had a record of a birth to provide to the local papers was through filing of some form of birth certificate, however "valid" or "invalid" that certificate was.
3. In 1961, as reflected in the two separate birth announcements, both local papers got their birth announcements from the "Health Statistics Bureau."
4. In 1961, neither local paper permitted the publication of birth announcements other than those provided by the "Health Statistics Bureau." (Today, neither local paper permits publication without submission of a BC to verify local birth.)
5. In 1961, within just a few days -- far fewer than 30 -- of Obama's reported birth (whether from the COLB or the "Kenyan BCs"), two local papers reported that birth, based on Health Bureau Statistics.

From that, the only reasonable deduction is that some birth certificate, however valid or invalid, was, in fact, filed with the Hawaii Health Statistics Bureau within days - far less than 30 days - of his birth.