If the mother has papers and the father does not you will not be able to research your pup since you will only be able to follow the family tree on one side. Since the father did not have papers then there really is no point as far as I can see. If as you say that your little one came from a BYB it can be assumed that even the papers of the mothers bloodlines might not be very accurate. The responsibility of keeping accurate track of the bloodline falls onto the breeder. Personally, I think way to much emphasis is placed on papers unless you are planning on either breeding or showing your dog which you say is not the case.
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