I think it may require a little bit specialised insight for people to understand how the Law and the Evidencing establishes as a fact that "A" is a father of "B".
Imagine the world just before 1980's when the DNA evidencing was not yet found by the Sciences.
How , in those times, was the relationship of Father and Son being established in Law and in Courts, through a systemic run of Logic ??
The answer lies in absorption of the mechanism in our Mind that it took a combination of three events to occur , concurrently, to 'prove' (through a Inferential Logic "अनुमान", not a Discreet Logic "प्रत्यक्ष प्रमाण") the relationship between 'A' and 'B'.
The three events which needed to occur concurrently were
1) 'A' claiming to be father of 'B'/ or , 'B' claim to be sired by 'A'.
2) 'A' or 'B', as relevant, not proceeding to refute the claim raised in the event 1.
3) There is no one else in the world to refute the claim.
The universal law is that whosoever makes a claim has to bear the burden to prove his claim.
Thus, in the three events above, whosoever produced a claim which was refuted by the affected party, had to bear the burden to prove it.
This information is intended to bring a right and purposed information to schools which insist on Birth Certificates as the proof of Parenthood (!), and wrongfully indulge into nitty-gritty of Birth Certificates of a child to accept or reject his admission. The birth certificates are intended to record the birth of a child in the government records. It cannot DIRECTLY establish the parenthood as a proof. The parenthood continues to be 'proven' through the older technique mentioned above.
The birth Certificates do not contain any photographs, and they refer to child as 'baby of XYZ(mother's name). Quite clearly , the doctors and the hospital which are involved in the birth process can stand witness to this fact only , along with the date of birth , and nothing beyond.
As a verification control, as to whether the birth Certificates actually belongs to a given person, the mother's name is the key link.
Even the child's own name is not the key link. Many times , many religious beliefs do not provide for naming a child just as he/she is born. Therefore the name of child is not an essential link. The child's name CANNOT BE a Mandatory information therefore. It can be seen only as a ''desired information'' by a Government Registrar, which serve the purpose of easy referral and scouring out the pinpointing certificate from a big bunch. Nothing more.