Incontrovertible evidence is a colloquial term for evidence

Evidence (law)

The law of evidence encompasses the rules and legal principles that govern the proof of facts in a legal proceeding. These rules determine what evidence can be considered by the trier of fact in reaching its decision and, sometimes, the weight that may be given to that evidence...

 introduced to prove a fact that is supposed to be so conclusive that there can be no other truth as to the matter; evidence so strong it overpowers contrary evidence, directing a fact-finder to a specific and certain conclusion.

Examples: a fingerprint

Fingerprint

A fingerprint in its narrow sense is an impression left by the friction ridges of a human finger. In a wider use of the term, fingerprints are the traces of an impression from the friction ridges of any part of a human hand. A print from the foot can also leave an impression of friction ridges...

 showing a person has been present in a room; a DNA test disproving a claim of parenthood.