“You're not supposed to be in here! You're going to ruin the surprise!”The following section contains spoilers.
Proof Fragments are quest items required to construct the Limbo Theorem key (not to be confused with the quest key). They can be obtained by killing the enemies from the quest, where the fragments take up the form of Nav Coordinates. A total of 9 fragments are required to build all the keys needed to complete the quest.
Supposedly, these fragments transmit the signals all across the system and may be found by investigating the wavelength. It is described by Ordis that the frequency--while constant, is far too weak to be caught by the Orbiter's antenna and that it would require a sophisticated antenna to fully catch the wave such as the satellite found in the Archwing Interception mission.
In a way, the Proof Fragments themselves can be interpreted as the remains and the relic of the original Limbo in the form similar to cosmic background radiation, as the fragments can be engineered into a theorem which leads into another Limbo piece.