The thargoid link message is a puzzle that provides us with the distances of an unknown system relative to three known systems. By a process of triangulation we are able to identify a pair of 3D coordinates one of which is the location of the unknown system.
However the link messages are calculated with a precision of three decimal places which means that the distances are not accurate enough to give us the precise location so we must search through a list of known stars to identify stars that are close to the calculated coordinates. Each candidate system has a error value measured in light years.
Once we have a list of candidate systems, we can run the calculation is reverse to give us the distances using the same precision used by the Thargoids to calculate their message. If we have identified the correct system then the recalculated distances will match the distances given in the message. We use the recalulated distances to generate a pair of coordinates and then compare these to the original decoded coordinates to give us a control value measured in ly. An exact match on the system would have a control value of exctly 0ly.
We also check to see if any of the recalculated distances match the original distances and this gives us a match value between 1 and 3. If we get a control value or zero and match value of 3 then we can be certain that we have the correct coordinates.