Why can I rest assured that GNU Parted has not corrupted a single bit after shrinking my partition?

I shrunk my root partition and it seems nice. But I am thinking about overwriting now at least the most important files from the backup copy (external drive, rsync, weekly backup) in order to be sure that none of my files got corrupted during the shrinking. That is probably a waste of time (and perhaps it may result in more fragmentation).

I can check that the files are OK after moving them during the shrinking by means of a CRC comparison with those in the backup (e.g. with md5sum) as one unser kindly says in his answer.

But specifically I would like a short explanation on the algorithm that GNU Parted uses in order to ensure that no data corruption happens while moving information from one sector of the disk to another, prior to the shrinking of the partition. Is there such algorithm, or the program copies bytes blindly? I would like to read a simple explanation.