There is a Shrine Chapel in the ancient city of Ephesus-(present-day Efes, Turkey) that is dedicated to Jesus' Mother, Mary, titled, "House of the Virgin Mary" which is administered by The Roman Catholic Church; (It is also referred to as, "Our Lady of Ephesus"). It is a simple and rather humble looking stone house located in the distant corner of ancient Ephesus. The lore behind the House is that Jesus' Mother lived there shortly after his death. She is also believed to have died in this House, thereby making it both a historical and a sacred site for practicing Christians-(in particular, Roman Catholics).
However, is there any incontrovertible historical proof that Mary traveled to Ephesus after Jesus' death and lived in this particular Ephesian House? Are there any written records? Is there any available archaeological evidence validating this claim? Or is this particular House part of the larger Christian lore?