This is of course a false analogy. We don't have a record of ownership at all; there is no such list. The shroud showed up in France in the 1300s or 1400s; it'

This is of course a false analogy. We don't have a record of ownership at all; there is no such list. The shroud showed up in France in the 1300s or 1400s; it's unclear exactly when, because it seems several shrouds were circulating at the same time. When written sources start talking about the current one, they don't say where it came crom. Nothing like "here's this shroud, taken by A from B, who had it after C, who found it raiding Byzantium, who got it from...". It just appears suddenly.