Nothing
You all keep missing the point. Of course faith matters. Muslims, Hindus, Buddhist all have faith. But Catholicism is founded on both faith and reason. The accounts of the Gospel and the teachings and practices of the early disciples are all part of that reason. The authenticity of the books assembled as part of the canonical text are all part of that reason too through historical scholarship and practice. While the Shroud is NOT necessary to affirm that belief because of the other historical sources, it does scientifically validate the belief. Now, isn’t that marvelous. Just as we know historically that the story of the Crucifixtion is historically a valid event.