[tjwmason]

Is ones faith so dependent upon the authenticity of such relics?

No.

What if it is proven fake? Should that diminish the depth of ones faith?

No.

If proved authentic, would it deepen ones faith?

Yes.

I should hope not in either case.

Why is that? Not doubting for one moment the reality of the events 200 years ago, if it were proved to be genuine one would be faced with such a close physical link to our Blessed Lord, that Faith could not help but be deepened.

[elbucko]

..that Faith could not help but be deepened.

If so, then one's faith would have been shallow. You are confusing the concepts of fact with faith. The instant an article of faith is proven by a fact, it is no longer an article of faith, but becomes a fact. It's only words, but the words are important. The Constitution is fact, the Gospels are faith. If you transpose their positions, you weaken them both.

As for the "Shroud", are we not cautioned about asking for "signs"?