Without/beyond a shadow of a doubt

Meaning:

• If something is true without/beyond a shadow of a doubt, there is no doubt that it is true.
• You are certain of it without the smallest amount of doubt.

Example sentence:

Are you sure this is going to work? It looks suspicious. - Yes, I'm certain - without a shadow of a doubt.


Questions for you to answer:

1. Can you think of any hypotheses that were recently proved without a shadow of a doubt?
2. Are you usually certain of things without a shadow of a doubt or are you rather suspicious and sceptical?
3. Are there any people you can trust without a shadow of a doubt?