The word I'm looking for would suggest that the thing in question was shown to be true even to the point of excess, and its veracity tested on multiple occasions or very publicly, so that there can be no residual doubt.
e.g.
'it was proven with great _______ that her methods were ineffective'
I've tried looking up synonyms for 'thoroughly' and 'excessively' which didn't turn it up. The word is right on the tip of my tongue and it's been bugging me for ages.