>"Positive proof" opposes the concept of falsification.

no. Positive proofs have nothing to do with falsification. They just tell you that there is no point in spending effort on searching for negative proofs and counter examples. They don't prevent nor prohibit you from spending that effort. They just advise you that that effort will be wasted.

It is like nobody prevents from experiments to turn lead into gold. Of from searching for a right angled triangle violating Pythagoras.