Your impression of how philosophically rigorous conclusions are reached is completely unnecessary to address; it is simply wrong.

You don't seem to understand that a rationalistic approach isn't going to lead you to conclusions that approximate accuracy about the world. See: philosophy that is over 100 years old as a reference, when people realized that this method of inquiry made no sense.

That being said, brushing aside your basic philosophical misunderstanding, it still follows that the burden of this challenge lies on the people who have outrageously claimed that they have uniquely solved it.

I make no such outlandish claims.