I take it that by "figuring out validity", the farthest you can take it is to avoid all new rite sacraments. But this positive doubt is not enough for you determine if Francis is legitimate or not.
You're completely missing the point.
The exact nature of the Crisis in the Church (what exactly happened in and around the 1960's, esp. with the Papacy, etc.) has not been solved yet. You might think it has, but it hasn't. All Catholics of moderate intelligence and good will are NOT on one side about this -- not yet.
It is my personal opinion that the Crisis in the Church is a supernatural mystery, like the Holy Trinity, that the mind of Man could NOT figure out on its own power, without God stepping in and revealing it to us.
So you see, trying to "determine if Francis is legitimate or not" would be a waste of time, since it's unreachable by human powers and reason -- at least according to my opinion.
Why do I think that? What brought me to that opinion? Oh, I don't know -- maybe
the past 53 years of Crisis during which time countless learned, brilliant and holy men from all parts of the earth have tried -- and failed -- to unite the whole of the Remnant behind one, exact, coherent explanation which answers ALL objections and leaves NO unanswered questions or objections.Sorry, but God is going to have to untie this knot for us. Until He deigns to do so, it shall remain tied.
And frankly, even if the solution HAD been uttered by some cleric(s) and/or laymen during this past 53 years, who's to force the entire Catholic world to submit to it? Who can bind consciences on a disputed point with no means to prove who is right or wrong? Who can say "I have the Answer Key/Teacher's Manual from God -- and it says here that I'm right!"
When the Crisis involves the very principle of unity and authority -- the Pope -- what makes us different from the Protestants BTW -- who can repair that? Who is higher than the Pope, who could fix a broken Pope situation?
God. Perhaps through the agency of one of His angels, St. Peter, etc. But that still involves God stepping in, so we're back to my main thesis.