I'll start with Mario/Laurentis's backstory as laid out by the VN. Laurentis was a model cardinal of the Holy Church, considered to be the ideal candidate to be the next Pope if it weren't for one fatal flaw. Laurentis adopted over 20 sons or grandsons under a pretense of charity, but the adopted children looked too much like Laurentis himself for people to buy that, so the rumor spread that he was this lustful man ignoring his chastity vows to bang every woman he found. That's all that's openly said and all else is implied.
Mario's goal in Tsukihime is to find Roa and ask him about immortality, so he can either make his "(grand)father" Laurentis perfectly immortal, or remove his imperfect immortality (his curse of eternal youth). Roa's answer was that he became a vampire because it's impossible to get immortal while retaining his humanity, and the vulture who scavenged his documents and ignored this clearly written detail got what was coming to them.
Later in Roa's flashback talk with Nrvnqsr, Roa explain to his friend that he shifted his research subjected from the body to the soul because "the 'eternal youth' he was working with was retrogression itself". So the conclusion of the theories is that Mario and all of his older brothers are actually Laurentis himself aging backwards like Benjamin Button because he used Roa's eternal youth magecraft without caring about the drawbacks.
Most of the other bits of evidence presented around are mismatches in either time, relationships, and identity. Going over them one by one:
- Time: Mario is stated to be 12 but claims to be acquainted with Arcueid and to have experience pacifying a rampaging True Ancestor before, but those are both impossible because Arcueid's last activity was 13 years before. He also called the brother saved by Ciel a "brat not even on his 20s", which a very unnatural thing for 12-year-old younger brother to say. In the confrontation against Roa, he also talks about not having much time left to live, even though he's the youngest character here.
- Relationships: Arcueid and Ciel technically don't know Mario, but Mario talks to them like he knows them on a personal level, at least enough to recognize the huge changes in Arcueid's post-Shiki personality and say Ciel is "still merciless as always". He uses "reading his (grand)father's files" as an excuse for his knowledge, but Arcueid clearly recognizes him by the "familiar smell of a Laurentis child", and Ciel makes a point to compare him to the brother whose life she saved in their first encounter.
- Identity: The thing I found the most curious about Mario in my own playthrough of Arc's route was how his motivations were completely not about himself. He was fighting for his father's goal as if they were his own. His hatred and disappointment at Roa's answer felt personal like he was the one who depended on it. In my playthrough I though he just loved his father that much, but the theory reframes his portrayal into something a lot more natural. And then there's his conversation with Shiki on the Ciel Normal End that practically spells everything out:
Miscellaneous extra evidence:
- Mario is constantly stated to be 12, but his materials list his age as "12-14 (estimated)".
- One of his dislikes is "the brother immediately before him", instead of the much more naturally worded "the brother immediately older than him".
- Laurentis is retired and hidden from the public.
- Laurentis is described as "human manipulator", which is something Mario's Piano Machine makes literal.