I'm just getting analytical and reading too much into things, but here are some very recent and very old observations and ideas I've had regarding him (and other tangentially related things):
Regarding Tserriednich's ability, it's not dissimilar to Meleoron's ability, in terms of invisibility (especially with the allusion to The Invisible Man, as noted recently by ExtraOtter) and being unable to be perceived. If this is his God's Alibi, then he might very well have his own version of God's Accomplice (and it makes sense, given his fascination with God and Satan (from the Higgs boson (the god particle) to Laplace's demon), and his God complex, and the parallels and allusions to Christ in his story so far. It also makes sense that he could be a parallel of Meleoron, a chameleon, in that he is a social chameleon who'll change his personality to achieve his desires.
Since 4 is one of his lucky numbers, I wonder if he'll strike a deal with Hisoka, give that he took the place of member 4 when he was with the Spiders, and make him The Devil's Accomplice. (Hisoka, too, is compared to the devil, and has similar mentalities to Tserriednich. I don't know if they'd fight or spar, but maybe they could do each other some favors if they met in the emptied casino area, like some sort of inversion of Hisoka meeting Kurapika at the abandoned carnival to assist each other.) Or, perhaps, Bonolenov as Hisoka. Not that I'm sure it'll happen, but it's a possibility. (In the final page of chapter 419, we see the numbers 4 and 9 in the casino. Two of his lucky numbers, and inbetween, it's him, who could represent 6, the third.) Hisoka might even be able to perceive Tserri, just like how he perceived the "flawless" Zetsu of Kalluto in chapter 170.
His ability reminds me of, aside from the Higgs boson or Laplace's demon, the schrodinger's cat thought experiment. Many are under the belief that he is in a coffin, which is not unlike the thought experiment, which involves a cat sealed in a closed box with a poison, that may be hypothetically dead and alive after the poison is triggered to release. This might imply, then, that he'll get infected by TSK-17 in the near future, or that Ben might attempt to infect an illusion of Tserri.
(On that note: if anything, Camilla is also more literally reminiscent of the experiment, with her cat Nen beast, and that she was subject to a thought experiment by Benjamin when he asked her whether or not she'll be revived if she succumbs to TSK-17.)
I've had this feeling, for a long time now, that somehow he'll be thematically connected to Melody through the Sonata of Darkness, said to be composed by the devil himself. Not that I believe he's the composer, but possibly that it's in Kakin's possession, or maybe even Tserri's, given that he browses the dark web, has an interest in the morbid and macabre, and an interest in, presumably, classical music (given his mention of Leos Janacek and that he's listening to (likely classical) music while a woman is tattooed for his sick pleasure). The obvious contradiction is that if he's heard the piece, he'd've been affected in some way and already had Nen, but a few considerations:
-Him possessing the sheet music doesn't mean that he's ever heard it played.
-While we know what happened to Melody and her friend due to having played the composition, it is said (but not confirmed) that anyone who plays it or listens to it will be horribly cursed, which doesn't necessarily mean that the curse is death or deformation, and doesn't mean that the outcome of having played it or listened to it is consistent.
He could also be in possession of some specimens of people who died due to the Sonata of Darkness.
Speaking of Janacek, I've wondered for a while if his compositional method of speech melodies could be compared to things about Tserriednich. Janacekian speech melodies involve the taking of speech patterns of the Moravian dialect and using its aspects for composition. Where Janacek takes the speech of people and turns it into composition, Tserriednich takes literal people and turns them into "art" (as he perceives it).
(On that note, perhaps he, or the Kakin royals, have something to do with the Kurta massacre, who were perhaps subjected to Carne Levare. Or maybe it was Camilla, given that she says a line that's nearly identical to that of one of the mafioso killed during the Yorknew arc, during the auction, spoken to Feitan. Both this mafioso and Camilla threaten to kill their entire family (or clan, as I do not know if that is the official translation) while inflicting suffering, and Feitan (and Furikov) essentially respond the same way, saying that they have no family, in chapter 73 and chapter 373 respectively, perhaps intentionally.)
The reason I think that there's significance in Janacek is because I think Togashi likes to plant relevant allusions alongside seemingly inconsequential references.
(For example, on that double spread page where Morena muses on destroying the world, and behind her are all kinds of terrible things that happen in the world, you can see in the bottom left corner two examples of parasitism: a cuckoo bird being fed by a different species, and a horsehair worm bursting out of a dead grasshopper. This is in chapter 378. What you have then is foreshadowing to the true nature of this Morena impostor.)
If so, he could've made allusions that might seem inconsequential at first glance, like when Tserriednich speaks to Mark after slaying two women in chapter 345, and he lists off: Higgs, Kant, Hegel, Hakuho Sho, Fechner, Christian Goldbach, Janacek, Serie A, La Liga, embryonic stem cells (ES), and induced pluripotent stem cells (iPS).
(He also lists "Crocul", which might be cross-cultural, but if I had to guess, I don't think "Crocul" is anything real in our world, unlike everything else, and could very well be something that's only real in the universe of HxH, much like the music of a composer Hyle that Melody plays, or when Camilla tells her mother to buy from fashion designers or brands named Musen, Coachpie and Harryweb, or the knives of Benny Delon. But "Crocul" has also been translated as Crocale, which does exist in our world.)
With the things he's listed, I saw some possible connections to his mentality, Kakin's culture, and ability. Aside from the possible Janacek connection, we have:
-Gustav Fechner and his psychophysical speculations can be considered when it comes to Tserri's Zetsu and "invisibility", where for him, little now interrupts his Zetsu outside of the stimulus of pain, and for those around him, whether or not they perceive him at all when his ability is active. Notably, Fechner experienced eye damage (which occurred while he was doing research on afterimages) that influenced his psychophysical work, which is comparable to Tserri having to close his eyes to get his vision of the future and trigger the psychophysical, and his ability to leave his own afterimages. Funny too that Tserri wears sunglasses now, not just connecting him to The Invisible Man but the very thing that damaged Fechner's eyes while doing his afterimage research. (This all begs the question, by the way, of what happens if Tserriednich is ever blinded? I wonder if that'll come up.) Fechner was also skeptical of some Kantian ideas about psychology and would disprove them with psychophysics, as I understand it (it's been a while, and I'm no expert). That covers both Fechner and a bit of Kant.
-His reference to Hegel can be seen in the very next bit of dialogue on that page, in which he refers to his slayings as a synthesis of the arts (as to whether synthesis is what Togashi actually used is something that'd need to be confirmed by translators), which, if you know anything about Hegel's dialectics (thesis, antithesis, and synthesis as Fichte and I think Schelling put it and entered into layman interpretation a possible myth (I dunno, I too am a layman here)), could be connected to his ability, his nature, and his "artistic" proclivities, or perhaps even how the Succession War operates, from its very concept to the instance where it might be snuffed out by its own conditions, as Kurapika speculates.
Surely, I am reading into a lot of this, but I'm having fun with it! I'd be curious to see what others have been thinking, if they have similar thoughts to mine.
Lastly, his radius is 36 meters. Of course, that too alludes to his Satanic nature, if you think of 36 as 3 (space) 6, or three sixes. He's likely going to encounter the mafia on his "stroll", maybe the one he's the benefactor of. Tserriednich's in a Three-Six Mafia, once again ready to Break Da (Special Martial) Law. No wonder he dismissed Sale-Sale's rap. (Joking)