⊥⊬
Nothing here literally translates to "sacrosanct". It's likely that this was a term perhaps thrown around by Terrence and it stuck with the charting/programming teams enough to get used internally.
But, when you search these glyphs individually, you find that they're math symbols. The first ⊥ ("up tack") has a few definitions, but they're all roughly shaped the same; it indicates "the bottom", "falsehood", "absurdity". x = ⊥ means "go home x, you're drunk".
⊬ is a "right tack" with a slash mark through it. This is the inverse of ⊢, which is modified from ⊦, which is used in the Principia Mathematica to mean, more or less, "proves", or "it is provable". It's part of an extremely terse notation system, higher math loves that shit
⊬, then, means "does not prove" or "is not provable."
So taken together: ⊥⊬
"The notion of [falsehood, absurdity, The Bottom] cannot be proven."
"Sacrosanct" means "sacred, inviolable, beyond alteration or criticism."
So it's an apt translation, in an allegorical sense.
⊥⊬ as a statement of formal logic is unsound, because ⊥ itself is tautological, it simply is what must be agreed upon. It merely represents the notion of falsehood, the same way the number 3 represents triplets of things. Attempting to question this seriously is vertiginous.
It induces that queasy existential feeling like perhaps even the ground you're standing on isn't actually real.
After all why would you question falsehood itself?
...Unless you simply can't stomach the alternative?
Is this not the way Lacrymira must feel right now, being faced with absurdity and flinching? Being faced with the absurdity of that which has no positive evidence in the relevant reality, but in the reality in which she was brought up, was simply assumed to be true?
Man, even thinking about it does things to my head that I kinda like even though I have a feeling they're not great for me. This is what I love about Arcaea's writing; the way it leverages the intellectual register to attack the reader in a very precise way.
Now that Act 2 (appears to be?) coming to a close, I have to write an essay on what it says, because it's probably more interesting, from a philosophical angle, than Act 1.
Anyways I'm now properly terrified to be left alone with Smith's writing for tens of hours for In Falsus.
Addendum: XOR
The composers of this song are Silentroom and かたぎり, credited as "Silentroom Dismantled XOR かたぎり".
"XOR" is an operator in Boolean arithmetic, short for "exclusive OR". It is true only when one of its inputs are true, not both. When done as a bitwise operation on two datasets, it returns the indices whose values differ.
I don't quite know yet what relevance this has lore-wise. Compositionally, it could be said that it refers to a process of rough-cutting, wherein Silentroom (who was the arranger on the piece) interspersed two tracks from himself and かたぎり, but listening to it, I'm unconvinced that's the case. According to Silentroom, though, there were points during its production where he was entirely unsure of what he was doing. I think that comes through in a constructive way, really adding to the sense of ontological collapse that it represents.