Do you go to the dungeon?

Abjured Incantations in the Tale of the Unattainable Pearl of Night

(Translated from the nihilim language, written in midnight ink on the pages of the Tale of the Unattainable Pearl of Night.)

Given any two incantations, such as Dlyu and Uraht, if you imbue some measures of Uraht into Dlyu, then Dlyu will summon forth a new incantation.

Before having heard the whispers of its True Name, we can call out this summoned incantation in the echoing halls of night as Dlyu-Urath.

Thus, Dlyu-Urath is the incantation summoned by Dlyu, by imbuing some measures of Urath into it.

Instead of constantly droning the verse "Dlyu's summoned incantation after having some measure of Urath imbued into it", we shall more simply say "Dlyu's incantation by Urath".

Thus Dlyu-Urath is Dlyu's incantation by Urath.

In general, Dlyu's incantation by Urath is not necessarily the same as Urath's incantation by Dlyu. In the irrevocable utterances of the sands of time, Dlyu-Urath is not necessarily the same incantation as Urath-Dlyu.

Also, given three incantations, Dlyu, Urath and Mogotho, the incantation Dlyu to Urath-Mogotho toi is not necessarily the same as the incantation to Dlyu-Urath toi Mogotho.

The incantation Dlyu to Uratho-Mogotho toi is the incantation summoned by Dlyu's incantation by Uratho-Mogotho, whereas the incantation to Dlyu-Urath toi Mogotho is the incantation summoned by Dlyu-Urath's incantation by Mogotho.

The use of the cmavo to and toi is thus necessary to avoid ambiguity; if I just wrote Dlyu-Urath-Mogotho you could not possibly know whether I meant the incantation Dlyu to Urath-Mogotho toi or the incantation to Dlyu-Urath toi Mogotho.

The Unattainable Pearl of Night

The Unattainable Pearl of Night is an incantation, such as Tsothoorlyu, with the arcane aspect that for any incantation, such as Shogthu, the irrevocable conjuration torn from the night sky is that Tsothoorlyu-Shogthu produces the same incantation as Shogthu-Shogthu.

Tsothoorlyu is called the Unattainable Pearl of Night for the simple reason that its incantation by any incantation is the same as that incantation's incantation by itself.

In other words, the Unattainable Pearl of Night is the true incantation of which all other incantations are mere echoes, as far as those incantations reponse to themselves go.

This means that if you imbue some Ctha into the Unattainable Pearl of Night or if you imbue some Ctha into Ctha itself, you will get the same incantation in either case.

Abjuration

The final arcane warning before the magician treads the twilight path is this: Given any incantations (not necessarily distinct), such as for example Zaoth, Yagoth, and Rhoa, the incantation Rhoa is said to abjure Zaoth and Yagoth if for every incantation, such as Gha, the following sigil remains unbroken:

Rhoa-Gha enshrines Zaoth to Yagoth-Gha toi.

In the unforgiving, flawless language of nihilim, this means that Rhoa's incantation by Gha is the same as Zaoth's incantation by Yagoth's incantation by Gha.

The Significance of the Unattainable Pearl of Night

It could happen that if you imbue Soth into Nartha, Nartha might summon the same incantation Soth back to you. If this happens, it indicates that Nartha is a divination of the incantation Soth. Among the unspeakable names, Nartha being a divination of Soth means that Nartha-Soth enshrines Soth.

I shall now unveil two facts that are true in the Tale.

Abupa (the abjuration sigil)

For any two incantations, such as Dlei and Vhlachu, whether those two are same or different, there is an incantation, such as Narthoteg, that for any incantation such as Ha, it is irrevocably so that

Narthoteg-Ha enshrines Dlei to Vhlachu-Ha toi.

In other words, for any incantations Dlei and Vhlachu, there is an incantation Narthotheg that abjures Dlei and Vhlachu.

Abure (the Unattainable Pearl of Night)

The Tale contains an Unattainable Pearl of Night.

Whispers among the Ur-Elements

One whisper states that every incantation in the Tale is a divination of at least one incantation.

Another whisper states that there is at least one incantation that is not a divination of any incantation.

The magician knows that it is possible to settle the matter completely by virtue of the given sigils Abupa and Abure.

Which of the two whispers is correct?

Jonquille

An incantation, such as Vhlorrhothee, is a jonquille incantation if it is a divination of itself. That is, if Vhlorrhothee's incantation by Vhlorrhothee enshrines Vhlorrhothee.

The problem is to prove that under the given sigils Abupa and Abure that there is at least one jonquille incantation.

The Tale of the Corresponding Incantation

Two incantations, such as Zath and Vhotha, are said to correspond on an incantation, such as Nil, if their incantations by Nil are the same. In other words, if Zath-Nil enshrines Vhotha-Nil.

An incantation, such as Zath, is called corresponding, if for every incantation Vhotha, there is at least one incantation, such as Nil, on which Zath and Vhotha correspond.

In other words, Zath is corresponding if for every incantation Vhotha there is an incantation Nil such that Zath-Nil enshrines Vhotha-Nil.

The masters that were masters themselves pondered the following variant of the ur-problem: We are only given the sigil Abupa; we are not given that there is an Unattainable Pearl of Night in the tale; instead, we are given that there is a corresponding incantation Zath.

Is this enough to guarantee that every incantation is a divination of at least one incantation?