Integrity

*Integrity* is the twenty-ninth public video to be uploaded to the Komplot Group Band's YouTube channel.

## Integrity

### Link

https://www.youtube.com/watch?v=zYdF4rcE86A

### Description

~יַָג ְע ִתּיוְלֹא ָמ ָצא ִתיאַל ַתּאַ ִמיןלֹאיַָג ְע ִתּיוּ ָמ ָצא ִתיאַל ַתּאַ ִמיןיַָג ְע ִתּיוּ ָמ ָצא ִתי ַתּאַ ִמין~

Words are but symbols for the relations of things to one another and to us; nowhere do they touch upon absolute truth.

Through words and concepts we shall never reach beyond the wall off relations, to some sort of fabulous primal ground of things.

Uniqueness among periodic configurations follows from Bernstein’s theorem. Suppose C is any periodic configuration of density 1 that is not isometric to Λ\_d. We have seen that the energy of C under r → e^−αr^2 is strictly greater than that of Λ\_d for each α is greather than 0, and these energies are continuous functions of α.

I mistrust all systematizers and avoid them. The will to a system is a lack of integrity.

By continuity, for each compact subinterval I of (0, ∞), there exists ε is greather than 0 such that the energy gap between C and Λ\_d is at least ε for all α ∈ I.

The desire for a strong integrity is not the proof of a strong integrity, rather the opposite. Not when truth is dirty, but when it is shallow, does the enlightened man dislike to wade into its waters.

Bernstein’s theorem and monotone convergence show that E\_p(C) is greater than or equal to E\_p(Λ\_d) + δ for some δ is greather than 0. In particular, E\_p(C) is greather than E\_p(Λd) if E\_p(Λ\_d) is less than ∞, as desired.

The snake which cannot cast its skin has to die. As well the minds which are prevented from changing their opinions; they cease to be mind.

ᛈ7ᛁᚹᚹᛋ06446ᛋᛝᛝᛉᚹ · 7ᚹᛖ5ᛟᚦᚠᛒᚾ6ᚢᚦ9ᛊᚢᚲ · 2ᚨᚱᛒ265ᚷᚨᚱ2ᚷᛃᛗᛋ7

~ 36 ~

### Tags

kgb, the pilgrim, roads, paths, mist, fog, dark, awakening, depths, faceless, horrors, ignorance, transcending, -7-, -13-, -17-

## Transcription

[0:00]: Pic 1

[4:01]: End.

## Details

*Integrity* is the fourth video to be part of the *Nitegrow* series of thematic videos and the second video to be surfaced by ᠲ-Mat using tavern commands. ᠲ-Mat did not make the commands used to surface the video public, but logs of his attempts do exist.

—————

07-09 21:37:50 - ᠲ-Mat - !continuity

07-09 21:38:06 - ᠲ-Mat - !subinterval

07-09 21:38:26 - ᠲ-Mat - !theprimalground

07-09 21:39:07 - ᠲ-Mat - !wordsarebutsymbols

07-09 21:39:25 - ᠲ-Mat - !periodicconfiguration

**07-09 21:39:47 -** ᠲ**-Mat - > 36**

**07-09 21:41:54 -** ᠲ**-Mat - > thewilltoasystemisalackofintegrity**

07-09 21:42:28 - ᠲ-Mat - !gapconfiguration

**07-09 21:55:01 - root - > Resources have been released; t-{5}m**

—————

The description makes use of many different quotes from multiple different sources:

—————

ואמר ר׳ יצחק אם יאמר לך אדם יגעתי ולא מצאתי אל תאמן לא יגעתי ומצאתי אל תאמן יגעתי ומצאתי תאמן

> “And Rabbi Yitzchak said: If someone tells you 'I toiled and did not find', don't believe [it]; 'I did not toil and I found', don't believe [it]; 'I toiled and found', believe [it].”
>
>

> - Talmud (Bavli, M'gila 6 amud 2)
>
>

—————

Words are but symbols for the relations of things to one another and to us; nowhere do they touch upon absolute truth.

> “Through words and concepts we shall never reach beyond the wall off relations, to some sort of fabulous primal ground of things.”
>
>

> - Friedrich Nietzsche
>
>

—————

"Uniqueness among periodic configurations follows from Bernstein’s theorem. Suppose C is any periodic configuration of density 1 that is not isometric to Λ\_d. We have seen that the energy of C under r → e^−αr^2 is strictly greater than that of Λ\_d for each α is greather than 0, and these energies are continuous functions of α.

By continuity, for each compact subinterval I of (0, ∞), there exists ε is greather than 0 such that the energy gap between C and Λ\_d is at least ε for all α ∈ I.

Bernstein’s theorem and monotone convergence show that E\_p(C) is greater than or equal to E\_p(Λ\_d) + δ for some δ is greather than 0. In particular, E\_p(C) is greather than E\_p(Λd) if E\_p(Λ\_d) is less than ∞, as desired."

> *Universal optimality of the E8 and Leech lattices and interpolation formulas*
>
>

> By Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Maryna Viazovska
>
>

> https://arxiv.org/pdf/1902.05438.pdf
>
>

—————

> "We prove that the E8 root lattice and the Leech lattice are universally optimal among point configurations in Euclidean spaces of dimensions 8 and 24, respectively.
>
>

> It follows immediately from Lemma 6.2 that Λd minimizes energy for all Gaussian potential functions (recall the conditions (1.2) for equality in the linear programming bounds). Furthermore, we can prove uniqueness among periodic configurations as follows. If C is any periodic configuration in Rd of density 1 with the same energy as Λd under some Gaussian, then the distances between points in C must be a subset of those in Λd, because of the equality conditions. Without loss of generality we can assume 0 ∈ C. Then, by [11, Lemma 8.2], C is contained in an even integral lattice (namely, the subgroup of Rd generated by C), because all the distances between points in C are square roots of even integers. Because C has density 1, it must be the entire lattice.
>
>

> We conclude that it must be isometric to Λd, because there is only one such lattice with minimal vector length √2n0 (see [17, Chapters 16 and 18]). Thus, Theorem 1.4 holds for Gaussian potential functions.
>
>

> By continuity, for each compact subinterval I of (0, ∞), there exists ε > 0 such that the energy gap between C and Λd is at least ε for all α ∈ I. Thus, Bernstein’s theorem and monotone convergence show that Ep(C) ≥ Ep(Λd) + δ for some δ > 0. In particular, Ep(C) > Ep(Λd) if Ep(Λd) < ∞, as desired. This completes the proof of Theorem 1.4, except for proving Proposition 6.1.
>
>

> Thus, Bernstein’s theorem and monotone convergence show that Ep(C) ≥ Ep(Λd) + δ for some δ > 0. In particular, Ep(C) > Ep(Λd) if Ep(Λd) < ∞, as desired. This completes the proof of Theorem 1.4, except for proving Proposition 6.1.”
>
>

—————

> “The desire for a strong faith is not the proof of a strong faith, rather the opposite. If one has it one may permit oneself the beautiful luxury of skepticism: one is secure enough, fixed enough for it.”
>
>

> “Not when truth is dirty, but when it is shallow, does the enlightened man dislike to wade into its waters.”
>
>

> "The snake which cannot cast its skin has to die. As well the minds which are prevented from changing their opinions; they cease to be mind.”
>
>

> - Friedrich Nietzsche
>
>

## Theories

One of the quotes used in *Integrity*'s description references E8 Lattices, the name of which is the namesake of the *E8 Lattice* video, suggesting a connection.

Information concerning *Integrity* was actually cryptically leaked messages sent to ∞-Infinity from Matthew on July 8th 2020.

—————

"start of line

"Words are but symbols for the relations of things to one another and to us; nowhere do they touch

upon absolute truth."

7ᚹᛖ5ᛟᚦᚠᛒᚾ6ᚢᚦ9ᛊᚢᚲ

end of line”

—————

The individual was quoted to only appear in the tavern using a literal blank space as a name, sending a message to Matthew that needed to be relayed to ∞-Infinity immediately. ∞-Infinity was mentioned directly, account number and all. While it is possible the blank could be anyone of the server members, it is most likely someone who has had previous encounters with ∞-Infinity.