Multiplication Zones (19-30)

Warning

This page is referring to child section which source is inherited by the prime spin with partitions listed below. Please return always to the Home Page to track the hierarchy.

Assigning a lexer

You may learn that sets of algebraic objects has a multilinear relationship related to a vector space called tensor. Tensors may map between different objects such as vectors, scalars, even other tensors contained in a group of partitions.

By prime hexagon we can see that the number seven (7), hold the power to make the prime spin remain on the track. This power is then transfered to twelve (12) spins.

Note

Surprisingly, the 24-cell hexagon confines all natural numbers. The reason: no prime numbers occupy a cell with a right or left wall on the t-hexagon’s outer boundary, other than 2 and 3, the initial primes that forced the number line into this complex coil. Without a prime number in the outer set of triangles, the number line does not change to an outward course and remains forever contained in the 24 cells shown above. (HexSpin)

Therefore this 12's treatment will involve at least 11 groups of runner and one (1) profile of the 7's transformation. We collect them in 11 + 7 = 18 gists as below.

Tip

Gists provide a simple way to share code snippets with others. Every gist is a Git repository, which means that it can be forked and cloned. If you are signed in to GitHub when you create a gist, the gist will be associated with your account and you will see it in your list of gists when you navigate to your gist home page. (GitHub)

$ gh api -H "${HEADER}" /users/eq19/gists --jq '.[].url'

https://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 grammar 36
https://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 syntax
https://api.github.com/gists/dc30497160f3389546d177da901537d9 16 parser
https://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 lexer
https://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 feed
https://api.github.com/gists/f78d4470250720fb18111165564d555f 13 maps 30
                                                           --------
https://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77
https://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10
https://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9
https://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8
https://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7
https://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6
https://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5
https://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4
https://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3
https://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2
https://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1
https://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 37
  

By the prime hexagon the 19th spin is touching back to the first node. So the workflow will be proceeded as bilateral way and twisted them by such a kind of double strands.

https://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77
https://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10
https://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9
https://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8
https://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7
https://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6
https://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5
https://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4
https://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3
https://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2
https://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1
https://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 1
-------- bilateral
https://github.com/eq19/eq19.github.io/wiki                   19 identity 37
https://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 grammar
https://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 syntax
https://api.github.com/gists/dc30497160f3389546d177da901537d9 16 parser
https://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 lexer
https://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 feed
https://api.github.com/gists/f78d4470250720fb18111165564d555f 13 maps 30
  

We concluded later on that this bilateral would not come to be possible if only one (1) profile is assigned. Therefore we add another profile so they would be 11 + 2 = 13's.

These are the ones that bring 11 + 13 = 24 cell hexagons.

Orbital structure

The the main reason of assigning two (2) profiles instead of only one (1) is that we have to accommodate the major type of primes numbers called twin primes.

Note

This is a necessary but not sufficient condition for N to be a prime as noted, for example, by N= 6(4)+1= 25, which is clearly composite. We note that each turn of the spiral equals an increase of six units. This means that we have a mod(6) situation allowing us to write: N mod(6)=6n+1 or N mod(6)=6n-1 (equivalent to 6n+5). (HexSpiral-Pdf)

twin primes

By our project the scheme will be treated as the sun and the moon orbit where this 31 is the maximum days of a month:

https://api.github.com/gists/f78d4470250720fb18111165564d555f 13 maps 1
https://api.github.com/gists/765ddc69e339079a5a64b56c1d46e00f 14 feed
https://api.github.com/gists/b9f901cda16e8a11dd24ee6b677ca288 15 lexer
https://api.github.com/gists/dc30497160f3389546d177da901537d9 16 parser
https://api.github.com/gists/e84a0961dc7636c01d5953d19d65e30a 17 syntax
https://api.github.com/gists/e9832026b5b78f694e4ad22c3eb6c3ef 18 grammar
https://github.com/eq19/eq19.github.io.wiki                   19 identity 37
7 days (sun)
-------- bilateral 9 sums
12 months (moon)
https://api.github.com/gists/0ce5848f7ad62dc46dedfaa430069857 1 eq19/* 1
https://api.github.com/gists/b32915925d9d365e2e9351f0c4ed786e 2 group1
https://api.github.com/gists/88d09204b2e5986237bd66d062406fde 3 group2
https://api.github.com/gists/8cab5e72d52ecb338a2f2187082a1699 4 group3
https://api.github.com/gists/54600a56d20163c2da8910dd804ec406 5 group4
https://api.github.com/gists/f1af4317b619154719546e615aaa2155 6 group5
https://api.github.com/gists/6c89c3b0f109e0ead561a452720d1ebf 7 group6
https://api.github.com/gists/f21abd90f8d471390aad23d6ecc90d6d 8 group7
https://api.github.com/gists/6e2fcc2138be6fb68839a3ede32f0525 9 group8
https://api.github.com/gists/b541275ab7deda356feef32d600e44d8 10 group9
https://api.github.com/gists/80c8098f16f3e6ca06893b17a02d910e 11 group10
https://api.github.com/gists/4ffc4d02579d5cfd336a553c6da2f267 12 group11 77
  

We are going to manage the relation of all the involved things in the scheme above using wiki and gist available by GitHub. Here is the example of the code:

Tip

Gists and Wiki are actually Git repositories, which means that you can fork or clone any gist, even if you aren’t the original author.

#!/usr/bin/env bash

WIKI=https://github.com/$2/$1.wiki.git
BASE=https://github.com/eq19/eq19.github.io.wiki.git
rm -rf /tmp/workdir /tmp/gistdir && mkdir /tmp/gistdir

git ls-remote ${WIKI} > /dev/null 2>&1
git clone $([ $? == 0 ] && echo $WIKI || echo $BASE) /tmp/workdir
gh gist clone 0ce5848f7ad62dc46dedfaa430069857 /tmp/gistdir/addition

gh gist clone b32915925d9d365e2e9351f0c4ed786e /tmp/gistdir/identition/folder1
gh gist clone 88d09204b2e5986237bd66d062406fde /tmp/gistdir/identition/folder2
gh gist clone 8cab5e72d52ecb338a2f2187082a1699 /tmp/gistdir/identition/folder3
gh gist clone 54600a56d20163c2da8910dd804ec406 /tmp/gistdir/identition/folder4
gh gist clone f1af4317b619154719546e615aaa2155 /tmp/gistdir/identition/folder5
gh gist clone 6c89c3b0f109e0ead561a452720d1ebf /tmp/gistdir/identition/folder6
gh gist clone f21abd90f8d471390aad23d6ecc90d6d /tmp/gistdir/identition/folder7
gh gist clone 6e2fcc2138be6fb68839a3ede32f0525 /tmp/gistdir/identition/folder8
gh gist clone b541275ab7deda356feef32d600e44d8 /tmp/gistdir/identition/folder9
gh gist clone 80c8098f16f3e6ca06893b17a02d910e /tmp/gistdir/identition/folder10
gh gist clone 4ffc4d02579d5cfd336a553c6da2f267 /tmp/gistdir/identition/folder11

gh gist clone f78d4470250720fb18111165564d555f /tmp/gistdir/exponentiation/folder13
gh gist clone 765ddc69e339079a5a64b56c1d46e00f /tmp/gistdir/exponentiation/folder14
gh gist clone b9f901cda16e8a11dd24ee6b677ca288 /tmp/gistdir/exponentiation/folder15
gh gist clone dc30497160f3389546d177da901537d9 /tmp/gistdir/exponentiation/folder16
gh gist clone e84a0961dc7636c01d5953d19d65e30a /tmp/gistdir/exponentiation/folder17
gh gist clone e9832026b5b78f694e4ad22c3eb6c3ef /tmp/gistdir/exponentiation/folder18

find /tmp/workdir -type f -name "Home.md" -prune -exec sh -c 'mv -f "$1" "${1%/*}/README.md"' sh {} \;
find /tmp/workdir -type f -name "*zone.md" -prune -exec sh -c 'mv -f "$1" "${1%/*}/README.md"' sh {} \;
find /tmp/workdir/identition -type f -name "*.md" -prune -exec sh -c 'mv -f "$1" "${1%/*}/README.md"' sh {} \;
find /tmp/workdir/exponentiation -type f -name "*.md" -prune -exec sh -c 'mv -f "$1" "${1%/*}/README.md"' sh {} \;
find /tmp/gistdir -type d -name .git -prune -exec rm -rf {} \; && find /tmp/gistdir -type f -name "README.md" -exec rm -rf {} \;
  

So by the exponentiation zone they will end up as 7 days (sun) and 12 months (moon) while the 11 will represent the ones outside the orbit (stars or galaxies).

This eleven (11) things will be discussed later in identition zones.

MEC30 Structure

By the item factorization we will need to use the logarithm which is the inverse function to exponentiation. We end up by the tabulation as below.

$True Prime Pairs:
(5,7), (11,13), (17,19)
 
layer | node | sub |  i  |  f
------+------+-----+-----+------      ‹------------------------------ 0
      |      |     |  1  | --------------------------
      |      |  1  +-----+                           |    
      |  1   |     |  2  | (5)                       |
      |      |-----+-----+                           |
      |      |     |  3  |                           |
  1   +------+  2  +-----+----                       |
      |      |     |  4  |                           |
      |      +-----+-----+                           |
      |  2   |     |  5  | (7)                       |
      |      |  3  +-----+                           |
      |      |     |  6  |                          11s ‹------- (71)
------+------+-----+-----+------      } (36)         |
      |      |     |  7  |                           |
      |      |  4  +-----+                           |
      |  3   |     |  8  | (11)                      |
      |      +-----+-----+                           |
      |      |     |  9  |                           |
  2   +------|  5  +-----+-----                      |
      |      |     |  10 |                           |
      |      |-----+-----+                           |
      |  4   |     |  11 | (13) ---------------------
      |      |  6  +-----+            ‹------------------------------ 15
      |      |     |  12 |---------------------------
------+------+-----+-----+------------               |
      |      |     |  13 |                           |
      |      |  7  +-----+                           |
      |  5   |     |  14 | (17)                      |
      |      |-----+-----+                           |
      |      |     |  15 |                           7s ‹------- (43)
  3   +------+  8  +-----+-----       } (36)         |
      |      |     |  16 |                           |
      |      |-----+-----+                           |
      |  6   |     |  17 | (19)                      |
      |      |  9  +-----+                           |
      |      |     |  18 | --------------------------
------|------|-----+-----+------      ‹------------------------------- 30
  

These features are the solution to arrange 30 files located in in four (4) of zone folders as the lexer to cope with the Prime Spin and MEC30 Structure.

19 x 6 = 43 + 71 = 114

This scheme is showing a parsering result by repeating the positions in the next step. These positions: 1 7 11 13 17 19 23 29 refer as the basic system of MEC30.

The main different with gist is that wiki is allowing folder. So we can sort the files regardless where the folder that contained the file is located.

Note

Because the value 30 is the first (common) product of the first 3 primes. And this 30th order repeats itself to infinity. Even in the first 30s system, therefore, the positions are fixed in which the number information positions itself to infinity. We call it the first member of the MEC 30. (Google Patent DE102011101032A9)

You may see this scheme is build by 3 (three) layers where the next layer will continue the primes object by carrying the tensor of prime 31 and 71 of previous layer.

Let's find what we can do with it.