# The Mapping of Spacetime (spin 4)

Tip

This section is referring to wiki page-15 of gist section-11 that is inherited from the gist section-22 by prime spin-110 and span-8 with the partitions as below.

## Decay Frames

Note

As we’ve already alluded, to lay the foundation for a bijection with numbers not divisible by 2, 3, or 5, each of the pyramid’s four lateral faces is constructed from a 32-step triangular number progression (oeis.org/A000217: a(n) = n(n+1)/2 …).

7 = 4th prime

`````` Osp(1) |  1 |  2 |  3 |  4
--------+----+----+----+----
π(10)  |  2 |  3 |  5 |  7 ✔️
``````

19 = 8th prime

`````` Osp(2) |  1 |  2 |  3 |  4 | th
========+====+====+====+====+====
π(10)  |  2 |  3 |  5 |  7 | 4th
--------+----+----+----+----+----
π(19)  | 11 | 13 | 17 | 19 | 8th ✔️
``````

29 = 10th prime

`````` Osp(3) |  1 |  2 |  3 |  4 | th
========+====+====+====+====+====
π(10)  |  2 |  3 |  5 |  7 | 4th
--------+----+----+----+----+----
π(19)  | 11 | 13 | 17 | 19 | 8th
--------+----+----+----+----+----
π(29)  | 23 | 29 |  - |  - | 10th ✔️
``````

109 = 29th prime

`````` Osp(8|4) |  1 |  2 |  3 |   4 | th
==========+====+====+====+=====+====
π(10)    |  2 |  3 |  5 |   7 | 4th
----------+----+----+----+-----+----
π(19)    | 11 | 13 | 17 |  19 | 8th
----------+----+----+----+-----+----
π(29)    | 23 | 29 |  - |   - | 10th 👈 π(10) ✔️
==========+====+====+====+=====+====
π(❓)    | .. | .. | .. |  .. | ❓th
----------+----+----+----+-----+----
π(❓)    | .. | .. | .. |  .. | ❓th
----------+----+----+----+-----+----
π(❓)    | .. | .. | .. |  .. | ❓th 👈 π(19) ❓
==========+====+====+====+=====+====
π(❓)    | .. | .. | .. |  .. | ❓th
----------+----+----+----+-----+----
π(❓)    | .. | .. | .. |  .. | ❓th
----------+----+----+----+-----+----
π(109)   | .. | .. | .. | 109 | 29th 👈 π(29) ✔️
``````

12 + 18 + 13 = 43

`````` Osp(8|4) |  1 |  2 |  3 |   4 | th
==========+====+====+====+=====+====
π(10)    |  2 |  3 |  5 |   7 | 4th
----------+----+----+----+-----+----
π(19)    | 11 | 13 | 17 |  19 | 8th
----------+----+----+----+-----+----
π(29)    | 23 | 29 |  - |   - | 10th 👈 π(10)
==========+====+====+====+=====+====
π(29+12) | 31 | 37 | 41 |   - | 13th ✔️
----------+----+----+----+-----+----
π(41+18) | 43 | 47 | 53 |  59 | 17th ✔️
----------+----+----+----+-----+----
π(59+13) | 61 | 67 | 71 |   - | 20th 👈 π(19+1) ✔️
==========+====+====+====+=====+====
π(❓)    | .. | .. | .. |  .. | ❓th
----------+----+----+----+-----+----
π(❓)    | .. | .. | .. |  .. | ❓th
----------+----+----+----+-----+----
π(109)   | .. | .. | .. | 109 | 29th 👈 π(29)
``````

109 - 72 = 37

`````` Osp(8|4) |  1 |  2 |  3 |   4 | th
==========+====+====+====+=====+====
π(10)    |  2 |  3 |  5 |   7 | 4th
----------+----+----+----+-----+----
π(19)    | 11 | 13 | 17 |  19 | 8th
----------+----+----+----+-----+----
π(29)    | 23 | 29 |  - |   - | 10th 👈 π(10)
==========+====+====+====+=====+====
π(41)    | 31 | 37 | 41 |   - | 13th
----------+----+----+----+-----+----
π(59)    | 43 | 47 | 53 |  59 | 17th
----------+----+----+----+-----+- ---
π(72)    | 61 | 67 | 71 |   - | 20th 👈 π(19+1)
==========+====+====+====+=====+====
π(72+11) | 73 | 79 | 83 |   - | 23th ✔️
----------+----+----+----+-----+----
π(83+18) | 89 | 97 |101 |   - | 26th ✔️
----------+----+----+----+-----+----
π(101+8) |103 |107 |109 |   - | 29th 👈 π(29+1) ✔️
``````

## Decay Objects

Note

“Eliason’s work has been both praised and criticized within the academic community. Some scholars have praised his innovative approach to the study of the Torah and the insights that it has yielded. Others have criticized his methods as being overly subjective and lacking in scientific rigor. (Torah Geometry)

Note

Despite the controversy surrounding his work, Eric Eliason’s Torah geometry and gematria remain a fascinating subject of study for those interested in the mysteries of religious texts and the ways in which they can be interpreted and understood.

Note

Mathematically, this type of system requires 27 letters (1-9, 10–90, 100–900). In practice, the last letter, tav (which has the value 400), is used in combination with itself or other letters from qof (100) onwards to generate numbers from 500 and above. Alternatively, the 22-letter Hebrew numeral set is sometimes extended to 27 by using 5 sofit (final) forms of the Hebrew letters. (Wikipedia)

The first object symboled by "star" above is taken from one of the Higgs particles called neutral CP-odd (A) and behave as the base unit.

Note

The Higgs mechanism breaks electroweak symmetry in the Standard Model, giving mass to particles through its couplings.

• Current data from electroweak precision measurements points to a light Higgs {Mmggs < 199 GeV @ 95% CL [1]). However, the Higgs has never been definitively observed (MHiggs > 114 GeV at 95% CL [2]).
• A Standard Model Higgs suffers from the so called hierarchy problem. The theory needs fine-tuned parameters to accomodate a light Higgs mass. Supersymmetry offers a solution to this problem, through a symmetry between fermions and bosons.
• The Minimal Supersymmetric Standard Model contains two Higgs doublets, leading to five physical Higgs bosons: Two neutral CP-even states (h and H), one neutral CP-odd (A), and two charged states (H+ and H~).
• At tree-level, the masses are governed by two parameters, often taken to be mA and tan/3 [3]. When tan/3 > > 1 , A is nearly degenerate with one of the CP-even states (denoted φ). Where mA < 130 GeV (mA > 130), mA = mh (mA = mH).
• In this same large tan/3 region, the cross sections for some production mechanisms such as pp -» Α(φ) and pp -» A(\$i)bb are enhanced by factors of tan /32(sec/32). For example, with Λ/S = 2 TeV, tan/3 = 30 and mA = 100 GeV, the cross sections for pp —>· A and pp —> φ are each of or-der 10 pb[4].
• The cross section for pp -> Α/φΜ) is smaller, but within the same order of magnitude. In the same region, the branching ratios to Α/φ ->· bb and rr dominate, at ~ 90% and ~ 10% respectively, independent of mass.
• Due to their similar masses, cross-sections and branching ratios in the high tan/3 region, we search for *both A and φ simultaneously\$.
• At the Tevatron, we search for pp —>> Α/φ —► rr (the bb final state is expected to be overwhelmed by dijet background) and pp ->· Α/φΰ) -» bbbb.
• This search for pp -> Α/φ -> r+r~ is underway at CDF. The dominant issues for this analysis are: tau identification, ditau mass reconstruction, irreducible background from Z —► rr, and event loss at the trigger level.

Wherever not specified, we use the benchmark case of mA = 95 GeV and tan ß = 40 to quote efficiencies and cross-sections. (Search for MSSM Higgses at the Tevatron)

π(10) = 2,3,5,7

``````Sub  | i  |  β  | f
=======+====+=====+=======  ===   ===   ===   ===   ===   ===
1:1:0 | 1  |   1 | 2 {71}   1     1     |     |     |     |
-------+----+-----+-------  ---   ---    |     |     |     |
1:2:1 | 2  |   2 | 3 {71}         |     |     |     |     |
-------+----+-----+----            |     |     |     |     |
*1:2:2 | 3  |   3 |                |     |     |     |     |
-------+----+-----+----            |     |     |     |     |
*1:3:3 | 4  |   4 |                |     |     |     |     |
-------+----+-----+----            |     |     |     |     |
1:3:4 | 5  |   5 |                |     |     |     |     |
-------+----+-----+----            9     1‘    |    Δ100   |
*1:3:5 | 6  |   6 |                |     |     |     |     |
-------+----+-----+----            |     |     |     |     |
*1:4:6 | 7  |   7 |                |     |     |     |     |
-------+----+-----+----            |     |     |     |     |
1:4:7 | 8  |   8 |                |     |     |     |     |
-------+----+-----+----            |     |     |     |     |
*1:4:8 |{9} |   9 | 15 = 9 + 6 √   |     |     |     |     | ← 15 ✓
=======+====+=====+====           ===   ===    1"   ===    |
*1:4:9 |{10}|  10 | 19 = 9 + 10 √  |     |     |     |     |
-------+----+-----+----            |     |     |     |     |
2:1:0 | 11 |  20 | 20 = 19 + log 10 √   |     |     |     |
-------+----+-----+----                  |     |     |     |
2:2:1 | 12 |  30 |                      |     |     |     |
-------+----+-----+----                  |     |     |     |
*2:2:2 | 13 |  40 |                      |     |     |     |
-------+----+-----+----                  |     |     |     |
*2:3:3 | 14 |  50 |                      |     |     |     |
-------+----+-----+----                  |     |     |     |
2:3:4 | 15 |  60 |                      9‘    |   Δ200  Δ600
-------+----+-----+----                  |     |     |     |
*2:3:5 | 16 |  70 |                      |     |     |     |
-------+----+-----+----                  |     |     |     |
*2:4:6 | 17 |  80 |                      |     |     |     |
-------+----+-----+----                  |     |     |     |
2:4:7 |{18}|  90 | 32 = 26 + 6 √        |     |     |     |← 32 = 31 + ∆1✓
=======+====+=====+====                 ===   ===   ===    |
*2:4:8 |{19}| 100 | 36 = 26 + 10 √       |     |     |     |
-------+----+-----+----                  |     |     |     |
*2:4:9 | 20 | 200 | 38 = 36 + log 100 √        |     |     |
-------+----+-----+----                        |     |     |
3:1:0 | 21 | 300 |                            |     |     |
-------+----+-----+----                        |     |     |
3:2:1 | 22 | 400 |                            |     |     |
-------+----+-----+----                        |     |     |
*3:2:2 | 23 | 500 |                            |     |     |
-------+----+-----+----                        |     |     |
*3:3:3 | 24 | 600 |                            9"  Δ300    |
-------+----+-----+----                        |     |     |
3:3:4 | 25 | 700 |                            |     |     |
-------+----+-----+----                        |     |     |
*3:3:5 | 26 | 800 |                            |     |     |
-------+----+-----+----                        |     |     |
*3:4:6 | 27 | 900 | 46 = 40 + 6 √              |     |     |← 46 = 45 + ∆1 ✓
=======+====+=====+====                       ===   ===   ===
3:4:7 |{28}|1000 | 50 = 40 + 10 = 68 - 18 √
``````
Note

Valise adinkras, although an important subclass, do not encode all information present when a 4D supermultiplet is reduced to 1D. We extend this to non-valise adinkras providing a complete eigenvalue classification via Python code.

In order to describe real physical phenomena using string theory, one must therefore imagine scenarios in which these extra dimensions would not be observed in experiments so it would become the irrational partitions.

## Flavour and Colors

Note

You might imagine, right away, that there are nine gluons that are possible: one for each of the color-anticolor combinations possible. Indeed, this is what almost everyone expects, following some very straightforward logic.

• There are three possible colors, three possible anticolors, and each possible color-anticolor combination represents one of the gluons. If you visualized what was happening inside the proton as follows:
• a quark emits a gluon, changing its color,
• and that gluon is then absorbed by another quark, changing its color,

you’d get an excellent picture for what was happening with six of the possible gluons. (Why are there only 8 gluons)

There is also another explanation to the above color charge based on gluons transform in the adjoint representation of SU(3), which is 8-dimensional.

## Triangular Wave

One must therefore imagine scenarios in which these extra dimensions would not be observed in experiments so one of solution would be truncated approach.

Note

The first 3 triplets are prime and form the first triangle on top. Then we do the next two and the last one on the bottom because we will sandwich the other 3 in.

• These all match perfectly or one letter off on the bottom triangle, by sliding. The BGY slides, the YBG matches the YBR except one letter.
• Notice that the first 3 are prime. Then the next 4 are quite factorable. The 29 (RBR) is prime and there is no 29th letter, ending the pattern. 26 and 27 lead to 28 letters. Incidentally, the first 3 primes add to 99 and the primes add to 128. The last three to cover (RYY,YBY and RBR) match up with the top triangle’s bottom (except one letter) with RYY in reverse and make a matching triangle together. RYY has the most factors. The last 3 end in 29, suggesting an end to the pattern as there is no 29th letter.
• The final letter is B and it matches the middle letter, the two letters at the top and the two letters at the bottom if we do the BGY slide in one way.

Note

Speculating beyond the pyramidal model just described, the ratios seem to suggest that this geometry can be conceived sinusoidally as a Fourier series forming continuous triangular waves that reverse polarity in quarter cycles. For example, the 9th harmonic of the fundamental frequency 440 Hz = 3960 Hz (and keep in mind that 3960 = 1092 − 892, their relationship to the first 1000 primes covered in detail earlier in this section). Then consider that 8,363,520 (additive sum of the pyramid)/(1092 − 892) = 2112 (index # of the 1000th prime); 8/3/6/3/5/20 x (1092 − 892) x 360 = 2112; and that 443,520 (additive sum of the pyramidion)/(1092 − 892) = 112 (index # of 419, the 81st prime [as in 92, interestingly], and in turn 7919 x 28/528 = [419]; whole number part taken). (PrimesDemystified)

Here's a draft of what the proposed triangular wave might look like:

Base on the above discussions we conclude that the decay frames should behave as 4 times Triangular Waves as well, let have it done by The True Primer Pairs.

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)

``````The True Prime Pairs
(5,7), (11,13), (17,19)

Tabulate Prime by Power of 10
loop(10) = π(10)-π(1) = 4-0 = 4
loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114

--------------------------+----+----+----+----+----+----+----+----+----+-----
True Prime Pairs → Δ→π  |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum
==========================+====+====+====+====+====+====+====+====+====+=====
19 → π(∆10) → π(10)     |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
--------------------------+----+----+----+----+----+----+----+----+----+-----
17 → π(10+∆9) → π(19)   | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
==========================+====+====+====+====+====+====+====+====+====+===== 1st Twin
13 → π(19+∆10) → π(29)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th
--------------------------+----+----+----+----+----+----+----+----+----+-----
11 → π(29+∆12) → π(41)  | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
==========================+====+====+====+====+====+====+====+====+====+===== 1st Twin
7 → π(41+∆18) → π(59)  | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
--------------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
5 → π(59+∆13) → π(72)  | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th
==========================+====+====+====+====+====+====+====+====+====+===== 4th Twin
3,2 → 18+13+12 → 43    | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th
==========================+====+====+====+====+====+====+====+====+====+=====
Δ                                                            Δ
12+13+(18+18)+13+12   ← 36th-Δ1=151-1=150=100+2x(13+12)   ←   30th = 113 = 114-
``````
Note

Speaking of iterative digital division–a powerful tool for exposing structure–we get this astonishing equation: iteratively dividing the digital roots of the first 12 Fibonacci numbers times the divisively iterated 1000th prime, 7919, times 3604 gives us 1000.

• Keep in mind that the first two and last two digits of the Fibo sequence below, 11 and 89, sum to 100; that 89 is the 11th Fibo number; that there are 1000 primes between 1 and 892; and that 89 has the Fibonacci sequence embedded in its decimal expansion:

1/1/2/3/5/8/4/3/7/1/8/9 x 7/9/1/9 x 3604 = 1000

``````    |-------------------------------- 2x96 -------------------------------|
|--------------- 7¤ ---------------|---------------- 7¤ --------------|👈❓
〰️Osp(8|4) 👉------ {89} --------------|-------------- {103} -------------|
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
|--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----👉1/89
|---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|
|-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|
13 variations               48 variations          11 variations
``````

``````    |-------------------------------- 2x96 ---------------------|
|--------------- 7¤ ---------------|---------- 5¤ ----------| ✔️
〰️Osp(8|4) 👉------ {89} --------------|-------- {103} ---------|
+----+----+----+----+----+----+----+----+----+----+----+----+
|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|
+----+----+----+----+----+----+----+----+----+----+----+----+
|--------- {53} ---------|---- {48} ----|---- {48} ----|---👉109²-89²=11×360 ✔️
|---------- 5¤ ----------|------------ {96} -----------|-1¤-|
|-------- Bosons --------|---------- Fermions ---------|-- Graviton
13 variations               48 variations           11 variations
``````