diff --git a/.nojekyll b/.nojekyll new file mode 100644 index 00000000..e69de29b diff --git a/README.md b/README.md new file mode 100644 index 00000000..624a2469 --- /dev/null +++ b/README.md @@ -0,0 +1,180 @@ +--- +sort: 0 +spin: +span: +suit: 0 +--- +# + +# [Prime Identity](https://eq19.com/) + +By this part we are going to compile all topic we have discussed. Here we would like to explain the way we take on getting the arithmetic expresion of prime distribution to get an ***individual unit expression (identity)*** such as a taxicab number below. + +```note +It is a taxicab number, and is variously known as Ramanujan's number and the Ramanujan-Hardy number, after an anecdote of the British mathematician _[GH Hardy](https://en.wikipedia.org/wiki/G._H._Hardy)_ when he visited Indian mathematician _[Srinivasa Ramanujan](https://en.wikipedia.org/wiki/Srinivasa_Ramanujan)_ in hospital _([Wikipedia](https://en.wikipedia.org/wiki/1729_(number)))_. +``` + +[![Ramanujan-Hardy number](https://user-images.githubusercontent.com/36441664/103107461-173c2b00-4671-11eb-962c-da7e9eab022e.png)](https://en.wikipedia.org/wiki/1729_(number)) + +These three (3) number are [twin primes](https://en.wikipedia.org/wiki/Twin_prime). We called the pairs as _[True Prime Pairs](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#true-prime-pairs)_. Our scenario is mapping the distribution out of these pairs by taking the symmetrical behaviour of 36 as the smallest power (greater than 1) which is not a prime power. + +```tip +The smallest square number expressible as the sum of **four (4) consecutive primes** in two ways (5 + 7 + 11 + 13 and 17 + 19) which are also **two (2) couples** of prime twins! _([Prime Curios!](https://en.wikipedia.org/wiki/1729_(number)](https://primes.utm.edu/curios/page.php?number_id=270)))_. +``` + +```scss +$True Prime Pairs: + (5,7), (11,13), (17,19) + + layer| i | f + -----+-----+--------- + | 1 | 5 + 1 +-----+ + | 2 | 7 + -----+-----+--- } 36 » 6® + | 3 | 11 + 2 +-----+ + | 4 | 13 + -----+-----+--------- + | 5 | 17 + 3 +-----+ } 36 » 6® + | 6 | 19 + -----+-----+--------- +``` + +Thus in short this is all about the method that we called as the ***[19 vs 18 Scenario](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#the-%CE%B419-vs-18-scenario)*** of mapping [the quantum way](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-utilization-md) within a huge of [primes objects](https://github.com/eq19) (5 to 19) by [lexering](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-lexer-md) (11) the un[grammar](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-grammar-md)ed feed (7) and [parsering](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-parser-md) (13) across [syntax](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-syntax-md) (17). + +***Φ(1,2,3) = Φ(6,12,18) = Φ(13,37,61)*** + +```scss +$True Prime Pairs: +(5,7), (11,13), (17,19) + +layer | node | sub | i | f +------+------+-----+---------- + | | | 1 | + | | 1 +-----+ + | 1 | | 2 | (5) + | |-----+-----+ + | | | 3 | + 1 +------+ 2 +-----+---- + | | | 4 | + | +-----+-----+ + | 2 | | 5 | (7) + | | 3 +-----+ + | | | 6 | +------+------+-----+-----+------ } (36) + | | | 7 | + | | 4 +-----+ + | 3 | | 8 | (11) + | +-----+-----+ + | | | 9 | + 2 +------| 5 +-----+----- + | | | 10 | + | |-----+-----+ + | 4 | | 11 | (13) + | | 6 +-----+ + | | | 12 | +------+------+-----+-----+------------------ + | | | 13 | + | | 7 +-----+ + | 5 | | 14 | (17) + | |-----+-----+ + | | | 15 | + 3 +------+ 8 +-----+----- } (36) + | | | 16 | + | |-----+-----+ + | 6 | | 17 | (19) + | | 9 +-----+ + | | | 18 | +------|------|-----+-----+------ +``` + +The main background is that, as you may also aware, the prime number theorem describes the ***asymptotic distribution*** of prime numbers which is still a major problem in mathematic. + +## Zeta Function + +Instead of getting a proved formula we came to a unique expression called ***zeta function***. This expression first appeared in a paper in 1737 entitled _Variae observationes circa series infinitas_. + +```tip +This expression states that the sum of the zeta function is equal to the product of the reciprocal of one minus the reciprocal of primes to the power s. But what has this got to do with the primes? The answer is in the following product taken over the primes p (discovered by _[Leonhard Euler](https://en.wikipedia.org/wiki/Leonhard_Euler)_): +``` + +![image](https://user-images.githubusercontent.com/8466209/219739322-ebdc1916-249a-49da-8ded-ce0fe1205550.png) + +This issue is actually come from ***[Riemann hypothesis](https://en.wikipedia.org/wiki/Riemann_hypothesis)***, a conjecture about the distribution of complex zeros of the Riemann zeta function that is considered by many mathematicians to be ***the most important*** of _[unsolved problems](https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics)_ in pure mathematics. + +```note +In addition to the trivial roots, there also exist ***complex roots*** for real t. We find that the he first ten (10) non-trivial roots of the Riemann zeta function is occured when the values of t below 50. A plot of the values of ζ(1/2 + it) for t ranging from –50 to +50 is shown below. The roots occur each time ***the locus passes through the origin***. _([mathpages](https://www.mathpages.com/home/kmath738/kmath738.htm))_. +``` + +[![image](https://user-images.githubusercontent.com/8466209/219828222-615a2037-dbcd-4412-95bf-740bb32094de.png)](https://www.mathpages.com/home/kmath738/kmath738.htm) + +Meanwhile obtaining the non complex numbers it is easier to look at a graph like the one below which shows Li(x) (blue), R(x) (black), π(x) (red) and x/ln x (green); and then proclaim "R(x) is the best estimate of π(x)." Indeed it is for that range, but as we mentioned above, Li(x)-π(x) changes sign infinitely often, and near where it does, Li(x) would be the best value. + +[![image](https://user-images.githubusercontent.com/8466209/219214486-e6412fb0-d190-45ae-990f-524532661444.png)](https://primes.utm.edu/howmany.html#better) + +And we can see in the same way that the function Li(x)-(1/2)Li(x1/2) is 'on the average' a better approximation than Li(x) to π(x); but no importance can be attached to the latter terms in Riemann's formula even by repeated averaging. +The problem is that the contributions from the non-trivial zeros at times swamps that of any but the main terms in these expansions. + +```warning +A. E. Ingham says it this way: Considerable importance was attached formerly to a function suggested by Riemann as an approximation to π(x)... This function represents π(x) with astonishing accuracy for all values of x for which π(x) has been calculated, but we now see that its superiority over Li(x) ***is illusory***... and for special values of x (as large as we please) the one approximation will deviate as widely as the other from the true value _([primes.utm.edu](https://primes.utm.edu/howmany.html#better))_. +``` + +[![](https://user-images.githubusercontent.com/36441664/87958552-dea18f80-cadb-11ea-9499-6c2ee580a5ca.png)](https://primes.utm.edu/howmany.html#pnt) + +Moreover in it was verified numerically, in a rigorous way using interval arithmetic, that _[The Riemann hypothesis is true up to 3 · 10^12](https://arxiv.org/pdf/2004.09765.pdf)_. That is, all zeroes β+iγ of the Riemann zeta-function with 0<γ≤3⋅1012 have β=1/2. + +```danger +We have Λ ≤ 0.2. The next entry is conditional on taking H a little higher than 10*13, which of course, is not achieved by Theorem 1. This would enable one to prove Λ < 0.19. Given that our value of H falls between the entries in this table, it is possible that some extra decimals could be wrought out of the calculation. We have not pursued this _([arXiv:2004.09765](https://arxiv.org/abs/2004.09765))_. +``` + +[![image](https://user-images.githubusercontent.com/8466209/219715694-751fe538-378d-4f58-ae82-ac9e6823ad65.png)](https://arxiv.org/pdf/2004.09765.pdf) + +This Euler formula represents the distribution of a group of numbers that are positioned at regular intervals on a straight line to each other. Riemann later extended the definition of zeta(s) to all complex numbers (***except the simple pole at s=1 with residue one***). Euler's product still holds if the real part of s is greater than one. Riemann derived the functional equation of zeta function. + +```danger +The Riemann zeta function has the trivial zeros at -2, -4, -6, ... (the poles of gamma(s/2)). Using the Euler product (with the functional equation) it is easy to show that all the other zeros are in the critical strip of non-real complex numbers with 0 < Re(s) < 1, and that they are symmetric about the critical line Re(s)=1/2. The unproved Riemann hypothesis is that all of the nontrivial zeros are actually on the critical line _([primes.utm.edu](https://primes.utm.edu/notes/rh.html))_. +``` + +![image](https://user-images.githubusercontent.com/8466209/219720444-e5ba30ac-e000-4c85-8678-186676b93d2b.png) + +If both of the above statements are true then mathematically this Riemann Hypothesis is proven to be incorrect because it only applies to certain cases or limitations. So first of all the basis of the Riemann Hypothesis has to be considered. + +[![Riemann hypothesis,](https://user-images.githubusercontent.com/8466209/218374273-729fee09-5480-4fb3-a3a6-0dc050bdbe26.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-parser-md) + +{:.bg-white.text-black.m-5} +_Sehr leider Herr Riemann. Leute können den Fall immer noch nicht lösen.._. + +On the other hand, the possibility of obtaining the function of the distribution of prime numbers shall go backwards since it needs significant studies to be traced. Or may be ***start again from the Euleur Function***. + +## Euler's identity + +_[Freeman Dyson](https://en.wikipedia.org/wiki/Freeman_Dyson#Quantum_physics_and_prime_numbers)_ discovered an intriguing connection between quantum physics and [Montgomery's pair correlation conjecture](https://en.wikipedia.org/wiki/Montgomery%27s_pair_correlation_conjecture) about the zeros of the [zeta function](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#zeta-function) which dealts with the distribution of primes. + +```note +The Mathematical Elementary Cell 30 (***MEC30***) standard _[unites](https://gist.github.com/eq19/e9832026b5b78f694e4ad22c3eb6c3ef#centralizing)_ the mathematical and physical results of 1972 by _the mathematician Hugh Montgomery and the physicist Freeman Dyson_ and thus reproduces energy distribution in systems as a path plan ***more accurately than a measurement*** _([Google Patent DE102011101032A9](https://patents.google.com/patent/DE102011101032A9/en#similarDocuments))_. +``` + +[![Euler's identity](https://user-images.githubusercontent.com/36441664/74366957-992db780-4e03-11ea-8f26-cca32bd26003.png)](https://patentimages.storage.googleapis.com/6f/e3/f0/b8f7292f1f2749/DE102011101032A9.pdf) + +The path plan assume that a symmetric distribution of prime numbers with equal axial lengths from a ***middle zero axis = 15*** is able to determine the distribution of primes in a given number space. This assumption finally bring us to the equation of ***[Euler's identity](https://en.wikipedia.org/wiki/Euler%27s_identity)***. + +```note +***Euler's identity*** is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula +e^ix = cos x + i sin x when evaluated for x = π. _([Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_identity))_. +``` + +[![image](https://user-images.githubusercontent.com/8466209/219584666-703f4584-db7c-4f2d-9714-f52067869ef3.png)](https://en.wikipedia.org/wiki/Euler%27s_identity) + +The finiteness position of Euler's identity by the said _MEC30_ opens up the possibility of accurately representing the self-similarity based on the distribution of _[True Prime Pairs](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857)_ so that all number would belongs together with [their own identitities](https://www.eq19.com/identition/). + +```tip +Euler's identity is considered to be an exemplar of deep mathematical beauty as it shows a profound connection between the most fundamental numbers. Three (3) of the basic arithmetic operations occur exactly once each: ***addition***, ***multiplication***, and ***exponentiation*** _([Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_identity))_. +``` + +[![image](https://user-images.githubusercontent.com/8466209/253148763-4a982982-4f70-4d7d-b524-51b72c6f17e9.png)](/identition). + +See that there are multiple repetition from addition to multiplication which may lead up to the concept of [11th-dimension](https://www.techtarget.com/whatis/definition/11th-dimension). This path is being applied as you can find on the left sidebar. (Please change the view to desktop mode if you are on mobile browser). + +Nothing is going to be easly about the nature of prime numbers but they demonstrably congruent to something organized. Let's discuss starting with the _[addition zones](https://www.eq19.com/addition/)_. diff --git a/exponentiation/index.html b/exponentiation/index.html new file mode 100644 index 00000000..cc71bdcb --- /dev/null +++ b/exponentiation/index.html @@ -0,0 +1,78 @@ + Exponentiation Zones (31-36) · eQuantum
eQuantum
eQuantum

Exponentiation Zones (31-36)

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This section is referring to wiki page-4 of zone section-4 that is inherited from the zone section-zones by prime spin-19 and span-exponentiation with the partitions as below.

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/Toko-Chetabahana

Background of exponentiation

Untitled

gradien

In the standard (Mispar hechrechi) version of gematria, each letter is given a numerical value between 1 and 400, as shown in the following table. In the Mispar gadol variation, the five final letters are given their own values, ranging from 500 to 900.

Δ prime = 114th prime - 19 = (6 x 19)th prime - 19 = 619 - 19 = 600

  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 | 7 = 1 + 2x3    |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+*1:3:3 | 4  |   4 | 10 = 9 + 1     |     |     |     |     |  
+-------+----+-----+----            |     |     |     |     |
+ 1:3:4 | 5  |   5 | 11 = 9 + 2     |     |     |     |     |
+-------+----+-----+----            9     1‘    |    Δ100   |
+*1:3:5 | 6  |   6 | 12 = 9 + 3     |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+*1:4:6 | 7  |   7 | 13 = 9 + 4     |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+ 1:4:7 | 8  |   8 | 14 = 9 + 5     |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+*1:4:8 |{9} |   9 | 15 = 9 + 6     |     |     |     |     |
+-------+----+-----+----            |     |     |     |     |
+*1:4:9 |{10}|  10 | 19 = 9 + 10    |     |     |     |     |
+=======+====+=====+====           ===   ---    1"   ---    |
+ 2:1:0 | 11 |  20 | 20 = 19 + log 10¹    |     |     |     |
+-------+----+-----+----                  |     |     |     |
+ 2:2:1 | 12 |  30 | 26 = 20 + 2x3        |     |     |     |
+-------+----+-----+----                  |     |     |     |
+*2:2:2 | 13 |  40 | 27 = 26 + 1          |     |     |     |
+-------+----+-----+----                  |     |     |     |
+*2:3:3 | 14 |  50 | 28 = 26 + 2          |     |     |     |
+-------+----+-----+----                  |     |     |     |
+ 2:3:4 | 15 |  60 | 29 = 26 + 3          9‘    |   Δ200  Δ600
+-------+----+-----+----                  |     |     |     |
+*2:3:5 | 16 |  70 | 30 = 26 + 4          |     |     |     |
+-------+----+-----+----                  |     |     |     |
+*2:4:6 | 17 |  80 | 31 = 26 + 5          |     |     |     |
+-------+----+-----+----                  |     |     |     |
+ 2:4:7 |{18}|  90 | 32 = 26 + 6          |     |     |     |
+-------+----+-----+----                  |     |     |     |
+*2:4:8 |{19}| 100 | 36 = 26 + 10         |     |     |     |
+=======+====+=====+====                 ===   ---   ---    |
+*2:4:9 | 20 | 200 | 38 = 36 + log 10²          |     |     |
+-------+----+-----+----                        |     |     |
+ 3:1:0 | 21 | 300 | 40 = 36 + 2 x log 10²      |     |     |
+-------+----+-----+----                        |     |     |
+ 3:2:1 | 22 | 400 | 41 = 40 + 1                |     |     |
+-------+----+-----+----                        |     |     |
+*3:2:2 | 23 | 500 | 42 = 40 + 2                |     |     |
+-------+----+-----+----                        |     |     |
+*3:3:3 | 24 | 600 | 43 = 40 + 3                9"  Δ300    |
+-------+----+-----+----                        |     |     |
+ 3:3:4 | 25 | 700 | 44 = 40 + 4                |     |     |
+-------+----+-----+----                        |     |     |
+*3:3:5 | 26 | 800 | 45 = 40 + 5                |     |     |
+-------+----+-----+----                        |     |     |
+*3:4:6 | 27 | 900 | 46 = 40 + 6                |     |     |
+-------+----+-----+----                        |     |     |
+ 3:4:7 |{28}|1000 | 50 = 40 + 10               |     |     |
+=======+====+=====+====                       ===  ====  ----
+*3:4:8 |{29}|2000 | 68 = 50 + 3 x (2x3)      {10³} Δ600  Δ300
+=======+====+=====+====                        Δ         ====
+ 3:4:9 |{30}|3000 |{71}= 68 + log 10³ ---------¤         Δ900   
+

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. So it will return to the beginning position within 60+40=100 nodes per layer.

Relation to the primes

Let's combine them all then we will get 168 which is the total primes out of 1000 numbers. This 168 we will get it also when we combine the 1's and 17's cell of (31+37)+(35+65)=68+100=168.

recycle

The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later.

Both Ulam and Gardner noted that the existence of such prominent lines is not unexpected, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial x²-x+41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with major unsolved problems in number theory such as Landau's problems (Wikipedia).

prime Sacks_spiral

According to the results of Princeton University USA in 1972, the distribution of the prime numbers shows in the Riemann zeta function between the position of its complex zeros and middle axis is identical with the rotation curve of energy distribution.

37 + 12 = 61 - 12 = 49 = 7 x 7 = d(13)

image

In the second opposing member, the position 19 in the second term gives a redundant value of the template 7 of 7 × 7 = 49. The opposite prime position 11 as a prime number is now forced to determine a new axis-symmetrical zero position.

Note that when 77 contains ‘Lucky 7 and 11' as prime factors it is also the product of the middle two numbers of this sequence (11*7 = 77) (Prime Curios!).

MEC30 Localization

Subclasses of partition

tensorflow

When the subclasses of partitions are flatten out into a matrix, you want to take the Jacobian of each of a stack of targets with respect to a stack of sources, where the Jacobians for each target-source pair are independent .

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It’s possible to build a Hessian matrix for a Newton’s method step using the Jacobian method. You would first flatten out its axes into a matrix, and flatten out the gradient into a vector (Tensorflow).

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Batch Jacobian)

By parsering π(1000)=168 primes of the 1000 id's across π(π(10000))-1=200 of this syntax then the (Δ1) would be initiated.

forex-traders-lessons?page=330

gann hexagon chart

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\ No newline at end of file diff --git a/exponentiation/span17/spin_5.txt b/exponentiation/span17/spin_5.txt new file mode 100644 index 00000000..185ff0aa --- /dev/null +++ b/exponentiation/span17/spin_5.txt @@ -0,0 +1,33 @@ +1009 3 -1 -3 +1013 2 -1 -3 +1019 2 1 -3 +1021 3 1 -3 +1031 4 1 -3 +1033 5 1 -3 +1039 5 -1 -3 +1049 4 -1 -3 +1051 3 -1 -3 +1061 2 -1 -3 +1063 1 -1 -3 +1069 1 1 -3 +1087 1 -1 -3 +1091 0 -1 -3 +1093 5 -1 -4 +1097 4 -1 -4 +1103 4 1 -4 +1109 4 -1 -4 +1117 3 -1 -4 +1123 3 1 -4 +1129 3 -1 -4 +1151 2 -1 -4 +1153 1 -1 -4 +1163 0 -1 -4 +1171 5 -1 -5 +1181 4 -1 -5 +1187 4 1 -5 +1193 4 -1 -5 +1201 3 -1 -5 +1213 3 1 -5 +1217 4 1 -5 +1223 4 -1 -5 +1229 4 1 -5 diff --git a/exponentiation/span17/spin_6.txt b/exponentiation/span17/spin_6.txt new file mode 100644 index 00000000..c3605570 --- /dev/null +++ b/exponentiation/span17/spin_6.txt @@ -0,0 +1,800 @@ +1231 5 1 -5 +1237 5 -1 -5 +1249 5 1 -5 +1259 0 1 -4 +1277 0 -1 -4 +1279 5 -1 -5 +1283 4 -1 -5 +1289 4 1 -5 +1291 5 1 -5 +1297 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4 1 -16 +7741 5 1 -16 +7753 5 -1 -16 +7757 4 -1 -16 +7759 3 -1 -16 +7789 3 1 -16 +7793 4 1 -16 +7817 4 -1 -16 +7823 4 1 -16 +7829 4 -1 -16 +7841 4 1 -16 +7853 4 -1 -16 +7867 3 -1 -16 +7873 3 1 -16 +7877 4 1 -16 +7879 5 1 -16 +7883 0 1 -15 +7901 0 -1 -15 +7907 0 1 -15 +7919 0 -1 -15 +7927 5 -1 -16 diff --git a/exponentiation/span18/spin_1.txt b/exponentiation/span18/spin_1.txt new file mode 100644 index 00000000..bd007e8a --- /dev/null +++ b/exponentiation/span18/spin_1.txt @@ -0,0 +1,10 @@ +0 0 0 0 +1 0 0 0 +2 0 1 0 +3 1 1 0 +5 2 1 0 +7 3 1 0 +11 4 1 0 +13 5 1 0 +17 0 1 1 +19 1 1 1 diff --git a/exponentiation/span18/spin_2.txt b/exponentiation/span18/spin_2.txt new file mode 100644 index 00000000..8d1f1b47 --- /dev/null +++ b/exponentiation/span18/spin_2.txt @@ -0,0 +1,30 @@ +23 2 1 1 +29 2 -1 1 +31 1 -1 1 +37 1 1 1 +41 2 1 1 +43 3 1 1 +47 4 1 1 +53 4 -1 1 +59 4 1 1 +61 5 1 1 +67 5 -1 1 +71 4 -1 1 +73 3 -1 1 +79 3 1 1 +83 4 1 1 +89 4 -1 1 +97 3 -1 1 +101 2 -1 1 +103 1 -1 1 +107 0 -1 1 +109 5 -1 0 +113 4 -1 0 +127 3 -1 0 +131 2 -1 0 +137 2 1 0 +139 3 1 0 +149 4 1 0 +151 5 1 0 +157 5 -1 0 +163 5 1 0 diff --git a/exponentiation/span18/spin_3.txt b/exponentiation/span18/spin_3.txt new file mode 100644 index 00000000..5f896030 --- /dev/null +++ b/exponentiation/span18/spin_3.txt @@ -0,0 +1,60 @@ +167 0 1 1 +173 0 -1 1 +179 0 1 1 +181 1 1 1 +191 2 1 1 +193 3 1 1 +197 4 1 1 +199 5 1 1 +211 5 -1 1 +223 5 1 1 +227 0 1 2 +229 1 1 2 +233 2 1 2 +239 2 -1 2 +241 1 -1 2 +251 0 -1 2 +257 0 1 2 +263 0 -1 2 +269 0 1 2 +271 1 1 2 +277 1 -1 2 +281 0 -1 2 +283 5 -1 1 +293 4 -1 1 +307 3 -1 1 +311 2 -1 1 +313 1 -1 1 +317 0 -1 1 +331 5 -1 0 +337 5 1 0 +347 0 1 1 +349 1 1 1 +353 2 1 1 +359 2 -1 1 +367 1 -1 1 +373 1 1 1 +379 1 -1 1 +383 0 -1 1 +389 0 1 1 +397 1 1 1 +401 2 1 1 +409 3 1 1 +419 4 1 1 +421 5 1 1 +431 0 1 2 +433 1 1 2 +439 1 -1 2 +443 0 -1 2 +449 0 1 2 +457 1 1 2 +461 2 1 2 +463 3 1 2 +467 4 1 2 +479 4 -1 2 +487 3 -1 2 +491 2 -1 2 +499 1 -1 2 +503 0 -1 2 +509 0 1 2 +521 0 -1 2 diff --git a/exponentiation/span18/spin_4.txt b/exponentiation/span18/spin_4.txt new file mode 100644 index 00000000..153f4bd7 --- /dev/null +++ b/exponentiation/span18/spin_4.txt @@ -0,0 +1,70 @@ +523 5 -1 1 +541 5 1 1 +547 5 -1 1 +557 4 -1 1 +563 4 1 1 +569 4 -1 1 +571 3 -1 1 +577 3 1 1 +587 4 1 1 +593 4 -1 1 +599 4 1 1 +601 5 1 1 +607 5 -1 1 +613 5 1 1 +617 0 1 2 +619 1 1 2 +631 1 -1 2 +641 0 -1 2 +643 5 -1 1 +647 4 -1 1 +653 4 1 1 +659 4 -1 1 +661 3 -1 1 +673 3 1 1 +677 4 1 1 +683 4 -1 1 +691 3 -1 1 +701 2 -1 1 +709 1 -1 1 +719 0 -1 1 +727 5 -1 0 +733 5 1 0 +739 5 -1 0 +743 4 -1 0 +751 3 -1 0 +757 3 1 0 +761 4 1 0 +769 5 1 0 +773 0 1 1 +787 1 1 1 +797 2 1 1 +809 2 -1 1 +811 1 -1 1 +821 0 -1 1 +823 5 -1 0 +827 4 -1 0 +829 3 -1 0 +839 2 -1 0 +853 1 -1 0 +857 0 -1 0 +859 5 -1 -1 +863 4 -1 -1 +877 3 -1 -1 +881 2 -1 -1 +883 1 -1 -1 +887 0 -1 -1 +907 5 -1 -2 +911 4 -1 -2 +919 3 -1 -2 +929 2 -1 -2 +937 1 -1 -2 +941 0 -1 -2 +947 0 1 -2 +953 0 -1 -2 +967 5 -1 -3 +971 4 -1 -3 +977 4 1 -3 +983 4 -1 -3 +991 3 -1 -3 +997 3 1 -3 diff --git a/exponentiation/span18/spin_5.liquid b/exponentiation/span18/spin_5.liquid new file mode 100644 index 00000000..9c329cb6 --- /dev/null +++ b/exponentiation/span18/spin_5.liquid @@ -0,0 +1,6 @@ +{% assign test1="virtual/file68.md" %} +{% assign test2="virtual/file50.md" %} + +{% include {{ test1 }} all=true %} +{% include {{ test2 }} all=true %} + diff --git a/file01.html b/file01.html new file mode 100644 index 00000000..1dfe731f --- /dev/null +++ b/file01.html @@ -0,0 +1,263 @@ + Addition Zones (1-18) · eQuantum
eQuantum
eQuantum

Addition Zones (1-18)

+
+ + Tip +
+
+

This section is referring to wiki page-2 of zone section-2 that is inherited from the zone section-zones by prime spin-19 and span-addition with the partitions as below.

+
+

/Toko-Chetabahana

  1. Addition Zones (1-18)
  2. Multiplication Zones (19-30)
  3. Exponentiation Zones (31-36)
  4. Identition Zones (37-102)

Prime Hexagon

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+ + Note +
+
+

The Prime Hexagon is a mathematical structure developed by mathematician T. Gallion. A Prime Hexagon is formed when integers are sequentially added to a field of tessellating equilateral triangles, where the path of the integers is changed whenever a prime number is encountered (GitHub: prime-hexagon).

+
+ 
(5, 2, 1, 0)
+(7, 3, 1, 0)
+(11, 4, 1, 0)
+(13, 5, 1, 0)
+(17, 0, 1, 1)
+(19, 1, 1, 1)
+(23, 2, 1, 1)
+(29, 2, -1, 1)
+(31, 1, -1, 1)
+(37, 1, 1, 1)
+(41, 2, 1, 1)
+(43, 3, 1, 1)
+(47, 4, 1, 1)
+(53, 4, -1, 1)
+(59, 4, 1, 1)
+(61, 5, 1, 1)
+(67, 5, -1, 1)
+(71, 4, -1, 1)
+(73, 3, -1, 1)
+(79, 3, 1, 1)
+(83, 4, 1, 1)
+(89, 4, -1, 1)
+(97, 3, -1, 1)
+(101, 2, -1, 1)
+(103, 1, -1, 1)
+(107, 0, -1, 1)
+(109, 5, -1, 0)
+(113, 4, -1, 0)
+(127, 3, -1, 0)
+(131, 2, -1, 0)
+(137, 2, 1, 0)
+(139, 3, 1, 0)
+(149, 4, 1, 0)
+(151, 5, 1, 0)
+(157, 5, -1, 0)
+(163, 5, 1, 0)
+(167, 0, 1, 1)
+(173, 0, -1, 1)
+(179, 0, 1, 1)
+(181, 1, 1, 1)
+(191, 2, 1, 1)
+(193, 3, 1, 1)
+(197, 4, 1, 1)
+(199, 5, 1, 1)
+(211, 5, -1, 1)
+(223, 5, 1, 1)
+(227, 0, 1, 2)
+(229, 1, 1, 2)
+(233, 2, 1, 2)
+(239, 2, -1, 2)
+(241, 1, -1, 2)
+(251, 0, -1, 2)
+(257, 0, 1, 2)
+(263, 0, -1, 2)
+(269, 0, 1, 2)
+(271, 1, 1, 2)
+(277, 1, -1, 2)
+(281, 0, -1, 2)
+(283, 5, -1, 1)
+(293, 4, -1, 1)
+(307, 3, -1, 1)
+(311, 2, -1, 1)
+(313, 1, -1, 1)
+(317, 0, -1, 1)
+(331, 5, -1, 0)
+(337, 5, 1, 0)
+(347, 0, 1, 1)
+(349, 1, 1, 1)
+(353, 2, 1, 1)
+(359, 2, -1, 1)
+(367, 1, -1, 1)
+(373, 1, 1, 1)
+(379, 1, -1, 1)
+(383, 0, -1, 1)
+(389, 0, 1, 1)
+(397, 1, 1, 1)
+(401, 2, 1, 1)
+(409, 3, 1, 1)
+(419, 4, 1, 1)
+(421, 5, 1, 1)
+(431, 0, 1, 2)
+(433, 1, 1, 2)
+(439, 1, -1, 2)
+(443, 0, -1, 2)
+(449, 0, 1, 2)
+(457, 1, 1, 2)
+(461, 2, 1, 2)
+(463, 3, 1, 2)
+(467, 4, 1, 2)
+(479, 4, -1, 2)
+(487, 3, -1, 2)
+(491, 2, -1, 2)
+(499, 1, -1, 2)
+(503, 0, -1, 2)
+(509, 0, 1, 2)
+(521, 0, -1, 2)
+(523, 5, -1, 1)
+(541, 5, 1, 1)
+(547, 5, -1, 1)
+(557, 4, -1, 1)
+(563, 4, 1, 1)
+(569, 4, -1, 1)
+(571, 3, -1, 1)
+(577, 3, 1, 1)
+(587, 4, 1, 1)
+(593, 4, -1, 1)
+(599, 4, 1, 1)
+(601, 5, 1, 1)
+(607, 5, -1, 1)
+(613, 5, 1, 1)
+(617, 0, 1, 2)
+(619, 1, 1, 2)
+(631, 1, -1, 2)
+(641, 0, -1, 2)
+(643, 5, -1, 1)
+(647, 4, -1, 1)
+(653, 4, 1, 1)
+(659, 4, -1, 1)
+(661, 3, -1, 1)
+(673, 3, 1, 1)
+(677, 4, 1, 1)
+(683, 4, -1, 1)
+(691, 3, -1, 1)
+(701, 2, -1, 1)
+(709, 1, -1, 1)
+(719, 0, -1, 1)
+(727, 5, -1, 0)
+(733, 5, 1, 0)
+(739, 5, -1, 0)
+(743, 4, -1, 0)
+(751, 3, -1, 0)
+(757, 3, 1, 0)
+(761, 4, 1, 0)
+(769, 5, 1, 0)
+(773, 0, 1, 1)
+(787, 1, 1, 1)
+(797, 2, 1, 1)
+(809, 2, -1, 1)
+(811, 1, -1, 1)
+(821, 0, -1, 1)
+(823, 5, -1, 0)
+(827, 4, -1, 0)
+(829, 3, -1, 0)
+(839, 2, -1, 0)
+(853, 1, -1, 0)
+(857, 0, -1, 0)
+(859, 5, -1, -1)
+(863, 4, -1, -1)
+(877, 3, -1, -1)
+(881, 2, -1, -1)
+(883, 1, -1, -1)
+(887, 0, -1, -1)
+(907, 5, -1, -2)
+(911, 4, -1, -2)
+(919, 3, -1, -2)
+(929, 2, -1, -2)
+(937, 1, -1, -2)
+(941, 0, -1, -2)
+(947, 0, 1, -2)
+(953, 0, -1, -2)
+(967, 5, -1, -3)
+(971, 4, -1, -3)
+(977, 4, 1, -3)
+(983, 4, -1, -3)
+(991, 3, -1, -3)
+(997, 3, 1, -3)
+
+
+ + Note +
+
+

Cell types are interesting, but they simply reflect a modulo 6 view of numbers. More interesting are the six internal hexagons within the Prime Hexagon. Like the Prime Hexagon, they are newly discovered. The minor hexagons form solely from the order, and type, of primes along the number line (HexSpin).

+
+

Structure: Minor Hexagons

Structure: True Prime Pairs

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

A Prime Hexagon is formed when integers are sequentially added to a field of tessellating equilateral triangles, where the path of the integers is changed whenever a prime number is encountered. Since prime numbers are never multiples of two or three, all numbers from “2” to infinity are confined within a 24-cell hexagon (GitHub: prime-hexagon).

+
+

Euler Partition

By having the total of 168, the 102 and the 30+36=66 will take the 1st and 2nd prime on The Primes Platform. This leads to 168 - 29 - 96 = 139 - 96 = 43 primes on the last of 7th row. That what and why 18+13+12=43 by the last 9 cells is standing for!

  -----------------+----+----+----+----+----+----+----+----+----+-----
+  The last 9 cells |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
+  =================+====+====+====+====+====+====+====+====+====+=====
+  3,2→18+13+12→43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th →13th→ 2,3
+  -----------------+----+----+----+----+----+----+----+----+----+-----
+
+- This 43 is 18+13+12 in bilateral on perfect square of 9 goes to 89 → π(89²) = 1000
+

Structure: Minor Hexagons

Within a cycle this scheme would generate the prime platform which is performing the rank of 10 shapes starting with the primes 2,3,5,7. Via the 11 partitions as the lexer and 13 frames as the parser we do a recombination to build the grammar in 6 periods.

+
+ + Note +
+
+

We color-code the six hexagons, identifying patterns in key number sequences, including the Fibonacci sequence, powers of two and three, and power of pi. For the series of consecutive powers of pi, we have found that no two fall within the same six-cell hexagon. We have computed this for pi^32, which has less than a 1/400 chance of occurring randomly (GitHub: prime-hexagon).

+
+

6 minor hexagons

I wondered if that property might hold for the incremental powers of phi as well. For this reason I chose to see numbers in the hexagon as quantum, and truncate off the decimal values to determine which integer cell they land in.

+
+ + Note +
+
+

That is what I found. Phi and its members have a pisano period if the resulting fractional numbers are truncated (HexSpin).

+
+

Truncate to Determine Integer Values

eQuantum
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\ No newline at end of file diff --git a/file02.html b/file02.html new file mode 100644 index 00000000..54454ca8 --- /dev/null +++ b/file02.html @@ -0,0 +1,125 @@ + Multiplication Zones (19-30) · eQuantum
eQuantum
eQuantum

Multiplication Zones (19-30)

+
+ + Tip +
+
+

This section is referring to wiki page-3 of zone section-3 that is inherited from the zone section-zones by prime spin-19 and span-multiplication with the partitions as below.

+
+

/Toko-Chetabahana

  1. Addition Zones (1-18)
  2. Multiplication Zones (19-30)
  3. Exponentiation Zones (31-36)
  4. Identition Zones (37-102)

Assigning Repositories

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.

image

So basically there is a power transformation between an addition of 3 and 4 to 7 in to their multiplication in to 12 where this 7 will be treated as one of their member.

(11 x 7) + 13 x (6 + 1) = 24 x 7 = 168

  #8 |----------- 5® --------|------------ 7® --------------|
+     |  1  |---------------- 77 = 4² + 5² + 6² -------------|
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+ repo| {1} | {2} | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |{12}| 1,77=11x7
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+ user|  7  |  -  | - | - | - | 7 | 8 | - | - |  8 |  8 |  3 |
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+ 7,78=13x6
+ main|  -  |  9  | 7 | 9 | 6 | - | - | 8 | 5 |  - |  - |  - |
+-----+-----|-----+---+---+---+---+---+---+---+----+----+----+
+               Δ | Δ             |                       Δ  |   Δ
+              Φ17|Φ29            |                     96-99|  168
+                 |--- A,T,G,C ---|                          |   └── 77
+                 Δ    2x2 = 4x   |-------  2x3 = 6x  -------|   └── 78
+                {98}                                        |   └── 13
+

Therefore the 12 will consist of 11 groups runner and 1 profile of the transformation. We collect them in 18 gists as below.

$ 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:

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
+

Orbital Structure

This scheme will become the orbit as 7 days (sun) and 12 months (moon) so the cinfiguration is end up like this:

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
+

Gists 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
+
+rm -rf /tmp/workdir
+
+WIKI=https://github.com/${OWNER}/$1.wiki.git
+BASE=https://github.com/eq19/eq19.github.io.wiki.git
+
+git ls-remote ${WIKI} > /dev/null 2>&1
+git clone $([ "$?" == 0 ] && echo $WIKI || echo $BASE) /tmp/workdir
+mv -f /tmp/workdir/Home.md /tmp/workdir/README.md
+
+gh gist clone 0ce5848f7ad62dc46dedfaa430069857 /tmp/workdir/addition
+mv -f /tmp/workdir/file01.md /tmp/workdir/addition/README.md
+
+gh gist clone 4ffc4d02579d5cfd336a553c6da2f267 /tmp/workdir/multiplication
+mv -f /tmp/workdir/file02.md /tmp/workdir/multiplication/README.md
+
+mv -f /tmp/workdir/identition/file04.md /tmp/workdir/identition/README.md
+gh gist clone 0ce5848f7ad62dc46dedfaa430069857 /tmp/workdir/identition/folder1
+gh gist clone b32915925d9d365e2e9351f0c4ed786e /tmp/workdir/identition/folder2
+gh gist clone 88d09204b2e5986237bd66d062406fde /tmp/workdir/identition/folder3
+gh gist clone 8cab5e72d52ecb338a2f2187082a1699 /tmp/workdir/identition/folder4
+gh gist clone 54600a56d20163c2da8910dd804ec406 /tmp/workdir/identition/folder5
+gh gist clone f1af4317b619154719546e615aaa2155 /tmp/workdir/identition/folder6
+gh gist clone 6c89c3b0f109e0ead561a452720d1ebf /tmp/workdir/identition/folder7
+gh gist clone f21abd90f8d471390aad23d6ecc90d6d /tmp/workdir/identition/folder8
+gh gist clone 6e2fcc2138be6fb68839a3ede32f0525 /tmp/workdir/identition/folder9
+gh gist clone b541275ab7deda356feef32d600e44d8 /tmp/workdir/identition/folder10
+gh gist clone 80c8098f16f3e6ca06893b17a02d910e /tmp/workdir/identition/folder11
+
+mv -f /tmp/workdir/exponentiation/file03.md /tmp/workdir/exponentiation/README.md
+gh gist clone f78d4470250720fb18111165564d555f /tmp/workdir/exponentiation/folder13
+gh gist clone 765ddc69e339079a5a64b56c1d46e00f /tmp/workdir/exponentiation/folder14
+gh gist clone b9f901cda16e8a11dd24ee6b677ca288 /tmp/workdir/exponentiation/folder15
+gh gist clone dc30497160f3389546d177da901537d9 /tmp/workdir/exponentiation/folder16
+gh gist clone e84a0961dc7636c01d5953d19d65e30a /tmp/workdir/exponentiation/folder17
+gh gist clone e9832026b5b78f694e4ad22c3eb6c3ef /tmp/workdir/exponentiation/folder18
+
+find /tmp/workdir -type d -name .git -prune -exec rm -rf {} \;
+

The implementation from addition folder 1 will be exposed by the exponentiation folder 7 meanwhile the folder 12 of multiplication goes to identition zone of 11 folders.

So they are 4 folders (1, 7, 11, 12) remain inviolable by the gist.

Transformation to exponentiation

Here we can see that the transformation from 7 to 12 is actually started from the prime 13. So the power of 7 is transfered to 77 by the prime pair 11 and 13.

Lexers, Parsers and Interpreters with Chevrotain

By observing more detail we spread the power of 7.

168 + 329 + 289 - 619 - 30 - 30 - 5 = 786 - 619 - 65 = 102

exponentiation zones

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\ No newline at end of file diff --git a/identition/index.html b/identition/index.html new file mode 100644 index 00000000..6d8d181d --- /dev/null +++ b/identition/index.html @@ -0,0 +1,71 @@ + Identition Zones (37-102) · eQuantum
eQuantum
eQuantum

Identition Zones (37-102)

+
+ + Note +
+
+

Five consistent versions of superstring theory were developed before it was conjectured in the mid-1990s that they were all different limiting cases of a single theory in 11 dimensions known as M-theory (Wikipedia).

+
+

Extra dimensions play a crucial role in string theory and typically take a very complicated form.

+
+ + Tip +
+
+

The concept of eleven dimensions is a theoretical one in physics and cosmology, specifically in the realm of string theory and M-theory. These theories propose that our observable universe is made up of 11 dimensions, rather than the traditional three dimensions of length, width, and height, and the fourth dimension of time. The additional dimensions are thought to be compactified or curled up, meaning that they are not directly observable by us in our everyday experience.As for the cosmic philosophy, it is important to note that these theories are still considered speculative and have not been proven through experimental evidence. However, they do offer a new perspective on the nature of our universe and the fundamental forces that govern it. Some scientists and philosophers argue that these theories may provide new insights into the origins of the universe and the nature of reality itself. Ultimately, the concept of eleven dimensions is a fascinating area of study that continues to inspire new research and discoveries in the field of physics and cosmology. (ChatGPT)

+
+

M-theory

Below is a model of E11 (shown by 11 dimensions). Its absolute dimensions represent all related key knowledges of modern physics. Moreover a model that represents Quark-Gluon Plasma, with fundamental forces in the early stage after Big Bang.

default

Orbital Transformation

Plottng 40th prime scheme of the three (3) layers with all the features of 3rd prime identity as explained above then they would form their recycing through the three (3) times bilateral 9 sums as shown below.

89^2 - 1 = 7920 = 22 x 360 = 66 x 120 = (168 - 102) x 120

default

The nodes is converted from 7 to 77 which is 7 times 11. By the prime pair 11 and 13, the total nodes is involving 1 + 7 + 29 + 77 = 37 + 77 = 114 nodes

  Δ1 + Δ7 + Δ29  →  | Δ37 + Δ77 = Δ114 = Δ113 + Δ1 → 
+
+     |         1st (Form)          |         2nd (Route)         |         3rd (Channel)       |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ 150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  Δ1 | 19 |  - | 31 | 37 |  - |  - |  - |  - |  - |  - |  - |  - |  - |  - | 103|  - |  - |  - |  
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ2 | 20 | 26 |  - | 38 |  - |  - |  - |  - |  - | 74 |  - |  - |  - | 98 | 104|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ 
+  Δ3 | 21 | 27 |  - | 39 |  - |  - |  - |  - |  - | 75 |  - |  - |  - | 99 | 105|  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ4 | 22 | 28 |  - | 40 |  - |  - |  - |  - |  - | 76 |  - |  - |  - | 100|  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ5 | 23 | 29 |  - | 41 |  - |  - |  - |  - |  - | 77 |  - |  - |  - | 101|  - |  - |  - |  - | 
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ6 | 24 |  - |  - | 42 |  - | 54 |  - |  - | 72 | 78 |  - | 90 | 96 |  - |  - |  - |  - | 114|
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  Δ7 | 25 |  - |  - | 43 |  - | 55 |  - |  - | 73 | 79 |  - | 91 | 97 |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ8 |  - |  - |  - | 44 |  - | 56 |  - |  - |  - | 80 |  - | 92 |  - |  - |  - |  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+  Δ9 |  - |  - |  - | 45 |  - | 57 |  - |  - |  - | 81 |  - | 93 |  - |  - |  - |  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ10 |  - |  - |  - | 46 | 52 | 58 |  - | 70 |  - | 82 | 88 | 94 |  - |  - |  - |  - | 112|  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ11 |  - |  - |  - | 47 | 53 | 59 |  - | 71 |  - | 83 | 89 | 95 |  - |  - |  - |  - | 113|  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ12 |  - |  - |  - | 48 |  - | 60 | 66 |  - |  - | 84 |  - |  - |  - |  - |  - | 108|  - |  - |
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+ Δ13 |  - |  - |  - | 49 |  - | 61 | 67 |  - |  - | 85 |  - |  - |  - |  - |  - | 109|  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ14 |  - |  - | 32 | 50 |  - | 62 | 68 |  - |  - | 86 |  - |  - |  - |  - |  - | 110|  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ15 |  - |  - | 33 | 51 |  - | 63 | 69 |  - |  - | 87 |  - |  - |  - |  - |  - | 111|  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ16 |  - |  - | 34 |  - |  - | 64 |  - |  - |  - |  - |  - |  - |  - | -  | 106|  - |  - |  - |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ17 |  - |  - | 35 |  - |  - | 65 |  - |  - |  - |  - |  - |  - |  - | -  | 107|  - |  - |  - |
+     +----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+ Δ18 |  - | 30 | 36 |  - |  - |  - |  - |  - |  - |  - |  - |  - | -  | 102|   -|  - |  - |  - |
+=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
+  1  |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | 10 | 11 | 12 | 13 | 14 | 15 |  16|  17| 18 | 19 |
+-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
+     |       Δ    Δ    Δ           |                     Φ12     |       Δ                   Δ |
+           -113 +150 = +37                                             +102 = +139    -113 -114
+

As conclution the behaviour of this 7 is happen between the sequence of 30 and 36 while the 12 is happen between the sequence of 36 and 102.

Euler partition

By The Δ(19 vs 18) Scenario those three are exactly landed in the 0's cell out of Δ18. See that the sum of 30 and 36 is 66 while the difference between 36 and 102 is also 66.

0 + 30 + 36 + 102 = 168 = π(1000)

19vs18

The function that appears in the denominator is Partition Function. The equality between the product on the first line and the formulas in the third and fourth lines is Euler's pentagonal number theorem where p(33) = 10143 landed exactly by n - 7.

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Using Euler’s method to find p(40): A ruler with plus and minus signs (grey box) is slid downwards, the relevant terms added or subtracted. The positions of the signs are given by differences of alternating natural (blue) and odd (orange) numbers. In the SVG file, hover over the image to move the ruler (Wikipedia).

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Euler_partition_function

Each result goes to the 9th object of prime 67 which is 19th prime. So when the cycle has passed the 10th object then the 43 objects will be laid by 9 collumns and slightly forming a recombination which facilitate them to finaly generate 1000 primes

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\ No newline at end of file diff --git a/index.html b/index.html new file mode 100644 index 00000000..881959c1 --- /dev/null +++ b/index.html @@ -0,0 +1,139 @@ + eQuantum · Mapping the quantum way across prime identity
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#

Prime Identity

By this part we are going to compile all topic we have discussed. Here we would like to explain the way we take on getting the arithmetic expresion of prime distribution to get an individual unit expression (identity) such as a taxicab number below.

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+ + Note +
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It is a taxicab number, and is variously known as Ramanujan’s number and the Ramanujan-Hardy number, after an anecdote of the British mathematician GH Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital (Wikipedia).

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+

Ramanujan-Hardy number

These three (3) number are twin primes. We called the pairs as True Prime Pairs. Our scenario is mapping the distribution out of these pairs by taking the symmetrical behaviour of 36 as the smallest power (greater than 1) which is not a prime power.

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The smallest square number expressible as the sum of four (4) consecutive primes in two ways (5 + 7 + 11 + 13 and 17 + 19) which are also two (2) couples of prime twins! (Prime Curios!).

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+ 
$True Prime Pairs:
+ (5,7), (11,13), (17,19)
+ 
+ layer|  i  |   f
+ -----+-----+---------
+      |  1  | 5
+   1  +-----+
+      |  2  | 7
+ -----+-----+---  } 36 » 6®
+      |  3  | 11
+   2  +-----+
+      |  4  | 13
+ -----+-----+---------
+      |  5  | 17
+   3  +-----+     } 36 » 6®
+      |  6  | 19
+ -----+-----+---------
+

Thus in short this is all about the method that we called as the 19 vs 18 Scenario of mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17).

Φ(1,2,3) = Φ(6,12,18) = Φ(13,37,61)

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

The main background is that, as you may also aware, the prime number theorem describes the asymptotic distribution of prime numbers which is still a major problem in mathematic.

Zeta Function

Instead of getting a proved formula we came to a unique expression called zeta function. This expression first appeared in a paper in 1737 entitled Variae observationes circa series infinitas.

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This expression states that the sum of the zeta function is equal to the product of the reciprocal of one minus the reciprocal of primes to the power s. But what has this got to do with the primes? The answer is in the following product taken over the primes p (discovered by Leonhard Euler):

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image

This issue is actually come from Riemann hypothesis, a conjecture about the distribution of complex zeros of the Riemann zeta function that is considered by many mathematicians to be the most important of unsolved problems in pure mathematics.

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In addition to the trivial roots, there also exist complex roots for real t. We find that the he first ten (10) non-trivial roots of the Riemann zeta function is occured when the values of t below 50. A plot of the values of ζ(1/2 + it) for t ranging from –50 to +50 is shown below. The roots occur each time the locus passes through the origin. (mathpages).

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image

Meanwhile obtaining the non complex numbers it is easier to look at a graph like the one below which shows Li(x) (blue), R(x) (black), π(x) (red) and x/ln x (green); and then proclaim "R(x) is the best estimate of π(x)." Indeed it is for that range, but as we mentioned above, Li(x)-π(x) changes sign infinitely often, and near where it does, Li(x) would be the best value.

image

And we can see in the same way that the function Li(x)-(1/2)Li(x1/2) is ‘on the average' a better approximation than Li(x) to π(x); but no importance can be attached to the latter terms in Riemann's formula even by repeated averaging. The problem is that the contributions from the non-trivial zeros at times swamps that of any but the main terms in these expansions.

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A. E. Ingham says it this way: Considerable importance was attached formerly to a function suggested by Riemann as an approximation to π(x)… This function represents π(x) with astonishing accuracy for all values of x for which π(x) has been calculated, but we now see that its superiority over Li(x) is illusory… and for special values of x (as large as we please) the one approximation will deviate as widely as the other from the true value (primes.utm.edu).

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Moreover in it was verified numerically, in a rigorous way using interval arithmetic, that The Riemann hypothesis is true up to 3 · 10^12. That is, all zeroes β+iγ of the Riemann zeta-function with 0<γ≤3⋅1012 have β=1/2.

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We have Λ ≤ 0.2. The next entry is conditional on taking H a little higher than 10*13, which of course, is not achieved by Theorem 1. This would enable one to prove Λ < 0.19. Given that our value of H falls between the entries in this table, it is possible that some extra decimals could be wrought out of the calculation. We have not pursued this (arXiv:2004.09765).

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image

This Euler formula represents the distribution of a group of numbers that are positioned at regular intervals on a straight line to each other. Riemann later extended the definition of zeta(s) to all complex numbers (except the simple pole at s=1 with residue one). Euler's product still holds if the real part of s is greater than one. Riemann derived the functional equation of zeta function.

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The Riemann zeta function has the trivial zeros at -2, -4, -6, … (the poles of gamma(s/2)). Using the Euler product (with the functional equation) it is easy to show that all the other zeros are in the critical strip of non-real complex numbers with 0 < Re(s) < 1, and that they are symmetric about the critical line Re(s)=1/2. The unproved Riemann hypothesis is that all of the nontrivial zeros are actually on the critical line (primes.utm.edu).

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image

If both of the above statements are true then mathematically this Riemann Hypothesis is proven to be incorrect because it only applies to certain cases or limitations. So first of all the basis of the Riemann Hypothesis has to be considered.

Riemann hypothesis,

Sehr leider Herr Riemann. Leute können den Fall immer noch nicht lösen...

On the other hand, the possibility of obtaining the function of the distribution of prime numbers shall go backwards since it needs significant studies to be traced. Or may be start again from the Euleur Function.

Euler's identity

Freeman Dyson discovered an intriguing connection between quantum physics and Montgomery's pair correlation conjecture about the zeros of the zeta function which dealts with the distribution of primes.

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The Mathematical Elementary Cell 30 (MEC30) standard unites the mathematical and physical results of 1972 by the mathematician Hugh Montgomery and the physicist Freeman Dyson and thus reproduces energy distribution in systems as a path plan more accurately than a measurement (Google Patent DE102011101032A9).

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Euler's identity

The path plan assume that a symmetric distribution of prime numbers with equal axial lengths from a middle zero axis = 15 is able to determine the distribution of primes in a given number space. This assumption finally bring us to the equation of Euler's identity.

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Euler’s identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler’s formula e^ix = cos x + i sin x when evaluated for x = π. (Wikipedia).

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image

The finiteness position of Euler's identity by the said MEC30 opens up the possibility of accurately representing the self-similarity based on the distribution of True Prime Pairs so that all number would belongs together with their own identitities.

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Euler’s identity is considered to be an exemplar of deep mathematical beauty as it shows a profound connection between the most fundamental numbers. Three (3) of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation (Wikipedia).

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image.

See that there are multiple repetition from addition to multiplication which may lead up to the concept of 11th-dimension. This path is being applied as you can find on the left sidebar. (Please change the view to desktop mode if you are on mobile browser).

Nothing is going to be easly about the nature of prime numbers but they demonstrably congruent to something organized. Let's discuss starting with the addition zones.

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