Dragon Mathimatia in the Matrix of Thuban

The Tridecagonal Twin Tetractys of Thuban
An Alphanumerical Dragon Matrix for a Starhuman World in JCCJ=13+13=26​

26x9 = 234 = 13x18
26x18 = 468 = 13x36
​

0.	1 2 3	...	13|14	...	24 25 26|27 28	...	35 36	Modulus 36n=26k+r
1.	A0B0C0	...	M0|N0	...	X0Y0Z0|A1B1	...	I1J1	36 = 26 + 10J1
2.	T2S2R2	...	H2|G2	...	W1V1U1|T1S1	...	L1K1	72 = 52 + 20T2
3.	U2V2W2	...	G3|H3	...	R3S3T3|U3V3	...	C4D4	108 = 104 + 4D4
4.	N5M5L5	...	B5|A5	...	Q4P4O4|N4M4	...	F4E4	144 = 130 + 14N5
5.	O5P5Q5	...	A6|B6	...	L6M6N6|O6P6	...	W6X6	180 = 156 + 24X6
6.	H8G8F8	...	V7|U7	...	K7J7I7|H7G7	...	Z6Y6	216 = 208 + 8H8
7.	I8J8K8	...	U8|V8	...	F9G9H9|I9J9	...	Q9R9	252 = 234 + 18R9
8.	B11A11Z10	...	P10|O10	...	E10D10C10|B10A10	...	T9S9	288 = 286 + 2B11
9.	C11D11E11	...	O11|P11	...	Z11A12B12|C12D12	...	K12L12	324 = 312 + 12L12
10.	V13U13T13	...	J13|I13	...	Y12X12W12|V12U12	...	N12M12	360 = 338 + 22V13
11.	W13X13Y13	...	I14|J14	...	T14U14V14|W14X14	...	E15F15	396 = 390 + 6F15
12.	P16O16N16	...	D16|C16	...	U15T15S15|R15Q15	...	H15G15	432 = 416 + 16P16
13.	Q16R16S16	...	C17|D17	...	N17O17P17|Q17R17	...	Y17Z17	468 = 468 + 0
14.	J1=19I1=19H1=19	...	...	...	...In Reflection...	...	C0=18B0=18A0=18	13 Rows reflected

​

WORLD BANK MONEY {A DEVIL LAW} WALL STREET MONEY = 432+36 = 234+234 = 468

13x36 = 36+12x36 = 36+6x72 = 36+3x144 = 36+432 = LAW + 432 = 468 = 234+234

144 + WORLD WORLD + 144 {LAW=36=63=PEN.IS=IN.OY=63=36=WAL} MONEY WORLD MONEY WORLD MONEY WORLD

Shiloh Za-rah, October 12th, 2014​

 

On the Origins and Al Qaeda of Theoretical Physics

A TWO BASE or AL QAEDA in the code KQ=28 for theoretical physics.

1. Title and Agenda
2. Introduction to Schismatic Science & Perfect Numbers
3. The Decoding of the Title and 'Baby-Talk'
4. The Question of the Count for the Reader
5. The Answer to the Count & Mathematical Complexity
6. Fundamental Constants from First Principles
7. The Pre-Big Bang Setting of Creation
8. The Algorithm of the Cosmogenesis in Strings



1. Title and Agenda

Welcome to all who may read this and all are invited to share or utilise this information given, irrespective of creeds political, scientific, religious, spiritual or otherwise.
This is a work in progress and under revision until notified by me, Tony B., the author.

This essay shall attempt to show the reader how there might exist a rather strange, yet powerful synthesis between the global edifice of contemporary theoretical physics and the tools or basis or foundation or 'Al Qaeda' for this same physics emerging through its scientific model-building and history.

So what is this strange title and the code KQ=28 and what is the connection of this encoding to theoretical physics?

The answer is found in 'Perfect Numbers' and the origins of all the sciences in the form of mathematics of various forms, albeit based on the foundation of the set of natural numbers or 'counting numbers' N.

So I shall show how the mathematics 'was born' or invented as the 'Mother of all Sciences' and how this 'Tool of Abstraction' relates to the contemporary world; also encompassing the subject matter not obviously related to the sciences based on the empiricism of measurement at the present time of the global history.
It was not always so and as the historians of science know rather well.

The so called renaissance of the 'Scientific Revolution' of the 17th century refined the worldviews of Aristotle, Plato and Pythagoras in the works of Isaac Newton and who we may call the Greek Alchemists, including Leibnitz, Kepler, Boscovich and many many others.
The Greek alchemists followed a tradition which encompassed both the science of measurement and a science of divinity, say the latter as a form of scientific inspiration.

And it is in this mileu, where the distinction between 'measurement physics' and 'divinity physics' is rather blurred; where this work before the reader assumes its true significance and where the 'decoding' will 'make sense' for the discerning reader.




2. Introduction to Schismatic Science & Perfect Numbers

The Greek alchemy of course became 'modern chemistry' and Plato's five elements mapped as his 'perfect solids' and later as say 'quantum gauge interactions' in the post-Newtonian science redefining itself.
The Aristotelean physics of precise measurement of the physical parameters was retained and the Platonist-Pythagorean physics of 'divine perfection' became largely abandoned in this scientific reformation.
Something of a remnant could not be erased in this new scientific paradigm however - the 'science of divinity' or the science of 'creative providence'.
This residue today pervades all sections and strata of society and is a powerful component of all political, religious and cultural institutions.

So even if this 'science of divinity' or 'omniscience' is a purely psychological construct and without any physical measurement significance whatsoever; it still plays an important, sometimes even dominant role in the affairs of states and national agendas of whatever political persuasion and affiliation.
So can one find a common factor UNITING all those psychological constructs in a form acceptable to the 'Mensuration Science' and perhaps in a form more akin the 'science of divinity' of Newton and the Greek alchemists?
One can do so, if one can discover a 'common denominator' for the divinity sciences, invariably coloured in the codes of language and interpretatations.

And here one can introduce certain 'emotion charged' labellings or words, such as ALLAH and GOD and AL QAEDA as factors of the omniscience.
Then in other words, using the psychology of the historical residue of divinity science, this also holds the key to unite the religions, say linked to political constructs and affairs of state. This could be followed perhaps, by a more global and political unity, born from a new understanding of its own linguistic codes.
And then it does not really matter if the 'gods and allahs' exist in a physical reality or only as psychological constructs, created or invented by sentient 'citizens'.
Because 'they' most assuredly exist as psychological creations; 'they' carry a significant 'emotional energy', which perhaps can be modelled in a form of 'consciousness' in physical parameters following an unification of the language codes underpinning 'their' reality as 'emotion-charged' and say mental energy constructions.

So then let us decode the title encoding and before we discover how the mathematics underpinning the modern sciences, became born from omniscience.
This will introduce a scenario, where no numbers exist at all; so the decoding following is necessarily post-facto and assuming the Set of Natural Numbers N, say given in a statement, such as:
N={1,2,3,4....n; n⇒n+1 PMI}; and where PMI is a label for a procedure termed Principle of Mathematical Induction.

'Perfect Numbers' or PN's are those numbers of the set N, which add all their factors to sum their eigenstate or self-identity.

Then the first PN is PN1=6=1+2+3=1.2.3=√(6²)=(1.2.3)¹.

The second PN is PN2=1+2+4+7+14=28=√(28²)=√(1.2.4.7.14)^½=√784.

PN3=496=1+2+4+8+16+31+62+124+248=(1.2.4.8.16.31.62124.248)^¼ and

PN4=8128=1+2+4+8+16+32+64+127+254+508+1016+2032+4064=
(1.2.4.8.16.32.64.127.254.508.1016.2032.4064)^1/6.

In more detail:

6=1+2+3=½[3][4]

28=1+2+3+4+5+6+7=½[7][8]=1³+3³=1+2+4+7+14

496=1+2+3+...+30+31=½[31][32]=1³+3³+5³+7³

=1+2+4+8+16+31+62+124+248

8128=1+2+3+...+127+128=½[127][128]=1³+3³+5³+7³+9³+11³+13³+15³

=1+2+4+8+16+32+64+127+254+508+1016+2032+4064

We shall reencounter the mathematical form of.. Σ=½[n][n+1] later, but note here, that there exists this 'special number' x=2 as the solution for the quadratic x+x=2x=x²=4 or x²-2x=0.

This is the only number of the set N, whose 'doubling' is identical to its 'squaring'.

It also defines the 'Derivative' of the 'Perfect Square' x² as d(x²)=2x.dx.

We may also define a set PN={PN1; PN2; PN3; PN4;...PNn}={6; 28; 496; 8128;...PNn} and as a subset of N.
We now write:

PN1+PN2=6+28=34=1+2+3+4+(4.6)=10+4.6 and
PN1.PN2=6.28=168=4.42=(4.7).6=(10+4.6).6.

Additional decompositions can then be constructed in 'Pure Number Theory. The emphasis here is on the factorisation of the factors 4,6 and 7; as those factors shall reappear in the cosmogenesis of the universe from an algorithmic number string.

10=1+2+3+4 is of course the Pythagorean Tetractys for the basis of dimensions and defines the Platonic Tetrahedron as the basic minimal structure for a 3D-Volume in a 4D-Spacetime.

1 point represents the 0th dimension or 'singularity', forming the 1st dimension in connecting to a second such point as a straight- or curved line, the latter being named geodesic and as the shortest connection between the two points.
2D is formed in connecting both points to a noncollinear 3rd point as a triangular plane, either flat or curved as say sperically convex or hyperbolically concave.
3D then is the introduction of a 4th point, noncoplanar to the 2D triangular plane constructing the Platonic Tetrahedron.
Omniscience aka the 'science of divinity' of the Greek alchemists now allows the arbitrary assignment of alphanumeric codes, which so enable us to proceed with the unification of the languages underpinning the politico-social and religio-cultural constructs of global societies.
We begin with ONE and TWO in assigning SOME alphanumeric mapping, say the Arabic Alphabet in a ONE-to-ONE correspondence with the set N, say in the set of pairings, given by:

§={(1,A);(2,B);(3,C);...;(24,X);(25,Y);(26,Z)}.

We also introduce a property of the set N in rootreducing a decimal 10-count in the repeatability of the 9 elements in a definition:

9=0+9=1+8=18*=2.9*=2+7=27*=3.9**=3+6=36***=49***=...(10-1)=99**********=11.9**********=....etc . etc.
We have ONE=15+14+5=34→3+4=7 and TWO=20+23+15=58→5+8=13=4*.

Now we apply a 'Perfect Symmetry' to some of our linguistic labellings, irrespective from the native language they derived, albeit translated.

ALLAH=ALHLA=34=ONE and ALHLA as an anagram of ALLAH is rendered perfectly symmetric in reading the same from right to left, as it does from left to right.
Also we have GOD=26=ALHLA-8 and where 26 represents the total number count of the applied alphanumeric code, so unifying two linguistics in a perfect symmetry in a first application. The code would extend in multiples akin the rootreduction applied before in A*=27; B*=28;...;A**=53 and so on.

GODDOG=DOGGOD=2.GOD=GOD²=52→5+2→7***=3+4→ONE=ALLAH.
GOD+H=ALLAH=GOD+8=GOD+∞, both symbolically and symmetrically.
TWO=GODDOG+6=52+6 and where now ABBA=6 defines the 1st BASE as the first Perfect Number in the selfsame 'Perfect Symmetry'.
So alphanumerically, ALLAH encompasses GOD as ONE in a 'Perfect Symmetry' and this symmetry 'Doubles GOD' in the ONE as TWO in the addition of the first basic PN1=6=1+2+3=1.2.3.




3. The Decoding of the Title and 'Baby-Talk'

A TWO BASE or AL QAEDA in the code KQ=28.
ABASE=1+27=28=PN2=QAEDA=17+1+5+4+1=17+11=28=GOD+2=PN1+4+5+6+7

and where PN1 =6=1+2+3 becomes the basis for PN2.
TWO=58→5+8=13=AL=1+12=4*=2*+2*=(2*)².
K=11 and Q=17 for K+Q=28 and K.Q=187=1+8+7→16→1+6=7→7***=ALLAH.
A TWO BASE=86→14→5→AL QAEDA=41=5****

{Aside: ATWOBASE=MELCHISEDEC as the 'New Testament' version for the 'Old Testament' or Torah or Dead Sea Scroll form for MELCHIZEDEK=101.

Define another and not language based mapping between the set N and the Set p of PRIME NUMBERS:

P={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101} for the 26 elements of our applied alphanumeric code of the Arabic Alphabet.

Also define a Set B, to map the Set N in binary notation for the 26 elements in §.
B={1,10,11,100,101,110,111,...,11010}.

The 5-sequence is: 5→14→23→32→41→50→59→68→77→86→95→104→... and so 86=5*********=41**** etc.

This allows us to relate 86dec=41dec****= 5dec*********→5dec→5bin=101

in the pairings: §5={5dec,E}={101bin,E}={11prime,E}→§26={26dec,Z}={101prime,Z}.

So the 26th prime number in N is 101 completes all primes whose digits are less than 3 in(ex)cluding the identity element 1}.

So we have the first two 'Perfect Numbers' defining two most potent cultural labellings in ALLAH=28 and GOD=26=ALLAH-2 with ABBA=6.
ABBA=BABA=BAAB=6 and in many languages relates to 'Baby Talk' and the first 'perfectly symmetric' utterings of tonal expressions such as PAPA=PAAP and POP and MOM and MUM and MAMA=MAAM and NAN and NUN and so on for both fatherly and motherly name callings and identifications.
ABBA is encoded in scripture, say in Galatians.4.6; Romans.8.15 and Mark.14.36 and one finds similar like PUP for young animals and even in the name of a Swedish popgroup.




4. The Question of the Count for the Reader

If a set PN={Perfect Numbers} can be used to harmonise languages with a mathematics of 'Pure Number Theory' and in the utility of abstract symbolic mappings and the set PN is itself a subset of the set of natural numb ers N; then where did this set N come from?

Allow me then to relate a simple story and ask YOU, the reader to answer a question in this context.
If YOU then are able to answer the question, then YOU will know where the set N came from from first principles, being created by your own makings.

Imagine yourself to live a long time ago, say about 30,000 years on the planet earth in an era known as the Late Pleistocene epoch (about 130,000 to 10,000 years ago) and presume, that no such thing as science or mathematics in its abstract nomenclatures has entered your perception.
But YOU live in a world of survival and say have become aware of your environment to various degrees. YOU know the elements of air, water, fire and earth and their immediate effects on you in terms of qualities, such as coldness, hotness, wetness and dryness say.
YOU know about survival and food and instinctually blend into your environs.
YOU also have accumulated and collected things, including a number of 'tamed' animals, say wild fowl or prehistoric cattle or sheep.
Say YOU have a 'flock' of Pleistocene Bighorns, which YOU have confined in some enclosure of some sort.
Then for your Bighorns to graze and to be be fertile and to multiply, YOU must release them periodically, say in the early mornings and regather them in the late afternoons.

Now YOU have found out a 'secret' about the behaviour of your Bighorns.
YOU can 'control' them to a great extent, in concentrating your efforts of collecting your flock on their leader. YOU have found out by observation, that the flock appears to follow their leader, say what would today be labelled as an alpha-(fe)male and your strategy engages the fellowship of the flock with that leader.
So after releasing the flock in the mornings, YOU seek for that leader in the afternoon and in bringing him or her back into the enclosure, the others will follow.

This you have done for a while, when YOU notice something odd. One day YOU gain the perception, that your flock of Bighorns has diminished. YOU get the distinct impression, that there were more Bighorns in the morning, than there seem to be in the afternoon; and this despite the leader appearing 'constant' as normal.
Puzzled by this, YOU work out a way of establishing for certain if your flock has shrunk or not.
Remember that YOU do not know how to count - numbers of any sort do not exist.
So the question is how YOU can ascertain the size of your flock of Bighorns in using the environment YOU do know.
I am sure, that most readers will have little difficulties in answering this question and in doing so those readers will have found out, how the set N of the natural numbers came into existence in say the Pleistocene environments.




5. The Answer to the Count & Mathematical Complexity

The invention of the set N of the Natural Numbers N={1;2;3;...;n;n+1;...} became a set of correspondences, say between a 'bag of pebbles' and the 'sheep' to be counted.
The shepherd(dess) transfers one pepple for every sheep from a full bag into a originally empty bag say. So if all the pebbles or sticks or stones or tokens are transferred, then all the sheep are accounted for.
In such or similar manner proceeded the manifestation of the set N as the basis for theoretical physics in particular and the overall measurement dependent sciences in general.
A next order of complexity would be the distiction between the tokens, say the introduction of coloured or otherwise differentiated pebbles for the purpose to identify individual 'sheep' or groupings of them as subsets of N.
Mathematical complexity then eventuates in the extension of the set N into the Integers or set Z, which include both positive and negative members of N and also introduce the 'Identity for Addition' element 0 in say n+(-n)=0.

This introduces our previously encountered formulation Σ=½[n][n+1] from first principles.

T(n)=n(n+1)=2Σ defines a 'doubled count' for the Arithmetic Progression or A.P. of 'absolute' values for the set N AS the set Z. An 'absolute number' can be defined in the form -(-a)=a via the 'additive identity' element 0=a+(-a).

T(n) so becomes the Sum to n terms of this doubled set from Z={-n;...-3;-2;-1;0;+1;+2;+3;...;n}.

For example; adding all integers, both positive and negative, from 1 to 5 as 1+2+3+4+5=15 gives T(n)=T(5)=5.6=30 as 2Σ for the A.P. Count Σ=½T(n).
This is also the foundation for the 'Perfect Numbers' in:

PN1=1+2+3=2¹(2²-1)=2.3=6 and

PN2=1+2+3+4+5+6+7=2²(2³-1)=4.7=28=1+2+4+7+14 and

PN3=½(31)(32)=2⁴(2⁵-1)=16.31=496=1+2+4+8+16+31+62+124+248 and

PN4=½(127)(128)=2⁶(2⁷-1)=64.127=8,128.

These are the classical PN's known to the Greeks, the more complex and meaning longer' PN's begin with:

PN5=33,550,336=2¹²(2¹³-1)=4096.8191=½(8191)(8192)=Σ{1³+3³+5³+...+127³} and

PN6=8,589,869,056=2¹⁶(2¹⁷-1)=(65536)(131071)=Σ{1³+3³+5³+...+511³} and so on continue for prime number exponents 'n' in the expression 2^n-1(2ⁿ-1).

So one can see, that exponent n=2,3,5,7,13,17,19,31,61,89 defines a subset of

P={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101} in say
P*={2,3,5,7,13,17,19,31,61,89 } for 10 members, which are 'missing' in the coset
P'={11,23,29,37,41,43,47,53,59,67,71,73,79,83,97,101}.

One can question as to why the exponent n=11 does NOT define a Perfect Number.

2¹¹-1=(2048-1)=2047=23.89 and so the first of the 'Mersenne' factors (2ⁿ-1),
which is NOT prime (2²-1=3; 2³-1=7; 2⁵-1=32-1=31).

So the fifth iteration, defining the first 'modern' PN also discriminates the prime numbers in the first element of the complementary set P* as subset of P.
The number 11 is also the first element of the Maria Numbers; whose prime elements are: PM={11;131;197;263;383;449;...}.

The Maria-Code is a matrix from the Genesis Code using the decimal monad and is defined in:
n²+n-66k=0; M(k)+99=M(k+12); S(n)=½n(n+1)=>33k.

The first Maria Numbers are: 11,21,32,33,44,54,65,66,77,87,... Every Maria Number describes One of the integers, which being the last term of the SUM of all the integers preceeding it, is divisible by the number 33, i.e mod33.}

For example 1+2+3+4+5+6+7+8+9+10+11=½11.12=66 and this is 2.33 as the first Maria Number being divisible by 33.

Why mod 33?
Add up the following rootreductions of Maria Numbers.
A defining matrix is:

11	65	110	164	209	263	.......This is the rootreduced 2
21	66	120	165	219	264	.......This is the rootreduced 3
33	77	131	176	230	275	.......This is the rootreduced 5
33	87	132	186	231	285	.......This is the rootreduced 6
44	98	143	197	242	297	.......This is the rootreduced 8
54	99	153	198	252	297	.......This is the rootreduced 9
65	110	.....	.....	.....	.....	.......Repeat as 2
66	120	.....	.....	.....	.....	.......Repeat as 3

But 2+3+5+6+8+9=33 AS the space dimensions in Quantum Relativity.

The time-dimensions of the fourfolded nesting are of course then the missing numbers 1+4+7=12.

Furthermore, the prime number 23=2³ +2³ +1³+1³+1³+1³+1³+1³+1³ represents the rootreduction in showing the maximum decomposition of a prime number into cubes to be the number 9 and for the general case for any positive integer of N.

22=2.8+6; 21=2.8+5; 20=2.8+4; 19=2.8+3; 18=2.8+2; 17=2.8+1; 16=2.8; 15=1.8+7; 14=1.8+6;.....always less than 9.
24=3.8; 25=3.8+1; 26=3.8+2; 27=3.3.3; 28=1.27+1;....; etc.

We also find a HARMONIC Property for the Perfect Numbers in their inverses and giving our 'special number' 2 from x² =2x.

2=1/1+1/2+1/3+1/6=1/1+1/2+1/4+1/7+1/14+1/28
=1/1+1/2+1/4+1/8+1/16+1/31+1/62+1/124+1/248+1/496 and so on.

Mathematical Complexity indeed!

But our elementary summation T(n)=n(n+1) can also be used as a basis for counting 'particle histories', as in Feynman's path-Integral in quantum mechanics and as a proportionality factor in the first oder differential equation for our universal wavefunction: dB(n,T)/dT(n)+alpha.B(n,T)=0.

This defines a Gaussian 'Normal' Statistical' distribution of spacetimes and transforms to the integral equation:
∫dB/B=-Alpha.dT for solution ln(B/B_o)=-Alpha.T(n) or B(n,T)=B_o.℮^-Alpha.T(n).

This is of course a standard template for a multitude of solutions for eigenvalues of differential equations, because the derivative of the exponential function ℮^x is its own identity as d(℮^x)/dx=℮^x for the natural logarithmic function f(x)=ln(x) = log_e(x) for the defining property ℮^f(x)=x, say as ln(x)=N=3 for e^N=e³=x=20.08553....

The fundamental cosmogenesis of Quantum Relativity applies this property in association with the T(n) summation as dimensionless cycletime n and in utility of the mathematical definition of the exponential function f(x)=℮^x from first principles.
We have of course omitted the emergence of more complex number systems, algebras and geometries from the set of integers Z from this T(n) definition.
The set Z leads to the set of the rational numbers Q, which are expressible in the form a/b, with both a and b elements of Z and applying the principle of inversion with 'inversion identity 1' given in say the statement a.(1/a)=1 and where the '.' implies multiplication in the basic definition as a 'shortcut' for addition (3.x=x+x+x, say).

Algebras are then constructed in additional properties, such as distributive and associative laws formally defined in statements, such as a(b+c)=ab+ac (distributive) and a+(b+c)=(a+b)+c and a(bc)=(ab)c (associative).
The set Q then extends to the Real Numbers R in algebraic solutions (as roots) to polynomial equations
P(x)=(x-a)(x-b)(x-c)...(x-k)..=A+Bx²+Cx² +...

If no such roots can be found, then the real numbers so given are termed transcendental or nonalgebraic and include ℮ and p.

We can define ℮ as a limit of an infinite series: ℮ = lim(1+1/n)ⁿ for n→∞.

This results in a series of approximations for ℮ as say:
℮={(n,℮_n) = [1,2]; [2,9/4=2.25]; [3,64/27=2.37037..]; ...; [100,2.7048..];...}.

Quantum Relativity now uses this definition to model the expansion of the universe from first principles in defining the expansion parameter 'a' in General Relativity in the definition:

1/'a'=R_max/R(n)=(1+1/n) for R(n)=R_max(n/(n+1))=R_max(1-1/(n+1)).

This so gives an asymptotic expansion for the universe in integral cycles of the set N.
At the Big Bang, n≠0, but very close to it in a definition of an 'absolute minimum' no=λ_min/R_max=H_o.t_min, say and where dn/dt=H_o=c/R[/sub]max[/sub] and as a 'nodal' frequency constant for the expansion parameter.

Subsequently, R(n_o)=R_max(1-1/(n_o+1))=R_max(λ_min/(R_max+λ_min))=λ_min to the order of 10^-49 if n_o=6.25..x10^-49 say

So the 'TIME' of the Big Bang in the 'End of the Inflation' is:

t_o=n_o/H_o=R_max.λ_min/c.R_max=λ_min/c=1/f_max. in the identity c=f_maxλ_min=H_o.R_max.

The universe so becomes nodally defined in the fractals of the expansion parameter:
{(1-1); (1-1/2); (1-1/3); (1-1/4); ...; (1-1/[n+1]}={0; 1/2; 2/3; 3/4; ...; n/[n+1]}.
This is an asymptotic expansion ever approaching, but never reaching the unitary state and mimicking the mathematical abstract definition of the natural exponent ℮.

This expansion will be 'perfectly flat' and of Zero Curvature as required in the Friedmann-Einstein-Walker cosmology described in General Relativity; the latter utilising spacetime metrics lower bounded in the λmin parameter of Quantum Relativity. We shall detail this scenario later in this discourse.
Extending the set R to the set C of the Complex Numbers, which then can be further manipulated to give Quaterniaons and Octonions; provides a kind of limit however.

The set R is often depicted as a Numberline in a 1D setting of the Count. The set C uses a 2D representation, where the 'Real Part' of a Complex Number is given as the first member of a couple and the 'Imaginary Part' as a second member; say z=(a,b)=a+ib and so allows a 'Vector' definition of say the Cartesian Coordinates (x,y) as Polar Coordinates (r,θ). Here |r| is the modulus of z and defined as |r|=√(x²+y²) via the transformation (x,y)=(rcosθ,rsinθ). The Identity i is defined as i=√(-1) for i²=1.

Addition properties for complex numbers so become vector additions in the plane and so relate to theoretical physics in a fundamental manner.
Multiplication of complex numbers become rotations in that plane in the addition of the angles θ, also termed arguments or arg(z).
As complex numbers can also be written in the modulus-argument form of:

z=|r|cis(iθ)=r(cosθ+isinθ)=|r|.℮^iθ (Euler Formula).

So multiplying complex numbers in the Euler formula shows that the geometric interpration of that multiplication is a rotation in the plane in an addition of the arguments or angles θ.

z₁.z₂=(a₁+ib₁).(a₂+ib₂)=[a₁.a₂-b₁.b₂]+i[a₁.b₂+a₂.b₁]=r₁.℮^iθ₁ r₂.℮^iθ₂ =(r₁r₂).℮^{i[θ₁+θ₂]}.

Example:

Let z₁=3+4i=(3,4) and z₂=12-5i=(12,-5) for arg(z₁)=arctan(4/3)=53.13010235.......°
with r₁=√(3²+4²)=5 and θ₂=arg(z₂)=arctan(-5/12)=-22.61986495...° for modulus r₂=√(25+144)=13.

Then z₁z₂=(r₁r₂).℮^{i[θ₁+θ₂]}=(5.13).℮^{i[θ₁+θ₂]}=(5.13).℮^{i[53.13010235..-22.61986495..°]} for z₁z₂=65.cis[30.5102374..°]=z₃=(3+4i).(12-5i)=[36+20]+i[-15+48]=56+33i=(56,33).

But modulus z₃=√(56²+33²)=√(4225)=65 and arg(z₃)=arctan(33/56)=30.51023741....° and as required.


Theoretical physics utilises the described mathematical properties of the complex numbers in association with the properties of the natural exponent extensively. The function f(x)=℮^x has its derivative as its own identity and so many differential equations will have solutions in exponential forms and particularly as superpositions of exponential and trigonometric series, given in most basic form by the Euler Formula z=|r|.℮^iθ.

Bohr's 'Theory of the Atom' of 1913 lead to the quantum state of the hydrogen atom, given by:

E_n=-m_e.e⁴/(8h².e_o²n²) for reduced electronmass m_e, charge e, permittivity e_o and Planck's constant h. When the atom goes to a state of lower energy, electromagnetic radiation is emitted via E=hf, with f the frequancy of the emitted photon.

Now Bohr only used classical physics, such as conservation of angular momentum and in conjunction with the quantisation of the orbital pathlength to derive this formula.

The solution of Schrödinger's wave equation gives the same formula, using the modern nonclassical approach of quantum mechanics and Quantum-Field-Theory; which replaces classical mass, velocity and momentum by quantum 'Hamiltonian' operators.

"The Schrödinger equation plays the role of Newton's laws and conservation of energy and momentum in classical mechanics and so predicts the future behavior of a dynamic system. It is a wave equation in terms of the wavefunction which predicts analytically and precisely the probability of events or outcome. The detailed outcome is not strictly determined, but given a large number of events, the Schrodinger equation will predict the distribution of results.



http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schr.html#c1

The kinetic and potential energies are transformed into the Hamiltonian which acts upon the wavefunction to generate the evolution of the wavefunction in time and space. The Schrödinger equation gives the quantized energies of the system and gives the form of the wavefunction so that other properties may be calculated."

This paper so shows are more elementary approach to theoretical physics, attempting to indicate the 'initial- and boundary' conditions for the cosmogenesis and as emergent from a 'pure number mathematics'.
The mathematical complexities of the modern theoretical physicist have evolved to such an extent, that increasing specialisation is required to broaded the frontiers in the interrelated but intrinsicating fields.
But where did it all come from? And what is the true nature of an electric charge and mass and inertia and what is space and time beyond the metrics?



6. Fundamental Constants from First Principles

The Mother of all Boundary Conditions must be the statement of:
"No Boundary conditions apply!"

So we consider a NullTime and a NullSpace in an undefined, say Platonic-Penrosian 'Space' of mathematical abstraction. This is like a 'thought' or an 'idea'; how can IT become real or even manifest as a physical and quantifiable universe?

In hindsight one knows how to answer this. An idea is born from observations; mental energy is linked to passion and the emotions, breeding the inventiveness to engage in a course of experimentation and to bring the idea (say a lightbulb, following the observation of a lightning strike) into physical manifestation.
But how can one apply foresight, when no observational reference frame exists in the NullState of the NAKED SINGULARITY or the GENESIS BOSON?
This then is the 'Boundary Condition' for the NullState, nothing exists and everything requires to become invented. The Everything is the Nothing as the All and so one can model this state onthe 'idea' of an infinite selfrepeating computer loop, representing the 'Father of all Algorithms'.

This can only be one thing, namely a mathematical representation of the Nothing, say in the numeral 0 representing circular closure, which linearises in the cipher 1. Angular multivalued Complex Infinity is linearised in negative and positive polarity of a Doubled-Infinity.
The hindsight then defines the closed circular NullState continuumas a closed looped superstring class I of the Planck-Scale, also containing the openended members of that same family.
But that wasn't the beginning program of the primary algorithm, butthis is a secondary algorithm, which can be stated as:
"ADD THE END TO THE BEGINNING AND START WITH THE OLD END"!

This specifies the methodology of RECIRCULARISING the linearised dimensions of the binary dyad (0,1) into the root-reductive decimal monad (1,2,3,4,5,6,7,8,9,0) (or some other number system).

Here then we define: 10=1+0=1*; 11=1+1=2*; 12=1+2=3* and so on until 26=2+6=8** and 27=2+7=9** give a kind of closure in the doubled or squared application of the algorithm, reflecting the 'Doubling of Infinity' by the identity x²=2x.

The hindsight then one day discovers, that there exists a mathematical entity, called the 26-dimensional Bosonic Superstring, which folds up the Ricci-Metric in Calabi-Yau manifolds in 6- and in Joyce manifolds in 7 circularised dimensions. A An heterosis of 26-dimensional counterclockwise rotating vibration patterns becomes 'married' to such states of frequency, rotating in 10 dimensions in a clockwise manner.

A DEFINITION of TIME then became effected, once the first algorithmic definitions had reset themselves in the pattern:

CIRCULARISED - LINEARISED - RECIRCULARISED - ENERGY=FALSE VACUUM- QUANTUM TUNNELLING OF TEMPERATURE WELL = QUANTUM BIG BANG.

Curling up the 16-dimensional anticlockwise patterns in special toroidal geometries, then would allow a definition of Heterotic classes of superbranes (HE(8x8) and HO(32)), one of whom would become the sought after MINIMUM condition for the Naked Singularity to manifest itself in its escape from the infinity-loop.

The primary algorithm results from the application of 10 elementary principles/antiprinciples which defined the algorithm as itself. And because this algorithm engages a fivefolded symmetry, there wouldbe five classes of 10-dimensional superstrings, upon whom the secondalgorithm could then act.

The ten principalities are:

1. Identity/Antiidentity
2. Expansion/Contraction
3. Order/Disorder or Entropy or Chaos
4. Symmetry/Asymmetry or Distortion or Nonparity
5. Divergence or Infinity/Convergence or Limit
6. Inversion or Reciprocity/Constancy or Invariance
7. Reflection/Absorption
8. Relativity/No Antiprinciple
9. Quantization/No Antiprinciple
10. New Identity/No New AntiIdentity, because of the application of the other 9 principalities to effect the transformation of One Self into Two Selves, yet as the One Unity of One extended Self.

The purpose for the establishment of the first algorithmic program is its cosmogenetic self-reproduction.
Adding Self/Infinity to Self/Infinity still gives Self/Infinity,but somehow, the second Self is different (more), than the first Self. The first algorithm becomes the mapping of two integral numberseries onto each other, complementing each other in a filling inthe gaps, created by one of the sequences as a one-to-one correspondence (like even and odd numbers for example, together forming the set of integers).

Now, this one-to-one correspondence resulted in the following data set:

۞={(266561); (151618); (141524); (151032);11; (091016); (061015); 7; 6; 4}={E°; 1/k; A²; 1/h; 11; c²; 1/L_o; 7; 6; 4}
and with a natural limit of 12, set and generated by the principalities as boundary condition for the selfiterative programming.

The secondary algorithm then utilised the initiatory number constant E=(266561) and generated the continuation, which would allow the Temperature Gradient or Energy-Wall to manifest in the linearisation of the physical parameters defined by the permutations of the code from the first algorithm.

The secondary code became (with initialising counter E):
BEGIN; ABCDEFG(H=ABCD) with E=(266561); F=(136656); G=(673665);
STOP GENERATION because 5+6=11=2* is rootreductive;
CONTINUE D=(465612);C=(256124); B=(361242); A=(312423);
STOP GENERATION because no monadic archetype can yield Z(Z+A)BCXY=312423 from its precursor ABCXYZ=(1-Z)24233, ending in root reduction (1-Z)=1-3=-2=-11=-2*;
END of 2nd algorithm.

The first algorithm applied the Ordering Principality to DEFINE TIMESPACE and the ordering of the constants as given.

Constant#1=E became the Number of Spacequanta defining the compactified 16 dimensions of the superbrane scenario upon initialisationof the second algorithm.
All principalities are engaged and the ORDER of the Constant application uniquely sets the physical parameters manifest in the orderspecified; (i.e. Temperature before Radiation before Restmass, etc.).

Constant#2 defined ENERGY=(Constant#2).TEMPERATURE.

Constant#3 defined ENERGY in terms of ELECTROMAGNETIC CHARGES and in a Universal wavefunction, normalised about the pentagonal symmetry of the first algorithm.
Hindsight would discover that a local application of this wavefunction would result in summation of integer states or probabilities, which upon normalisation and the 'squaring' of the statewould reproduce the Unity of the original wavefunction in the pentagonal symmetry. These would be known as the wave equations of quantum mechanics.

In particular one summation: T(n)=n(n+1) would, upon unitising; define the universal wavefunction explicitely in a Feynman-Path-Summation and allow the following identity to engage the timespace evolution of certain parameters, including the linking of Constant#3 to Constant#6.

The all encompassing Identity is: XY=X+Y=-1=i²=℮^ip for the generating waveequation:
B(n)=[2e/hA].℮^{(-Alpha.T(n)).}

Here A²=Constant#3 and the roots X and -Y form the Bounds for the NullTime definition in both real-positive and imaginary-negative linearised time parameters about the normalised Mean of B(n) for n=0 becoming reflective in n=-½.

C-Space is n-real from n=0 and F-Space is n-imaginary from n=-1 towards the negative integral count. In between in the interval [-1,0], is the M-Space further symmetrised about the Functional-Riemann-Bound: FRB=-½ and as the Point of Origin.

Three orthogonal axes so define 3D-Space, about which a 6D-Twistor-Space indicates two further degrees of freedom, each of the arbitrary up-down, left-right and in-out linear axes setting the NullTime Space as defined by B(n) allowing a clockwise or anticlockwise chirality in the compactification of the circularised Linespace. This extended definition for 3D-Line-Space into 6D-Hyper-Space subsequently transforms into 9D-Quantum-Space in introducing the degree of stretching/contacting by the application of Principality #2, following the Identity/Antiidentity initiation.

All principalities are engaged in their defined Order, indicating that 9D-Quantum-Space manifests the identity of an expanding and ordered and selfcontained continuum within the symmetry principality. 9D-Quantum-Space then diverges/converges in the setting of certain boundary conditions, which must incorporate the principles of inversion and of reflection with their antiprinciples. Henceforth, 9D-Quantum-Space sets a limiting condition, which hindsight would define in all manners of temporal parameters.

The relativity principle then allows the perception of being located at either of two observation points, namely the principalled or antiprincipalled vantage point, given in the kaleidoscope of all the combined principalities. Thus, a 10D-Omni-Space is created, which reflects/absorbs itself under engagement of inversion/invariance, becomes relative and subject to the 9th principality of the quantisation.

This defines Omni-Space to quantize itself in 3D-Line-Space, following the definition of the root-reductive decimal monad, so birthing the New Identity as Antiidentity to itself in the completion of the selfiterative and selfrelative programming of the first algorithm. Omni-Space hence requires to be 12-dimensional in the construction of the mastercode, becoming physically implemented in the Universal Cosmic Wavefunction B(n).

The interval [-X,X-1] specifies the maximum for B(n) as a probability interval with B(-½)=[2e/hA].℮[sup(¼Alpha)[/sup] and a standard deviation about the first moment by the multiplier √(Alpha/2p.

Hindsight would discover this as the Schwinger numbers to extend the QED-Feynman diagrams to account for multiple particle interactions as permutational possibilities in perturbation dynamics.

Constant#4 defines ENERGY=(Constant#4)FREQUENCY.

Constant#5=11 defines the Identity-Relation between Constant#4 and Constant#6 in Equality by DimensionCounter 11.

Constant#6 defines ENERGY=RESTMASS(Constant#6) as the Parity-Mirror.

Hindsight would define:

(1) hf = m_oc²
(2) Energy=hf iff m_o=0
(3) Energy=m_oc² iff f_o=f_limit=f_min=f_ss.

Hence all restmass carrying entities must possess a minimum eigen-frequency to exist and this existence relies upon the definition of TIME as the Inverse of some frequency: TIMEINSTANTENUITY=t_ps=1/f_ps; and where f_ps is the MAXIMUM FREQUENCY modular dual to the MINIMUM FREQUENCY defined in f_ss.

One then applies the Schwarzschild-Solution to the HE(8x8) Supermembrane. Hindsight would discover a best fit for the observed and experimentally measured physical parameters, as given by that superstring.

The Coupling Constants between the vibratory (MAXIMUM) part of that supermembrane (E_ps for Energy of primary source) and the winded or (MINIMUM) part (E_ss for Energy of secondary sink) are:
E_psE_ss=h² with E_ps/E_ss=f_ps²
and l_ps with l_ss=f_ps.f_ss=1.

A direct consequence is the Hawking Black Hole for a minimum temperature condition from the inverse proportionality between Mass and Temperature for the Black Hole spectra.

Wavelength l_ps=Wormhole-Perimeter=2pr_ps and r_ps=1/r_ss in modular duality of 2pl_ss=2G_oM_Hawking/c² in the Schwarzschild metric solution.

This is the manifestation of the mathematical modular duality for the B(n) definition in: X=1/-Y=1/(1+X).

Constant#7 defines a transformation from the Radiative Energy Stateinto the Restmassive one given above and the integers 7, 6 and 4 are dimension counters (#'s 8, 9&10), limited by the counter 12 as the holographic image for the summed lower dimensionalities, i.e in 4+6=10 & 4+7=11.

We have seen, that the concept of dimensional time was unnecessary to manifest the threefolded multispace of Line-Hyper-Quantum-Space in 9 dimensions.
This is mirrored in the decimal monad, allowing redefinition of the first principality in the tenth as an Identity/Antiidentity transformation into a Double-Identity.

The principalities became defined in the first subroutine of thegenerating master algorithm, which could be stated in generalisedform in the following manner to DEFINE THE (ABSTRACT) CONFIGURATIONSPACE in the form of AWARENESS-TRIPLETS represented by:

{OLDSTATE, EXPERIENCE, NEWSTATE} and selfiterative in the following algorithmic statement:

GENERATE NEWSTATE IN ADDING THE SECOND NEWEST OLDSTATE AS EXPERIENCETO THE NEWEST NEWSTATE AS THE NEWEST OLDSTATE.
...BEGIN (0,0,0)-DEFINE SELFSTATE=(1,0,1)-REDEFINE BINARY EIGENSTATE=(01,01,01)=(0+1,1,1+0)=(1,1,10)=(1,1,2)-(2,1,3)-(3,2,5)-...CONTINUE

INITIALISE: N=0; LIMIT=[REDEFINITION OF EIGENSTATE]={GOOGOLPLEX E}
-FOR (N=N+1 TO LIMIT) GOTO
-SUBROUTINE (DEFINE PARAMETERS FOR EIGENSTATE FOR M=M+1) GOTO
-SUBROUTINE (ALGO[M]) GOTO
-SUBROUTINE (...) GOTO
-SUBROUTINE (...) GOTO
-SUBROUTINE (SEARCH FOR LIMIT=[!])-STOP GOTO
-SUBROUTINE (!- GOTO BEGIN -REDEFINE SELFSTATE IN [!]) GOTO
-CONTINUE FOR O=M FOR LIMIT=[EIGENCODE IN !]={GOOGOLPLEX E} GOTO
-REPEAT FOR SUBROUTINE (O- [O]=[!], [!]=[!+1], [?]=[!]) GOTO
-REPEAT FOR LIMIT GOTO BEGIN...





7. The Pre-Big Bang Setting of Creation

We return to foresight and find ourselves equipped with a newpossible definition for TIME as: MINIMUM/MAXIMUM=CYCLETIME (n).

Algorithm #2 has defined the limiting boundary for a potentialexpansion of 10D into 11D in spacequanta counter E=Constant#1.
Quantum Geometry, applied to the concept of representing a 4D-Volume as a 3D-Surface defines the Riemannian Hypersphere with a toroidal volume 2p²R³, R taking the linearised form of the MINIMUM condition as ack]l_ps to define a spacequantum in the potential manifestation of monopolic space, hindsight would term 'The Vacuum'.
This Vortex-PE or VPE is still contained in the NAKED SINGULARITY of the GENESIS BOSON, whose eigendefinition in terms of physical parameters can now proceed.

Those quantities are necessarily BELOW the MINIMUM condition, manifesting as the last and most physically applicable form of the superbrane families in the E_psE_ss=HE(8x8) heterosis.

And so a subcontinuum, a dimensional divide becomes established to allow the 10D-universe, manifesting as a 3D-Surface, to expand into the 11D-universe as a 4D-Volume, the latter given as ½p²R⁴ in the 4-Sphere.

The 10D-Universe must be hyperbolic, hindsight measurements would detect and hindsight would also conclude, that the overall universe would be Euclidean flat and of zero curvature. Eventually, hindsight would understand, that the closed geometry of 11D-M-space mirrors the open geometry of 10D-C-space onto itself as a mapping into the holographic image of the 12D-F-space.

So just like one can observe both open and closed curvatures in the multiconnectedness of a 2D doughnut/torus; the inner hole curving hyperbolically encompassed in a spherical envelope, so is the universe multiple-connected within its own unity.

But the superbrane scenario maps the MINIMUM onto itself and becomes the MAXIMUM, the dimensional expansion of C-Space into the M-space in the duality perception of being located at the Point of origin as the Big Bang Singularity or as the Event Horizon Singularity at the wavefront of the selfsame expansion.

The vibrating E_ps becomes the MINIMUM SCALE and the winding E_ss the MAXIMUM SCALE in that subcontinuum.
Defining the toroidal volume generator as a consequence of the integral googolplexed H-count: H={R_max/r_ps}³ then define R_max as a 10D/11D boundary.

Hindsight would calculate: R_max=1.59767545x10²⁶ metre-units.

Hindsight would also discover that a dimensional DIM-factor would assume the value 7.56 at the time of its discovery; implying that so 7.56 10D-universes would 'fit' into the 11D-universe at that time, defining a discrepancy of matter in the cosmological calculations.We shall find that the baryonic matter is just 2.803% of thecritical density at the Big Bang; an inertial mass seed, which would grow to 3.68% at the time of discovery, adding to a kind of 'shadow' or 'dark' matter amounting to 27.8% of the necessary total for its Euclidean closure.

This is a function of the deceleration parameter, which as a scaleratio defines not only the architectural scale (Gravitationally bounding Sarkar Constant centred in the supercluster interval from236.1-472.2 Million lightyears), but also the Black Hole spectrumbounded by the critical density.

So Foresight defines TIME=l_ps/R_max=6.259093473x10^-49 =n_ps, the cycletime at time-instantenuity, after the second algorithm had implemented the cosmic interaction of the dimensionalities, which hindsight would term de Broglien hyperinflation, proceeding with a phasespeed of R_max.f_ps and a phase acceleration R_max.f_ps².

And here the 'False Vacuum' develops to energise the process.
TEMPERATURE=ENERGY/k=(h/k).FREQUENCY=h/(k.TIME)=hR_max/kl_ps and this calculates as 7.544809x10³⁷ Temperature units at Genesis Boson Time, which is the superbrane epoch.

RESTMASS becomes: Energy/c²=hR_max/c²l_ps=0.011834633 and leading to a definition of Avogadro's Constant upon application of Unified Field parameters, which span 8p radians of the 4-folded l_ps-wavelength of quadrupled 3D-LineSpace as Line-Hyper-Quantum-OmniSpace and integrating as the toroidal spacequantum in its sinusoidal propagation in:
¼p∫{sin(3x/2)-cos(3x/4)}²dx for the interval [-600°,840°]and the VPE-sourcesink quantum in:

VPE-Quantum=E_Vacuum-ZPE/V=4pE_ps/l_ps³=2.51327..x10⁶⁴ J/m³ as the energy desity in (Energy/Volume)-units.

Since 12 magnetopolic current 'knots' specify this field, the vacuum is energised by the magnetopolic energy.
This energy is given as [c³] unified F-space units and manifests in the lower dimensions as the Current/Linespace quantum [ec] or as precisely 27x10²⁴ eV, which is a monopole mass of [ec=4.82x10^-11] kg-units.

The VPE of the vacuum so becomes defined in wormhole parameters for the Naked Singularity putting 'some clothes' on.
In terms of TEMPERATURE however, the n_ps cycletime is lower than the Genesis Boson Time in 2.93516x10
³⁶ Temperature units.
The 'False Vacuum' so induces the tunneling of the higher temperature to its lower value. This becomes the decisive parametrisation for the mechanism and dynamics of the tunneling matter wave inflation.

The de Broglie phaseacceleration calculates as 1.437908x10⁸⁷ (m/s²) and the Temperature-Field of the universe as a 'Black Body' gives the Quintessence or Einstein-Lambda as the Schwarzschild expression: G_oM_o/l_ps²=2.015x10⁸⁵ (m/s²), with M_o a baryonic mass-seedling from the first algorithm defined as a function of E: Mass-Seedling: M_o=√E.(m_c.m_P/m_e)=1.813713x10⁵¹ kg-units.

m_c is the nucleonic prototype; m_P is the Planck-Mass and m_e is the effective electronmass. m_c and m_e derive from the couplings between superbrane classes, one of which gives the scale relation between the electromagnetic and the gravitational interactions as: [Alpha_GR]=[Alpha_EMR]¹⁸.

There are exactly 10¹⁰ l_ps/360 wavelengths in one electronic radius R_e=ke²/m_ec² as a consequence of linearising r_ps=l_ps/2p into l_ps over a 2p or 360 'degree' count. The 360-degree count is not arbitrary, because the dimensionless unification for the electric permittivity (e_o=1/120cp) with the magnetic permeability (μ_o=120p/c) specifies a half rotation inthe geometric definition of the number p as a trigonometric expansion and sets 180 as that limit.

Now the deceleration parameter, aptly so called in 'reducing' the de Broglie Phase acceleration to the instanton of the classical and metricated cosmic expansion of the quintessence calculates as:

q_o=G_oM_o/c²R_max=0.01401506=M_o/2M_critical=½Ω_o.
The critical Mass for closure for all definitions produced by the first algorithm is given in considering the universe as a 11D-Mother-Black Hole (F-M-C-Space=Father-Mother-Child-Space). Then, using the linearised time definition from cycletime n=H_ot and the Nodal Hubble-Definition: H_o=c/R_max, we obtain the critical volume as:
2p²R_max³ and the critical density as ρ_c=H_o²/4p²G_o.

Using the spherical 3D-volume would give the critical density as ρ_c=3H_o² and which differs in the Feigenbaum-Chaos-Delta δF=3p/2 as dimensional unifier for the curvatures.

M_critical, so becomes explicitely defined as the Mass-Total for the universe and as so 6.446x10⁵² kg-units.

If we set the instanton time as t_ps=f_ss (modular), then this gives the MINIMUM SCALAR HIGGS FIELD POTENTIAL from INFLATION MAXIMUM into the superbrane epoch as t_{inflatonlimit}=3.946x10^-32 seconds*.

The instanton relates as f_ss=1/fps=3.333...x10^-31 seconds*.

TIME as linear expression for the multivalued circular singularity spectrum 'BEGINS" at TIMEINSTANTENUITY=t_ps=f_ss (modular).

Now Newton's Gravitational constant 'G' was not defined in the first algorithm, so where did it derive from?

We begin with the Gravitational Finestructure being a scaled version of the Electromagnetic Finestructure Alpha, with a generalised formulation:

Dimensionless Constant=(Constant).(Charge)²/hc, a 'ForceCharge' taking either the form of Coulombic Charge 'e' or of Restmass Charge 'm', say.
We then relate the Force- or Interaction fields in the identity [ke²]=[G_om²], and where the Coulomb-Charge 'e' becomes defined (say in a Newton-Raphson Iteration) in the magnitude of the wavefunction B(n) for B(0)=B_o.

The primordial algorithm specifies A=h/(2e) as the manifestation of the supermembrane class IIA and that in modular duality to the neighbouring E_psE_ss heterotic supermembrane class HE(8x8). This relates to superconductive states in the Josephson Constant, the Conductance Quantum (2e²/h) and the Quantum Hall Effect, all derivatives from the F-Space ACTION-LAW of ACTION=CHARGE².

Generally, all mass definitions are defined in terms of the magnetic monopole, manifesting as class IIB. Hence all mass is rendered magneto-monopolic at this stage of the definition process.

The following expressions for the magnetocharge e* (measured in the StarCoulomb C'*) are applied in the mapping of magnetopole charge 'e*' in F-space unto the electropole charge 'e' in C-space. This transition relates to the superbrane epoch before timeinstantenuity.

(a) 2pG_o.mc²/hc=Alpha¹⁸ and m_c=m_P defines m_P for Alpha¹⁸=1.
(b) E_ps=hf_ps=E_ss.f_ps²=√ol]pG_o.m_e²/4Alpha.hc.e²]=1/e*.
(c) 2e.R_e.=e*.l_Planck√Alpha.
(d) E_o=e√(E/Alpha)=1.886461127x10³⁸ C* (Charge-Seed)
(e) M_o/m_c=1.813713x10⁵¹/9.92474572x10^-28
.....M_o/m_c=1.827469354x10⁷⁸.......(No of Seed-Nucleons)
.....M_critical/m_c=6.519663x10⁷⁹.......(No of Nucleons)
(f) Ol_Planck=l_Planck.√Alpha=e/c² (Stoney Units).

The last expression is the Planck-Length-Oscillation, unifying Gravitation with Electromagnetism. For unitary consistency in C-space the dimensionless nature of the Force-Charges must become linked to the monopolic spectrum and that is achieved in the mapping of e* onto e.

The C-Space relation 2R_e.c² maps the F-Space relation O_lPlanck.c² and the unitary symmetry is the relation between the electric permittivity and gravitation in the identity: G_o=4pe_o=1/30c (dimensionless) via unitary unity:
[metre/Farad=Joule.metre/Coulomb²]=[kg²/Newton.metre²] and for [StarCoulomb*]=[metres³/seconds²]=[Volume.Angular Acceleration].
This defines 'The Equivalence Principle' to relate 'Gravitational Mass' to electric permittivity via the interaction charges for a prior existence of (classical) electromagnetic mass before the inertial eigenstate induced per acceleration as spacetime curvature in geometric General Relativity.
The C-Space relation 2R_e.c² so crystallises in the diameter of the electronic spacial extent in manifesting the energy of F-space in magnetopolic equivalence to the electropolic size of an atomic nucleus in 3 dimensions.

We note the independence of the primordial Energy from the restmass.
Substituting k=1/G_o=1/4pe_o=30c into the electric constant from the Maxwell Constant gives the 1/30c numeracy, independent from the [kg] unit.
The generation of the masterconstants demands the establishment of a cosmic-standardised unitary system (*) and the only constant shared between both the (*) and the SI-system is the magnetic permeability constant μ_o=120p/c in the finestructured form.
Amongst other things, this becomes decisive in determining the lower dimensional 'dip' in the Alpha-Constant, which remains invariant in the higher dimensional settings, where Alpha is independent of c and so e_o




8. The Algorithm of the Cosmogenesis in Strings

The Algorithm for MasterConstant Generation.

The eigendefinition of E_ps; {originally standing for Energy-primary-source but today identifiable as the sourcesink supermembrane E_psE_ss of heterotic class HE(8x8), based on the maximised octonion composition algebra of exceptional lie group E8; also gnostically or esoterically E_ps=GoddoG and E_ss=DoggoD as GOD and AntiGOD=DOG as the coupling of vibratory (GOD) and winded (DOG) superstring parts under modular symmetry, say mirror or M-symmetry}
in the pre-O-time universe of omnispace ]{10D-13D=1D}, was found to be a consequence of the awareness triplets of (Old State,Experience,New State) and generally coded triplets of the form (a,b,c) became effective to quantumize integer definitions into the natural laws from quantum-space {7D-10D} into hyper-space {4D-7D} into spacetime {or line-space 1D-4D}.

We recall the sequence of experience factors:

SEps={0,1,1,2,3,5,8,13,21,34,55,89,...} and generalised via:

SEps(n)=[Yⁿ-Xⁿ/√5; n=0,1,2,3,4...; X=½(1-√5); Y=½(1+√5).

The aim is now to generate the complementary set to SEps, namely SEps* in the application of the primary seven fundamental principles.
We so define the two main {binary} operations of ADDITION and MULTIPLICATION:

(a,b)+=a+b and (a,b)x=axb, where both a and b are elements of SEps.

If the value obtained by either operation is a member of SEps, then it is rejected, otherwise it is accepted and becomes an element of CONSTANTSET, a subset of SEps*.
The principles of IDENTITY and EXPANSION are herewith fulfilled and the ORDER principle becomes the main mechanism for constant generation.

We further define 'Pure Number Constants' or PNC's, which will be integers of SEps* and Proportionality Constants or P-Constants of the form (a,b,c)=(axb^c)^j and with j=+1 or j=-1.

Starting with (a,b)+ an algorithm is applied until a generated constant is OOO or OUT OF ORDER.
This OOO-Constant becomes then the first element a1 of the first P-Constant.

Then the operation changes to (a,b)x until another OOO-Constant is found, with this second OOO-Integer becoming assigned to be b1 of the first P-Constant ONLY if it is greater than a1; if it is not, it becomes a2 for the second P-Constant.
If a b-element is defined, then an a-element must also be defined in the same triplet and the next element would become c and finalise the triplet and the P-Constant.
The principle of SYMMETRY is effected whenever a triplet element is generated OOO or when a prospective b or c must be reset as an a.

All P-Constants must be symmetric, with a's followed by b's followed by c's.
Whenever an a and a b are defined within any particular triplet, the operation of + or x is not altered and the next generated constant, being either pure or impure=OOO, becoming either the next PNC or finalising the next P-Constant.
The overall ORDERING must however always prevail with PNC's generated in ORDER, as well as the elements of the P-Constant triplets.
This is the general concept of the algorithm. We must however also account for the DUPLICATION of numbers, MULTIPLE IRREGULARITIES and INCOMPLETE TRIPLETS.

To apply a FINITE algorithm to SEps, we must define the ORDERED SUBSET NSTEP.

NSTEP-k=(a1,a2,a3,...,ak)=(0,1,1,2,3,...,ak) and the order is k, with ak the limiting element of SEps.

The LIMIT for constant generation now becomes that application of NSTEP, which does not generate at least one constant in SEps* and not having been generated in an earlier NSTEP application.

The complementary set to NSTEP is INSEQUENCE=(b1,b2,b3,...,bk')=(4,6,7,9,10,...,bk').

A necessary initialisation for NSTEP is so NSTEP-5=(0,1,1,2,3) with a5=3 and b1=4 with b1=4 the first element of INSEQUENCE to be generated by the algorithm, either as PNC or as a1 of a P-Constant#1.
NSTEP-5 is so limited by b1=4 and the algorithm ends if this number 4 is not generated via NSTEP-5.

Should however the first k' elements of INSEQUENCE be obtained, say 4,6,7,9,10 with k'=5, then NSTEP-6 is required to produce b6=11 for the continuation of the algorithm.

This process does not exclude the generation of any other missing numbers however and we define the set TOTALCONSTANTSET of which CONSTANTSET-k is a subset.
The algorithmic iterations must so be increased by a minimum of one for every application of NSTEP.

Formally then:

NSTEP-kÌSEps, such that (a1,a2,a3,...,ak)=(0,1,1,...,ak) with a(k+1)>ak " k];

INSEQUENCE-k'Ì SEps*, such that (b1,b2,b3,...,bk')=(4,6,7,...,bk') with b(k'+1)> bk' " k'.

Let us now define DUPLICATIONSET=DS as the set of all duplications, to which all new duplications of a particular application of NSTEP are added.

1+5=2x3=6 and 2+8=2x5=10 and the resulting numbers 8 or 10 can be obtained in a number of ways.

Say, we have 10 as a PNC and is duplicated in (7,10,12).
This represents an 'IRREGULARITY' and rectifying steps are applied via DS.

INCOMPLETE TRIPLETS at the end of an algorithm apply a subroutine in comparing the a-elements of all generated triplets and setting ascending ORDER for a's, b's and c's.
This regulation ensures redefinition of the largest a-triplet.

The principle of INFINITY {as the DIVERGENCE being antiprincipled in CONVERGENCE or LIMIT as primary principality #5} is utilized via the principle of INVERSION by RECIPROCATING the 'IRREGULARITIES' of DUPLICATION.
Every application of NSTEP resets CONSTANTSET to EMPTY after including all previously generated constants in TOTALCONSTANTSET.
All constants in DUPLICATIONSET are omitted from the next NSTEP.

There is only one exception to the strictly increasing nature of triplet elements a< b< c and this is the occurrence of MULTIPLE IRREGULARITIES and INCOMPLETE TRIPLETS.
For a single duplication the reciprocal is taken with adherence to ORDER.

The first OOO-Constant becomes a1 in the first P-Constant. If the next OOO< a, then that OOO becomes a2 in P-Constant#2, irrespective of duplication.
Yet if b>a and if b is duplicated as well as a, then this DOUBLE-DUPLICATION of a and b is ORDERED and a single inversion suffices.
Two ordered irregularities form a regular irregularity and a single rectification - inversion, is satisfactory.
Similarly, when a c is duplicated besides a and b, but a< b< c, then ordered duplication is a single irregularity.

Thus ORDER rules supreme and we must consider the possibilities of one or more triplets being INCOMPLETE at the end of a particular NSTEP with MULTIPLE IRREGULARITIES of uncompleted triplets.
In this situation, the triplets are formed not in terms of ORDER but in terms of their INITIALIZATION, which is another form of ORDER.
All a's are utilised before b's before c's and the remaining numbers are totalled and are combined via modulus 3 or modulus 2.

Example #1: (23,40, ) and (14,16, ) and (15, ) and (10,12, ) have members: a1=23, b1=14, c1=15, a2=10, b2=40 and the final exponent=(16+12)/2=14.

Example #2: (23,40 ) and (14,16, ) and (15,16, ) has members: a1=23, b1=14, c1=15, a2=40, b2=16 and c2=16 with the last triplet becoming (40x16¹⁶)^-1, because of the duplication of element 16.

These Examples therefore yield P-Constants 23x14¹⁵ and 10x40¹⁴ and 23x14¹⁵ and 1/(40x16¹⁶).

A multiple duplication not in order could occur in the generation of the final exponent and represents an irregular irregularity and so a regularity.
The initialisation process of a's before b's before c's has made the irregularity regular however and a single inversion negates this disorder.
The constants obtained in computing the final exponent are to be included in TOTALCONSTANTSET=TCS, as is the integer part of their result.

A final c=13+2/3=(12+12+17)/3=41/3 includes so 12, 17, 41 and 13 in TCS via CS.

It remains now to redefine all those duplicated P-Constants, which were not inverted, since in the process of their generation, their duplications were not members of CS, in which case they would have been inverted.
These triplets are 'purer', with the only irregularity being the inclusion of a number, which would become duplicated LATER within the same application of NSTEP.
So INVERSION is not justified, except in the case of incomplete triplets, with duplication becoming just one of the disorders.

If (9,12,17) and (14, ) and (12, ), then a1=9 and b1=14 and c1=41/4=13+ 2/3 and the three irregularities are the duplicated 12 and the modulus 3 of 41/3 and the disorder of the resulting (9,14,13+2/3).

We must apply a single inversion for the constant (9x14^{13+2/3})^-1.

This would delete 9x12¹⁷ from CS and TCS, but adding the triplet and 9,12,13,14,17,41 to TCS.

The {seventh and completing} principle of REFLECTION defines the triplets, which contain duplications, but are not inverted.
Say the triplet (7,16,20) is generated, but later in the same NSTEP, the element 16 is duplicated.

We set the Reflection-Function R(N)=(P-Constant)², i.e. we reflect +1 in -1 and define Unity (-1)²=(+1)²=1.

The resulting constant then is 'squared': (P-Constant)²=7x16²⁰.


General Structure of the Algorithm:

INITIALIZATION
MAIN LOOP (UNDEFINED=UD, INSEQUENCE=ISQ, (RML-CO=RC)
SEps?=NO->XÎ ISQ?=NO->a UD?=NO->b UD?=NO->c>b?=NO->c>a?=NO=FIX a-RC
|................................................................................................|YES=FIX b-RK
|................................................................................|YES=FIX c&triplet-RK
|.........................................................|YES=FIX b-(RML-KO)=RK IF b>a ELSE FIX a-RK
|...........................................|YES=FIX a-RML-CHANGE OPERATION=CO
|........................|YES=PNC-RML-KEEP OPERATION=KO
|YES=RETURN TO MAIN LOOP=RML[/SIZE]

​

 

The Maria Number Matrix of the 33-Summation-Tier and the Euler-Riemann-Fibonacci-Lucas Harmonics

The 'Perennial Philosophy' or the 'Wisdom of the Ancients' often points to what is commonly termed as 'Sacred Geometry', based on the Platonic Solids (of five regular polyhedra: Tetrahedron, Cube; Octahedron; Dodecahedron and Icosahedron) and the Tetraktys of Pythagoras (for the minimum mathematical points to define the four dimensions of 0D=1 Point; 1D=2 Points for a Line; 2D=3 Points for a Plane and 3D= 4 Points for a Space).

Also invoked is the pentagonal supersymmetry of quasiperiodicity as 'Nature's Preferred maximisation of 'packing efficiency' known as the Fibonacci Series and the 'Perfect Numbers' of Euclid and the 'Harmony of Numbers and the Spheres' of Pythagoras, Leonardo da Vinci and Kepler.
In Pythagoraen Numerology, the 'masternumbers' 11, 22 and 33 are often emphasised and this post shall introduce some relatively rigorous number theory (of the so called 'pure' mathematics) to validate the significance of the 'masternumbers' from frst principles.

The alphanumeracy of the Arabic-Hebrew semiotiks then is bounded in say 22 or 26 letters of alphabets, which can attain numerical values in the decad of three triplicities:

Round or Curved 'Mental Numbers' {3-6-9} characterised by masternumber 33;
Mixed or Discontinuous 'Emotional Numbers' {2-5-8} characterised by masternumber 22 and
Linear or Straight 'Physical Numbers' {1-4-7} characterised by masternumber 11.

The Maria-Code in the Riemann Analysis specifies the partitioning of the decimal monad around the primary Maria-Number and SE_ps-Constant '11'.
This generates the Prime Number Algorithm: +1+11+10+11 as 33-tiered segments, which transform the mechanics of SE_ps into the 64-codex of the DNA/RNA code for its eventual quadrupling as the 4x64=256-codex incorporative of dormant intron/intein codings.

All cellular consciousness coupled units so transfer their memory data-bases (as experience factors) by the Fibonacci quantum mechanics.

The Maria-Code is based on the distribution of the Maria-Numbers (M_N)given by:

M(p)+99=M(p+12); n=½[√(264k+1)-1] by n²+n-66k=0.

Maria Numbers are those IntegerCounts, which contain all previously counted integers as mod33.


Example: 1+2+3+4+5+6+7+8+9+10+11=66 = 2x33 → '11' is M_N#1 for k=2


11love65use110love164use209love263use......Archetype 2 (rootreductive)

21use66love120use165love219use264love......Archetype 3 (rootreductive)

32use77love131use176love230use275love......Archetype 5 (rootreductive)

33love87use132love186use231love285use......Archetype 6 (rootreductive)

44love98use143love197use242love296use......Archetype 8 (rootreductive)

54use99love153use198love252use297love......Archetype 9 (rootreductive)

65use110love164use209love263use308love....Archetype 2*... ...



Archetypes 2+3+5+6+8+9=33 and Archetypes 1+4+7+0=12 then define the imaginary time-dimensions as the archetypes not in the Sequence for E_ps=1/e* Coefficients used in the application of the seven fundamental principalities to define the F-Space.

We have used the (Hebrew-Isaac-encoding): 54=LOVE=12+15+22+5 with 45=USE=21+19+5; USELOVE=99 as the Maria-Code connectors.

The first 10 M_N's are: 11, 21, 32, 33, 44, 54, 65, 66, 77 and 87.

One can use the Maria-Code to establish a redefinition of infinity by defining a transfinite mapping Aleph-All from 12D-Omnispace as Cantorian transform of Cardinality Aleph-Null.


Limit (T(n)) for n→∞/Infinity = ∞/Infinity {Cantor Cardinality Aleph-Null}
Limit (T(n)) for n→X=0.618033........ = 1 {Cantor Cardinality Aleph-All}

This maps the Riemann pole about z=1 in the Functional-Riemann-Bound (FRB=-1/2) in the gaussian universal wavefunction B(n)=(2e/hA).exp(-Alpha.T(n)), T(n)=n(n+1) as the Feynman-Path-Integral.

This becomes the Riemann-Euler-Harmonic, defining the Gamma-Function geometrically in its nth Term T and nth Sum S and mapping the factotrial function onto the positive integer count:

T^k(E_n) = n^k.T^k(E_n-1) + [(n-1)!]^k and S^k(E_n) = T^k(E_n)/(n!)^k



This uses the Harmonic Series in the Zeta-Function ζ(z) with constant p.
The Sum (1 to Infinity) Σ(1/n^p)= 1/1^p+1/2^p+1/3^p+...+1/n^p and converges for any p>1, since for even terms:

2.2^-p ≥ 2^-p+3^-p, with geometric series 1^1-p+2^1-p+4^1-p+...summing to (1-2^[1-p]n)/(1-2^1-p)=1/[1-2^1-p] in the limit for n→Infinity.

Since every Maria Number contains all numbers before it as a sum, it is given that all the prime numbers must eventually crystallise out of the Maria Count.

Define a general number count n and a 'Mersenne-Count' 8n-1=M*.
For a number to be prime this number must be born in the Maria Code.
M* is either a prime or a product of primes in the immediate neighbourhood of the count # or its mapping to M*, which in a sense 'counts' the primes it generates.

This is the finestructure as octaves derived from integer n.
To test a number for primeness, so amounts to a testing for Marianess.
If the number is a member of the Maria-Matrix, then it must be denumerable in the form of M*.

This is the meaning behind the Mersenne-Code (for n prime) M(p)=2^p-1 and the Fermat-Code F(n)=2²ⁿ+1 and the 'Perfect Numbers' depicted as the Mersenne Numbers (M_p), as a subset of M*.
For the Mersenne Numbers, the exponent p is defined to be prime.
M₂=2²-1=3; M₃=2³-1=7; M₅=2⁵-1=31; M₇=2⁷-1=127; M₁₁=2¹¹-1=2047=23x89 and so is not a Mersenne Prime - yet M₁₃=2¹³-1=8191; M₁₇=2¹⁷-1=131,071; M₁₉=2¹⁹-1=524,287 are prime and M₂₃=2²³-1=8,388,607=47x178,481 and M₂₉=2²⁹-1=536,870,911=233x1103x2089 are not and M31=2³¹-1=2,147,483,647 is prime again in the 33-tier count.

The 'uniqueness' of the prime number 11 (and esoteric masternumber) recrystallizes in Mersenne primes as the (first) 'odd one out'.
But it gets better. First we notice that there are just five 'perfect Fermat Primes'.

F₀=2¹+1=3; F₁=2²+1=5; F₂=2⁴+1=17; F₃=2⁸+1=257 and F₄=2¹⁶+1=65,537 are all 'perfect' Fermat Primes, but F₅=2³²+1=4,294,967,297=641x6,700,417 and following are not. Only these five Fermat primes are known to date.

The 'Perfect Numbers' relate (for prime p) as 2^p-1.M_p :
P₂=2¹.(2²-1)=6=1+2+3=1x2x3;
P₃=2².(2³-1)=28=1+2+3+4+5+6+7=[7x8]/2=4x7=1³+3³=1+27;
P₅=2⁴.(2⁵-1)=496=1+2+3+...+30+31=[31x32]/2 =16x31=1³+3³+5³+7³=1+27+125+343;
P₆=2⁶.(2⁷-1)=8128=1+2+3+...+126+127=[127x128]/2=1³+3³+5³+7³+9³+11³+13³+15³
All 'Perfect Numbers' so are EVEN (it is hitherto unknown if any ODD 'Perfect Numbers' exist); and EXCEPT the basic 'First Perfect Number' 6=1+2+3=1x2x3, they all are the sums of the ODD NUMBERS CUBED.

Some elementary initial conditions for Francom Adjacency

We define the Euler-Riemann Summation, which defines the 'Mixing of the Count' in linking Arithmetic Progression to the multiplicative Factorial Function '!'.

Define E_o=0 as the singularity (interval), then for any integer n, we find for the Harmonic Form of Riemann's Zeta-Function (z=k=constant):

ζ(z)=ζ(1/n^z)=1/1^k+1/2^k+1/3^k+1/4^k +...+1/n^k

This Sum diverges for [ 0<k<1], i.e. for k=1/2: {1+√2/2+√3/3+...+√n/n} increases without limit.

For k>1, we have convergence, however.
Formally, let: Σ(1/n^p) = 1^-p+2^-p+3^-p+...
For even terms: 2.2^-p ≥ 2^-p+3^-p for a geometric series:
1^1-p+2^1-p+4^1-p+...+(2^n-1)^1-p
This Geometric Progression sums to: [1-(2^1-p)ⁿ]/[1-2^1-p]=1/[1-2^1-p]

So for p=2, this limit maximises in 1/(1-1/2)=2 , and for p=3 it becomes 4/3 converging towards 1 for increasing p.

We consider the special case for p=1 applied to the Singularity Interval E_o.

Define: for a nth term (numerator): T^k(E_n) = n^k.T^k(E _n-1) + [(n-1 )!]^k for the nth sum per n (denominator [n!]^k): S^k(E_n) = T^k(E_n)/(n!)^k


T¹(E₁)=1/1=1.0+0!=1=S¹(E₁)=1/1!=1; T²(E₂)=2.T¹(E₁)+1!=2+1=3
with S²(E₂)=T²(E₂)/2!=3/2=1+1/2;
T³(E₃)=3.T²(E₂)+2!=9+2=11 with S³(E₃)=T³(E₃)/3!=11/6=1+1/2+1/3=1+5/6 and so on.

Further Example: T¹(4)=4.11+3!=50; S¹(4)=50/4!=25/12 for the nesting: 4{3(2+1!)2!}3! with [4!]¹=24.
For 4 terms, the Euler-Riemann Summation so is: S¹(4)=1+1/2+1/3+1/4=25/12=2+1/12.
For 7 terms, S¹(7)=T¹(7)/7!=(7.T¹(6)+6!)/7!=13068/5040=363.36/(140.36)=2+83/140=1+1/2+1/3+1/4+1/5+1/6+1/7.


Project the Numberline with the Positive Integers mapping the Factorial-Function and the Negative Integers remaining invariant in Feyman Summation T(n) for T(n)=½n(n+1) as absolute value, mirroring the positive integers.

(n!)<---4...3...2...[E_o]...1...2...3---> (n); where Integer 1 maps 2! in suppression of -1=2* and in algoradius e_o=1.
Similarly, Integer 2 maps 3! in suppression of -2=3* and algoradius e₁=2=2e_o, etc. etc.


The singularity so mixes the interval [0!-1!]=[-1,0] with Functional-Riemann-Bound (FRB=-½) becoming 'real' in its mapping (FRB'=½) in [0,1] and the central limit or pole, about which the Zero's of the Riemann-Zeta-Function propagate.
The first annulus in the Riemann-Euler-Harmonic so phasemixes the numbers 2 and 1 and the nth number is mixed with (n+1) as crystallised in the Feynman-Path-Integral or T(n)=1 in n(n+1), as a summation for all possible particular histories in quantum mechanics.


This also maps the series:
SE_ps=Fibonacci#1=0,1,1,2,3,5,8,.....for a nth Term: T_n=|-Yⁿ - Xⁿ|/√5 , for absolute value || and obtained say via MacLaurin-Expansion of the coefficients (Experience-Factors) in the power series:


f(x)=1+x+2x²+3x³+...= ΣT_n.x^n-1
Set x.f(x) + x².f(x) = f(x) -1, then by (a+b)(a-b), f(x)=a/(x-X) + b/(x-Y) for a=-b=1/(Y-X) and (Y-X)=-√5.
SuperSE_ps=Fibonacci#2=Lucas#1=2,1,3,4,7,11,18,29,.... for a nth Term:

ST_n=|-Y²ⁿ - X²ⁿ|/|-Yⁿ - Xⁿ|=|T²ⁿ/Tⁿ|

for n=1,2,3,...; T(2n=0)=2 mapping T(n=0)=0.

The combined SE_ps-SuperSE_ps(T-ST)-sequence of experience factors {from the triplet propagation of [OldState, Experience, NewState]} can then be written as:

{T_n,ST_n}={(S_o=0,ST_o=2=S₃); (S₁=1=ST₁=S₂); (S₂,S₄=3=ST₂); (S₃,ST₃=4); (S₄=ST ₂,ST₄=7); (S₅,ST₅);...;(S_n,ST_n)...}
{T_n,ST_n}={(0,2), (1,1), (1,3), (2,4), (3,7), (5,11),...} containing integerset: {0,1,2,3,4,5,7,8,11,13,18,21,29,....}

We now represent the mappings in matrix form denoted as F-M-C, where the 'well behaved' terms for the mapping (from {T₅,ST₅}) sets algorithmic C-Space and the preceding elements the initialisation for the former.

Note we define Cantorian Denumerability Aleph-Null in Cardinality Aleph-All in the form:
Aleph-Null: limit{n→∞}[T(n)]=∞
Aleph-All: limit{n→X}[T(n)]=1 and so counting Infinities as mapped one-to-one onto the positive Integer set.


SEps= Fibonacci#1 maps SuperSEps=Fibonacci#2=Lucas#1
-----------------0 0 0*............................................................-4 7 3................n=-2=2i²
Fspace---------0* 0 1...........n=∞ via 0+0=∞=1*=0*=1.........3 -4 -1.............n=-1=i²
Mspace--------1 0* 1...........n=0 via (1,1,1)...........................-1 3 2*..............n=0
-----------------1 1 2.............n=1 via (1,1,10=2*=0/0=1*).......2* -1 1.............n=0 (Reflection-Interval)
-----------------2 1 3.............n=2 well behaved........................1 2* 3..............n=0
Cspace--------3 2 5..............n=3 well behaved........................3 1 4................n=1 well behaved
-----------------5 3 8.............n=4 well behaved.......................4 3 7.................n=2
........................................... n=5 continue downwards ................................... n=3

The linearity of the generating triplet configurations is extended in a complexification into a 2D symmetry.
SE_ps propagates the Experience Factors in an adjacent displacement of 1, in moving from one configuration state to the next - this is termed Francom Adjacency.
[0*,1,1,2,3,5,...] as OldStates transfigure in Experiences [0,0*,1,1,2,3,5,8,...] into NewStates [1,1,2,3,5,8,...].

This algorithmic configuration space is however broken in the mapping onto SuperSE_ps.
Here the matching 'good behaviour' of the n-count is delayed in a factor of 2 in a 'reflection interval'.
Algorithmic modelling for this Francom Adjacency must generate the mapping of SE_ps onto SuperSE_ps in an geometry of the pentagonal symmetries intrisic to the two series.

Hence a synthesis between linear propagation about an internal spiralling form is necessitated.
A longrange rotational- and a longrange translational order for the Experienc-Factors is indicated in the geometry of say Penrosian Tiling Patterns and the Schechtmanite Quasicrystals of empirical form (Mg₃₂[Al,Zn]₄₉).

The general form, physically akin to the propagation of magnetic fields, is the reduction of physical parameters to a state of information transmission, say in the data transfer between two neighbouring cells in mitosis and neuronal-synaptic processing.
A general modality for the cosmogenetic reproduction on all levels must crystallise, should the matrices above become sufficiently deciphered from their algorithmic encoding.

Derivation of SuperSEps

The relative primeness of the Fibonacci Numbers allows a one-to-one mapping between the SEps-Set and other such sets derived from it, particularly the Lucas Numbers as a logical derived set of such nature and given in the sequence: 2,1,3,4,7,11,18,29,....
All adjacent members of this set are relatively prime to each other.
7 is relatively prime to both 4 and 11 (no common divisors except 1) and 11 is relatively prime to both 7 and 18.
We now tabulate the sums and differences in our nth-term definition for SEps, so recalling the propagation for the natural numbers in counter n:

n	Tn	Xn	(-Y)n	{|-Y|n + |X|n}	{|-Y|n - |X|n}
		1	+1	+2
1	1	0.6180339885	-1.618033989	+2.236067978	+1
2	1	0.3819660109	+2.618033989	+3	+2.236067978
3	2	0.2360679772	-4.236067979	+4.472135955	+4
4	3	0.1458980335	+6.854101975	+7	+6.7082039375
5	5	0.0901699436	-11.09016995	+11.18033989	+11
6	8	0.0557280899	+17.94427193	+18	+17.88854384
7	13	0.0344418537	-29.03444189	+29.06888374	+29
8	21	0.0212862362	+46.97871382	+47	+46.95742758
9	34	0.0131556175	-76.01315572	+76.02631134	+76
10	55	0.0081306187	+122.9918696	+173	+122.983739
...	...	...	...	...	...
20	676555	0.0000661070	+15126.99998	+15127	+15126.99991
...	...	...	...	...	...

We see that for increasing n, the absolute magnitude for Y converges to an integral value in the Sum {+}, but only for even n.
For odd n, the difference Sum {-} gives a specific integer for specific n.

The product of the two sums is: {+}.{-} = |-Y|²ⁿ - |X|²ⁿ=√5.T_2n.
The sum of the two sums is: {+}+{-}= 2|-Y|ⁿ, with ST_n ={+}+{-} - T_n.√5) = |(-Y)ⁿ +Xⁿ|

Multiplying each term as: √5.({+}+{-}), we can form the alternating series:
(0+2.√5), (5+1.√5), (5+3.√5), (10+4.√5), (15+7.√5), .....as the alternating form of SuperSE_ps given in the term: [5.T_n+ √5.T'_n];

but for even n, we have: T'_n ={+} and for odd n, we have T'_n ={-}; then by (a-b)(a+b)=a²-b²:

ST_n.√5.T_n={+}.{-}=√5.T_2n & ST_n=T_2n/T_n = |-Y²ⁿ - X²ⁿ|/|-Yⁿ - Xⁿ|
(quod erat demonstrandum).

The significance of this result is that ST_n, T_2n and T_n are all integers.
We so have a primary extension for SE_ps with elements 1, 2 and 3 duplicated and resulting in the mappings as previously specified.

The Null-Initialisation (OS_j, EX_j, NS_j) as the Fibonacci-Triplet (A_n-1, A_n, A_n+1) then reflects ST_n about n=0* to define the complex number set as negative ST_n's mapped in a 0→1→∞ correspondence to T_n.
This is the mathematical mapping of Cantorian Enumerability as previously indicated.

Abraxasinas

 

2.2^-p≥ 2^-p+3^-p, with geometric series 1^1-p+2^1-p+4^1-p+...summing to (1-2^[1-p]n)/(1-2^1-p)=1/[1-2^1-p] in the limit for n→Infinity.