# A Revision of the Friedmann Cosmology

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A Revision of the Friedmann Cosmology

1. The Parametrisation of the Friedmann Equation

It is well known, that the Radius of Curvature in the Field Equations of General Relativity relates to the Energy-Mass Tensor in the form of the critical density ρcritical = 3Ho2/8πG and the Hubble Constant Ho as the square of frequency or alternatively as the time differential of frequency df/dt as a cosmically applicable angular acceleration independent on the radial displacement.

The scientific nomenclature (language) then describes this curved space in differential equations relating the positions of the 'points' in both space and time in a 4-dimensional description called Riemann Tensor Space or similar.

This then leads mathematically, to the formulation of General Relativity in Einstein's field Equations:

for the Einstein-Riemann tensor

and is built upon ten so-called nonlinear coupled hyperbolic-elliptic partial differential equations, which needless to say, are mathematically rather complex and often cannot be solved analytically without simplifying the geometries of the parametric constituents (say objects interacting in so called tensor-fields of stress-energy {Tμν} and curvatures in the Riemann-Einstein tensor {Gμν}, either changing the volume in reduction of the Ricci tensor {Rij} with scalar curvature R as {Rgμν} for the metric tensor {gμν} or keeping the volume of considered space invariant to volume change in a Tidal Weyl tensor {Rμν}).

The Einstein-Riemann tensor then relates Curvature Radius R to the Energy-Mass tensor E=Mc2 via the critical density as 8πG/c4=3Ho2Vcritical.Mcritical.c2/Mcritical.c4 = 3Ho2Vcritical/c2 = 3Vcritical/R2 as Curvature Radius R by the Hubble Law applicable say to a nodal Hubble Constant Ho = c/RHubble.

The cosmological field equations then can be expressed as the square of the nodal Hubble Constant and inclusive of a 'dark energy' terms often identified with the Cosmological Constant of Albert Einstein, here denoted ΛEinstein.
Substituting the Einstein Lambda with the time differential for the square of nodal Hubble frequency as the angular acceleration acting on a quantized volume of space however; naturally and universally replaces the enigma of the 'dark energy' with a space inherent angular acceleration component, which can be identified as the 'universal consciousness quantum' directly from the standard cosmology itself.

The field equations so can be generalised in a parametrization of the Hubble Constant assuming a cyclic form, oscillating between a minimum and maximum value given by Ho=dn/dt for cycle time n=Hot and where then time t is the 4-vector time-space of Minkowski light-path x=ct.

The Einstein Lambda then becomes then the energy-acceleration difference between the baryonic mass content of the universe and an inherent mass energy related to the initial condition of the oscillation parameters for the nodal Hubble Constant.

ΛEinstein = GoMo/R(n)2 - 2cHo/(n+1)3 = Cosmological Acceleration - Intrinsic Universal Milgröm Deceleration as: gμνΛ = 8πG/c4 Tμν - Gμν

then becomes Gμν + gμνΛ = 8πG/c4 Tμν and restated in a mass independent form for an encompassment of the curvature fine structures.

Energy Conservation and Continuity:

dE + PdV = TdS =0 (First Law of Thermodynamics) for a cosmic fluid and scaled Radius R=a.Ro; dR/dt = da/dt.Ro and d2R/dt2 = d2a/dt2.Ro

dV/dt = {dV/dR}.{dR/dt} = 4πa2Ro3.{da/dt}

dE/dt = d(mc2)/dt = c2.d{ρV}/dt = (4πRo3.c2/3){a3.dρ/dt + 3a2ρ.da/dt}

dE + PdV = (4πRo3.a2){ρc2.da/dt + [ac2/3].dρ/dt + P.da/dt} = 0 for the cosmic fluid energy-pressure continuity equation:

dρ/dt = -3{(da/dt)/a.{ρ + P/c2}} .........................................................................................(1)

The independent Einstein Field Equations of the Robertson-Walker metric reduce to the Friedmann equations:

H2 = {(da/dt)/a}2 = 8πGρ/3 - kc2/a2 + Λ/3 ...................................................................................(2)

{(d2a/dt2)/a} = -4πG/3{ρ+ 3P/c2} + Λ/3 ..................................................................................(3)

for scale radius a=R/Ro; Hubble parameter H = {da/dt)/a}; Gravitational Constant G; Density ρ; Curvature k ; light speed c and Cosmological Constant Λ.

Differentiating (2) and substituting (1) with (2) gives (3):

{2(da/dt).(d2a/dt2).a2 - 2a.(da/dt).(da/dt)2}/a4 = 8πG.(dρ/dt)/3 + 2kc2.(da/dt)/a3 + 0 = (8πG/3)(-3{(da/dt)/a.{ρ + P/c2}} + 2kc2.(da/dt)/a3 + 0

(2(da/dt)/a).{(d2a/dt2).a - (da/dt)2}/a2 = (8πG/3){-3(da/dt)/a}.{ρ + P/c2} + 2{(da/dt)/a}.(kc2/a2) +0
2{(da/dt)/a}.{(d2a/dt2).a - (da/dt)2}/a2 = 2{(da/dt)/a}{-4πG.{ρ + P/c2} + (kc2/a2)} +0 with kc2/a2= 8πGρ/3 + Λ/3 - {(da/dt)/a}2

d{H2}/dt = 2H.dH/dt = 2{(da/dt)/a}.dH/dt
dH/dt = {[d2a/dt2]/a - H2} = {-4πG.(ρ+ P/c2) + 8πGρ/3 + Λ/3 -H2} = -4πG/3(ρ + 3P/c2) + Λ/3 - H2} = -4πG/3(ρ + 3P/c2) + Λ/3 - 8πGρ/3 + kc2/a2 - Λ/3} = -4πG.(ρ + P/c2) + kc2/a2

dH/dt = -4πG{ρ+P/c2} as the Time derivative for the Hubble parameter H for flat Minkowski space-time with curvature k=0

{(d2a/dt2).a - (da/dt)2}/a2 = -4πG{ρ+ P/c2} + (kc2/a2) + 0 = -4πG{ρ + P/c2} + 8πGρ/3 - {(da/dt)/a}2 + Λ/3

{(d2a/dt2)/a} = (-4πG/3){3ρ + 3P/c2- 2ρ} = (-4πG/3){ρ + 3P/c2} + Λ/3 = dH/dt + H2
For a scale factor a=n/[n+1] = {1-1/[n+1]} = 1/{1+1/n}​

dH/dt + 4πGρ = - 4πGP/c2 .... (for V4/10D=[4π/3]RH3 and V5/11D=2π2RH3 in factor 3π/2)

areset = Rk(n)AdS/Rk(n)dS + ½ = n-∑∏nk-1+∏nk

Scale factor modulation at Nk={[n-∑∏nk-1]/Πnk } = ½ reset coordinate

{dH/dt} = areset .d{Ho/T(n)}/dt = - Ho2(2n+1)(n+3/2)/T(n)2 for k=0

dH/dt + 4πGρ = - 4πGP/c2

-Ho2(2n+1)(n+3/2)/T(n)2 + GoMo/{RH3(n/[n+1])3}{4π} = Λ(n)/{RH(n/[n+1])} + Λ/3
-2Ho2{[n+1]2-¼}/T[n]2 + GoMo/RH3(n/[n+1])3{4π} = Λ(n)/RH(n/[n+1]) + Λ/3
-2Ho2{[n+1]2-¼}/T(n)2 + 4π.GoMo/RH3(n/[n+1])3 = Λ(n)/RH(n/[n+1]) + Λ/3

For a scale factor a=n/[n+1] = {1-1/[n+1]} = 1/{1+1/n}

Λ(n)/RH(n/[n+1]) = - 4πGP/c2 = GoMo/RH3(n/[n+1])3 -2Ho2/(n[n+1]2)

and Λ = 0
for -P(n) = Λ(n)c2[n+1]/4πGonRH = Λ(n)Hoc[n+1]/4πGon = Moc2[n+1]3/4πn3RH3 - Ho2c2/2πGon[n+1]2

For n=1.13271:............ - (+6.696373x10-11 J/m3)* = (2.126056x10-11 J/m3)* + (-8.8224295x10-11 J/m3)*
Negative Dark Energy Pressure = Positive Matter Energy + Negative Inherent Milgröm Deceleration (cHo/Go)​

The Dark Energy and the 'Cosmological Constant' exhibiting the nature of an intrinsic negative pressure in the cosmology become defined in the overall critical deceleration and density parameters. The pressure term in the Friedmann equations being a quintessence of function n and changing sign from positive to negative to positive as indicated.

For a present measured deceleration parameter qdS=-0.5586, the DE Lambda calculates as -6.696x10-11 (N/m2=J/m3)*, albeit as a positive pressure within the negative quintessence.

2. An expanding multi-dimensional super-membraned open and closed Universe

The expansion of the universe can be revisited in a reformulation of the standard cosmology model Lambda-Cold-Dark-Matter or LCDM in terms of a parametrization of the standard expansion parameters derived from the Friedmann equation, itself a solution for the Einstein Field Equations (EFE) applied to the universe itself.
A measured and observed flat universe in de Sitter (dS) 4D-spacetime with curvature k=0, emerges as the result of a topological mirror symmetry between two Calabi Yau manifolds encompassing the de Sitter space time in a multi timed connector dimension.
The resulting multiverse or brane world so defines a singular universe with varying but interdependent time cyclicities.

It is proposed, that the multiverse initiates cyclic periods of hyper acceleration or inflation to correlate and reset particular initial and boundary conditions related to a baryonic mass seedling proportional to a closure or Hubble mass to ensure an overall flatness of zero curvature for every such universe parallel in a membrane time space but co-local in its lower dimensional Minkowski space-time.

On completion of a 'matter evolved' Hubble cycle, defined in characteristic Hubble parameters; the older or first universal configuration quantum tunnels from its asymptotic Hubble Event horizon into its new inflaton defined universal configuration bounded by a new Hubble node.
The multidimensional dynamics of this quantum tunneling derives from the mirror symmetry and topological duality of the 11-dimensional membrane space connecting two Calabi Yau manifolds as the respective Hubble nodes for the first and the second universal configurations.

Parallel universes synchronise in a quantized protoverse as a function of the original lightpath of the Instanton, following not preceding a common boundary condition, defined as the Inflaton.
The initial conditions of the Inflaton so change as a function of the imposed cyclicity by the boundary conditions of the paired Calabi Yau mirror duality; where the end of a Instanton cycle assumes the new initial conditions for the next cycle of the Instanton in a sequence of Quantum Big Bangs.

The outer boundary of the second Calabi Yau manifold forms an open dS space-time in 12-dimensional brane space (F-Vafa 'bulk' Omnispace) with positive spheroidal curvature k=+1 and cancels with its inner boundary as a negatively curved k=-1 hyperbolic AdS space-time in 11 dimensions to form the observed 4D/10-dimensional zero curvature dS space-time, encompassed by the first Calabi Yau manifold.

A bounded (sub) 4D/10D dS space-time then is embedded in a Anti de Sitter (AdS) 11D-space-time of curvature k=-1 and where 4D dS space-time is compactified by a 6D Calabi Yau manifold as a 3-torus and parametrized as a 3-sphere or Riemann hypersphere.
The outer boundary of the 6D Calabi Yau manifold then forms a mirror duality with the inner boundary of the 11D Calabi Yau event horizon and images the positive curvature in 12D-F-Vafa space in a 'convex lense' effect of 11-dimensional M-Witten spacetime.

Rps = λps/2π as the wormhole radius of the Instanton as a conformally transformed Planck-Length Lp = √{Goh/2πc3} from the Inflaton.
The Schwarzschild metric for 2Lp = 2GoMp/c2 transforms a 3D Planck-length in the Planck-mass Mp = √{hc/2πGo} from the Planck-boson gravitational fine structure constant 1 = 2πGoMp2/hc.

The Schwarzschild metric for the Weyl-wormhole radius Rps then defines a hypermass Mhyper as the conformal mapping of the Planck-mass Mp as Mhyper = ½{Rps/Lp}Mp = ½{Rps/Lp}2.Mps and where Mps = Eps/c2 = hfps/c2 = kTps/c2 in fundamental expressions for the energy of Abba-Eps as one part of the super membrane Eps.Ess in physical quantities of mass m, frequency f and temperature T.

c2 and h and k are fundamental constants of nature obtained from the initializing algorithm of the Mathimatia and are labeled as the 'square of lightspeed c' and 'Planck's constant h' and 'Stefan-Boltzmann's constant k' respectively. The complementary part of super membrane EpsEss is EssBaab. Eps-Abba is renamed as 'Energy of the Primary Source-Sink' and Ess-Baab is renamed as 'Energy of the Secondary Sink-Source'. The primary source-sink and the primary sink-source are coupled under a mode of mirror-inversion duality with Eps describing a vibratory and high energy micro-quantum quantum entanglement with Ess as a winding and low energy macro quantum energy. It is this quantum entanglement, which allows Abba to become part of Universe in the encompassing energy quantum of physicalized consciousness, defined in the magnetopolar charge.

The combined effect of the applied Schwarzschild metric then defines a Compton Constant to characterize the conformal transformation as: Compton Constant h/2πc = MpLp = MpsRps. Quantum gravitation now manifests the mass differences between Planck-mass Mp and Weyl mass Mps. The Black Hole physics had transformed Mp from the definition of Lp; but this transformation did not generate Mps from Rps, but rather hypermass Mhyper, differing from Mps by a factor of ½{Rps/Lp}2.

Every Inflaton defines three Hubble nodes or timespace mirrors; the first being the 'singularity - wormhole' configuration; the second the nodal boundary for the 4D/10D dS space-time and the third the dynamic lightpath bound for the Hubble Event horizon in 5D/11D AdS time-space.
The completion of a 'de Broglie wave matter' evolution cycle triggers the Hubble Event Horizon as the inner boundary of the time-space mirrored Calabi Yau manifold to quantum tunnel onto the outer boundary of the space-time mirrored Calabi Yau manifold in a second universe; whose inflaton was initiated when the light-path in the first universe reached its second Hubble node.

For the first universe, the three nodes are set in time-space as {3.3x10-31 s; 16.88 Gy; 3.96 Ty} and the second universe, time shifted in t1=to+t with to=1/Ho has a nodal configuration {to+1.4x10-33; to+3,957 Gy; to+972.7 Ty}; the latter emerging from the time-space as the instanton at time marker to.
A third universe would initiate at a time coordinate t2=to+t1+t as {1/Ho+234.472/Ho +5.8x10-36 s; to+t1+972.7 Ty; to+t1+250,223 Ty}; but as the second node in the second universe cannot be activated by the lightpath until the first universe has reached its 3.96 trillion year marker (and at a time for a supposed 'heat death' of the first universe due to exhaustion of the nuclear matter sources); the third and following nested universes cannot be activated until the first universe reaches its n=1+234.472=235.472 time-space coordinate at 3,974.8 billion years from the time instanton aka the Quantum Big Bang.

For a present time-space coordinate of npresent=1.13271 however; all information in the first universe is being mirrored by the time-space of the AdS space-time into the dS space-time of the second universe at a time frame of t = t1-to = 19.12 - 16.88 = 2.24 billion years and a multi-dimensional time interval characterizing the apparent acceleration observed and measured in the first universe of the Calabi Yau manifold compressed or compactified flat dS Minkowski cosmology. The solution to the Dark Energy and Dark Matter question of a 'missing mass' cosmology is described in this discourse and rests on the evolution of a multiverse in matter.

Yn = RHubble/rWeyl = 2πRHubbleWeyl = ωWeyl/Ho = 2πnWeyl = nps/2π = 1.003849x1049

2nd Inflaton/Quantum Big Bang redefines for k=1: RHubble(1) = n1RHubble = c/Ho(1) = (234.472)RHubble = 3.746x1028 m* in 3.957 Trillion Years for critical nk
3rd Inflaton/Quantum Big Bang redefines for k=2: RHubble(2) = n1n2RHubble = c/Ho(2) = (234.472)(245.813)RHubble = 9.208x1030 m* in 972.63 Trillion Years for critical nk
4th Inflaton/Quantum Big Bang redefines for k=3: RHubble(3) = n1n2n3RHubble = c/Ho(3) = (57,636.27)(257.252)RHubble = 2.369x1033 m* in 250.24 Quadrillion Years for critical nk
5th Inflaton/Quantum Big Bang redefines for k=4: RHubble(4) = n1n2n3n4RHubble = c/Ho(4) = (14,827,044.63)(268.785)RHubble = 6.367x1035 m* in 67.26 Quintillion Years for critical nk
...
(k+1)th Inflaton/Quantum Big Bang redefines for k=k: RHubble(k) = RHubble Π nk = c/Ho Π nk
.....

nk = ln{ωWeylRHubble(k)/c}/lnY = ln{ωWeyl/Ho(k)}/lnY

n1 = 234.471606...
n2 = 245.812422...
n3 = 257.251394...
n4 = 268.784888...

Dark Energy DE-Quintessence Λk Parameters:

A general dark energy equation for the kth universe (k=0,1,2,3,...) in terms of the parametrized Milgröm acceleration A(n); comoving recession speed V(n) and scale factored curvature radius R(n):

Λk (n) = GoMo/Rk(n)2 - 2cHo(Πnk)2/{n-ΣΠnk-1+Πnk)3} for negative Pressure Pk = -Λk(n)c2/4πGoRk

= {GoMo(n-ΣΠnk-1+Πnk)2/{(Πnk)2.RH2(n-ΣΠnk-1)2} - 2cHo(Πnk)2/{n-ΣΠnk-1+Πnk)3}

Λo = GoMo(n+1)2/RH2(n)2 - 2cHo/(n+1)3
Λ1 = GoMo(n-1+n1)2/n12RH2(n-1)2 - 2cHon12/(n-1+n1)3
Λ2 = GoMo(n-1-n1+n1n2)2/n12n22RH2(n-1-n1)2 - 2cHon12n22/(n-1-n1+n1n2)3
.....

Lambda-DE-Quintessence Derivatives:

Λk'(n) = d{Λk}/dn =
{GoMo/Πnk2RH2}{2(n-ΣΠnk-1+Πnk).(n-ΣΠnk-1)2 - 2(n-ΣΠnk-1).(n-ΣΠnk-1+Πnk)2}/{(n-ΣΠnk-1)4} - {-6cHo(Πnk)2}/(n-ΣΠnk-1+Πnk)4

= {-2GoMo/ΠnkRH2}(n-ΣΠnk-1+Πnk)/(n-ΣΠnk-1)3 + {6cHo(Πnk)2}/(n-ΣΠnk-1+Πnk)4

= {6cHo(1)2}/{(n-0+1)4} - {2GoMo/1.RH2}{(n-0+1)/(n-0)3}........................................ for k=0
= {6cHo(1.n1)2}/{(n-1+n1)4} - {2GoMo/n1.RH2}{(n-1+n1)/(n-1)3}................................ for k=1
= {6cHo(1.n1.n2)2}/{(n-1-n1+n1.n2)4} - {2GoMo/n1n2.RH2}{(n-1-n1+n1n2)/(n-1-n1)3}...... for k=2
.......

For k=0; {GoMo/3c2RH} = constant = n3/[n+1]5
for roots nΛmin = 0.23890175.. and nΛmax = 11.97186...
{GoMo/2c2RH} = constant = [n]2/[n+1]5

for Λo-DE roots: n+/- = 0.1082331... and n-/+ = 3.40055... for asymptote Λ0∞ = GoMo/RH2 = 7.894940128...x10-12 (m/s2)*

For k=1; {GoMo/3n13c2RH} = constant = [n-1]3/[n-1+n1]5 = [n-1]3/[n+233.472]5
for roots nΛmin = 7.66028... and nΛmax = 51,941.9..
{GoMo/2n14c2RH} = constant = [n-1]2/[n-1+n1]5 = [n-1]2/[n+233.472]5
for Λ1-DE roots: n+/- = 2.29966... and n-/+ = 7,161.518... for asymptote Λ1∞ = GoMo/n12RH2 = 1.43604108...x10-16 (m/s2)*

For k=2; {GoMo/3n13n23c2RH} = constant = [n-1-n1]3/[n-1-n1+n1n2]5 = [n-235.472]3/[n+57,400.794]5
for roots nΛmin = 486.7205 and nΛmax = 2.0230105x108
{GoMo/2n14n24c2RH} = constant = [n-1-n1]2/[n-1-n1+n1n2]5 = [n-235.472]2/[n+57,400.794]5
for Λ2-DE roots: n+/- = 255.5865... and n-/+ = 1.15382943...x107 for asymptote Λ2∞ = GoMo/n12n22RH2 = 2.37660590...x10-21 (m/s2)*

For k=3; {GoMo/3n13n23n33c2RH} = constant = [n-1-n1-n1n2]3/[n-1-n1-n1n2+n1n2n3]5 = [n-57,871.74]3/[n+1.47691729x107]5
for roots nΛmin = 67,972.496 and nΛmax = 8.3526797...x1011
{GoMo/2n14n24n34c2RH} = constant = [n-1-n1-n1n2]2/[n-1-n1-n1n2+n1n2n3]5 = [n-57,871.74]2/[n+1.47691729x107]5
for Λ3-DE roots: n+/- = 58,194.1... and n-/+ = 1.9010262...x1010 for asymptote Λ3∞ = GoMo/n12n22n32RH2 = 3.59120049...x10-26 (m/s2)*

and where

Πnk=1=no and Πnk-1=0 for k=0
with Instanton/Inflaton resetting for initial boundary parameters

= {GoMo(n-ΣΠnk-1+Πnk)2}/{[Πnk]2.RH2(n-ΣΠnk-1)2(ΠnkRHfps2)} = (Πnk)½Ωo

for Instanton-Inflaton Baryon Seed Constant Ωo = Mo*/MH* = 0.02803 for the kth universal matter evolution

k=0 for Reset n=nps=Hot and Λo/adeBroglie = GoMo(nps+1)2/{RH3nps2(fps2)} = GoMo/RHc2 = Mo/2MH = ½Ωo
k=1 for Reset n=1+nps and Λo/adeBroglie = GoMo(1+nps-1+n1)2/{[n1]2.RH3(1+nps-1)2(n1fps2)} = Mo/2n1MH = Mo/2MH* = ½Ωo*
k=2 for Reset n=n1+1+nps and Λo/adeBroglie = GoMo(n1+1+nps-1-n1+n1n2)2/{[n1n2]2.RH3(n1+1+nps-1-n1)2(n1n2fps2)} = ½Ωo**
k=3 for Reset n=n1n2+n1+1+nps and Λo/adeBroglie = GoMo(n1n2+n1+1+nps-1-n1-n1n2+n1n2n3)2/{[n1n2n3]2.RH3(n1n2+n1+1+nps-1-n1-n1n2)2(n1n2n3fps2)} = ½Ωo***
......

with nps = 2πΠnk-1.Xnkps/RH = Hotps = Ho/fps = ctps/RH and RH=2GoMH/c2

No=Hoto/no=Hot=n
N1=Hot1/n1=(n-1)/n1
N2=Hot2/n1n2=(n-1-n1)/n1n2
N3=Hot3/n1n2n3=(n-1-n1-n1n2)/n1n2n3
....
dn/dt=Ho
.....

Nk=Hotk/Πnk=(n-ΣΠnk-1)/Πnk
tk = t - (1/Ho)ΣΠnk-1 for no=1 and No=n

to=t=n/Ho=No/Ho=nRH/c
t1=t-1/Ho=(n-1)/Ho=[n1N1]/Ho
t2=t-(1+n1)/Ho=(n-1-n1)/Ho=(n1n2N2)/Ho
t3=t-(1+n1+n1n2)/Ho=(n-1-n1-n1n2)/Ho=(n1n2n3N3)/Ho
.......

R(n)=R(No)=noRH{n/[n+1]}=RH{n/[n+1]}
R1(N1)=n1RH{N1/[N1+1]}=n1RH{[n-1]/[n-1+n1]}
R2(N2)=n1n2RH{N2/[N2+1]}=n1n2RH{[n-1-n1]/[n-1-n1+n1n2]}
R3(N3)=n1n2n3RH{N3/[N3+1]}=n1n2n3RH{[n-1-n1-n1n2]/[n-1-n1-n1n2+n1n2n3}
.......

Rk(n) = ΠnkRH(n-ΣΠnk-1)/{n-ΣΠnk-1+Πnk}

.....= RH(n/[n+1]) = n1RH(N1/[N1+1]) = n1n2RH(N2/[N2+1]) =.....

Vk(n) = dRk(n)/dt = c{Πnk}2/{n-ΣΠnk-1+Πnk}2

.....= c/[n+1]2 = c/[N1+1]2 = c/[N2+1]2 =.....
.....= c/[n+1]2 = c(n1)2/[n-1+n1]2 = c(n1n2)2/[n-1-n1+n12n22]2 =.....

Ak(n) = d2Rk(n)/dt2 = -2cHo(Πnk)2/(n-ΣΠnk-1+Πnk)3

.....= -2cHo/(n+1)3 = -2cHo/n1(N1+1)3 = -2cHo/n1n2(N2+1)3=.....
..... = -2cHo/[n+1]3 = -2cHo{n1}2/[n-1+n1]3 = -2cHo(n1n2)2/[n-1-n1+n1n2]3 =.....

GoMo is the Gravitational Parameter for the Baryon mass seed; Curvature Radius RH = c/Ho in the nodal Hubble parameter Ho and c is the speed of light

Hubble Parameters:

H(n)|dS = {Vk(n)}/{Rk(n)} = {c[Πnk]2/[n-ΣΠnk-1+Πnk]2}/{Πnk.RH[n-ΣΠnk-1]/(n-ΣPnk-1+Πnk)} = ΠnkHo/{[n-ΣΠnk-1][n-ΣΠnk-1+Πnk]}

H(n)|dS = ΠnkHo/{[n-ΣΠnk-1][n-ΣΠnk-1+Πnk]}

.....= Ho/{[n][n+1]}=Ho/T(n) = n1Ho/{[n-1][n-1+n1]} = n1n2Ho/{[n-1-n1][n-1-n1+n1n2]} =..... for dS

H(n)'|dS = Ho/[n-ΣΠnk-1] for oscillating H'(n) parameter between nodes k and k+1 ||nps+ΣΠnk-1 - ΣΠnk||

.....= Ho/n = Ho/(n-1) = Ho/(n-1-n1) =..... for AdS

For initializing scale modulation Rk(n)Ads/Rk(n)dS + ½ = ΠnkRH(n-ΣΠnk-1)/{ΠnkRH(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)} + ½Πnk = {n - ΣΠnk-1 + Πnk + ½} reset coordinate

dH/dt = (dH/dn)(dn/dt) = -Πnk.Ho2{(2n-2ΣΠnk-1+Πnk)(n-ΣΠnk-1+Πnk+½Πnk)}/{n2-2nΣΠnk-1+(ΣΠnk-1)2+Πnk[n-ΣΠnk]}2
= -2ΠnkHo2{[n - ΣΠnk-1 + Πnk]2 - ¼ΣΠnk2}/{(n-ΣΠnk-1)(n-ΣΠnk-1+Πnk)}2

dH/dt|dS = -2ΠnkHo2{[n - ΣΠnk-1 + Πnk]2 - ¼(ΣΠnk)2}/{(n-ΣΠnk-1)(n-ΣΠnk-1+Πnk)}2

.....= -2Ho2([n+1]2-¼)/{n[n+1]}2 = -2n1Ho2{[n-1+n1]2-¼n12}/{[n-1][n-1+n1]}2 = -2n1n2Ho2{[n-1-n1+n1n2]2-¼n12n22}/{[n-1-n1][n-1-n1+n1n2]}2 =.....

dH/dt = (dH/dn)(dn/dt) = -Hoc/{(RH(n-ΣΠnk-1)2} = -Ho2/{n-ΣΠnk-1}2 for AdS

.....= -Ho2/n2 = Ho2/(n-1)2 = -Ho2/(n-1-n1)2 = .....

dH/dt + 4πGoρ = - 4πGoP/c2

dH/dt + 4πGoMo/Rk(n)3 = Λk(n)/Rk(n) = - 4πGoP/c2 = GoMo/Rk(n)3 - 2(Πnk)Ho2/{(n-ΣΠnk-1)(n-ΣΠnk-1+Πnk)2} for dS with

{-4π}P(n)|dS = Moc2/Rk(n)3 - 2Πnk(Hoc)2/{Go(n-ΣΠnk-1)(n-ΣΠnk-1+Πnk)2} = Moc2(n-ΣΠnk-1+Πnk)3/{Πnk.RH(n-ΣΠnk-1)}3 - 2ΠnkHo2c2/{Go(n-ΣΠnk-1)(n-ΣΠnk-1+Πnk)2}

Λk(n)/Rk(n) = -4πGoP/c2 = GoMo/Rk(n)3 - dH/dt = GoMo/{RH(n-ΣΠnk-1)}3 - Ho2/{n-ΣΠnk-1}2 for AdS with

{-4π}P(n)|AdS = Moc2/Rk(n)3 - (Hoc)2/{Go(n-ΣΠnk-1)2} = Moc2/{RH(n-ΣΠnk-1)}3 - Ho2c2/{Go(n-ΣΠnk-1)2}

Deceleration Parameters:

qAdS(n) = -Ak(n)Rk(n)/Vk(n)2 = -{(-2cHo[Πnk]2)/(n-ΣΠnk-1+Πnk)3}{ΠnkRH(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}/{[Πnk]2c/(n-ΣΠnk-1+Πnk)}2 = 2(n-ΣΠnk-1)/Πnk

qdS(n) = 1/qAdS+dS(n) - 1 = Πnk/{2[n-ΣΠnk-1} - 1

with Ak(n)=0 for AdS in areset = Rk(n)AdS/Rk(n)dS + ½ = {RH(n-ΣΠnk-1)}/{RH(n-ΣΠnk-1)/(n-ΣΠnk-1+1)} + ½ = n-ΣΠnk-1+1+½

Scalefactor modulation at Nk = {n-ΣΠnk-1}/Πnk = ½ reset coordinate

.....= 2n = 2(n-1)/n1 = 2(n-1-n1)/(n1n2) = 2(n-1-n1-n1n2)/(n1n2n3) = ..... for AdS

.....= 1/{2n} -1 = n1/{2[n-1]} -1 = n1n2/{2(n-1-n1)} -1 = n1n2n3/{2(n-1-n1-n1n2)} -1 = ..... for dS

Dark Energy Initiation for qdS=1 with qAdS=1

k=0 for n = ½ = 0.50000 for qdS=0 with qAdS=1
k=1 for n = ½n1+1 = 118.236.. for qdS=0 with qAdS=1
k=2 for n = ½n1n2+n1+1 = 29,053.605.. qdS=0 with qAdS=1
k=3 for n = ½n1n2n3+n1n2+n1+1 = 7,471,394.054.. qdS=0 with qAdS=1

Temperature:

T(n) ={Moc2/(1100σπ2.Rk(n)2.tk)} and for tk = (n-ΣΠnk-1)/Ho

Tk(n) ={HoMoc2(n-ΣΠnk-1+Πnk)2/[1100σπ2.RH2.(n-ΣΠnk-1)3]}
={(Ho3Mo(n-ΣΠnk-1+Πnk)2)/[1100σπ2(n-ΣΠnk-1)3]} = {18.199(n-ΣΠnk-1+Πnk)2/(n-ΣΠnk-1)3}

T(n) .....= {18.2[n+1]2/n3} ={18.2[n-1+n1]2/(n-1)3} = {18.2[n-1-n1+n1n2]2/(n-1-n1)3} =.....

Comoving Redshift:

z + 1 = √{(1+v/c)/(1-v/c)} = √{([n-ΣΠnk-1+Πnk]2+[Πnk]2)/([n-ΣΠnk-1+Πnk]2-[Πnk]2)} =
√{([n-ΣΠnk-1]2+2Πnk(n-ΣΠnk-1)+2(Πnk)2)/([n-ΣΠnk-1]2+2Πnk(n-ΣΠnk-1)} = √{1 + 2(Πnk)2/{(n-ΣΠnk-1)(n-ΣΠnk-1+2Πnk)}

z+1 = √{ 1 + 2/{[n2-2nΣΠnk-1 +(ΣΠnk-1)2+2n-2ΣΠnk-1} = √{1+2/{n(n+2-2ΣΠnk-1) + ΣΠnk-1(ΣΠnk-1-2)}}

....= √{1+2/(n[n+2])} = √{1+2/([n-1][n-1+2n1])} = √{1+2/([n-1-n1][n-1-n1+2n1n2])} =......

Baryon-Dark Matter Saturation:

ΩDM = 1-ΩBM until Saturation for BM-DM and Dark Energy Separation

ρBM+DM/ρcritical = ΩoY{[n-ΣΠnk-1]/Πnk}/{(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3 = MoY{[n-ΣΠnk-1]/Πnk}/{ρcriticalRk(n)3}

Baryon Matter Fraction ΩBM = ΩoY{Nk} = Ωo.Y{[n-ΣΠnk-1]/Πnk}

Dark Matter Fraction ΩDM = ΩoY{[n-ΣΠnk-1]/Πnk}{1-{(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3/{(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3 = ΩoY{[n-ΣΠnk-1]/Πnk}{(n-ΣΠnk-1+Πnk)3-(n-ΣΠnk-1)3}/{n-ΣΠnk-1}3
= ΩoY{[n-ΣΠnk-1]/Πnk}{(1+Πnk/[n-ΣΠnk-1])3 -1} = ΩBM{(1+Πnk/[n-ΣΠnk-1])3 -1}

Dark Energy Fraction ΩDE = 1- ΩDM - ΩBM = 1 - ΩBM{(1+Πnk/[n-ΣΠnk-1])3}

ΩBM=constant=0.0553575 from Saturation to Intersection with Dark Energy Fraction

ΩoY{[n-ΣΠnk-1]/Πnk} = ρBM+DMRk(n)3/MH = [Nk]3/[Nk+1]3 = {(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3 = Rk(n)3/VH = VdS/VAdS
for ρBM+DM = MH/RH3 = ρcritical and for Saturation at Ni = 6.541188... = constant ∀ Ni

(Mo/MH).Y{[n-ΣΠnk-1]/Πnk} = {(n-ΣΠnk-1)/(n-ΣΠnk-1+Πnk)}3 with a Solution for f(n) in Newton-Raphson Root Iteration and first Approximation x0

xk+1 = xk - f(n)/f'(n) = xk - {(Mo/MH).Y{[n-∑∏nk-1]/Πnk} - (n-∑∏nk-1)/(n-ΣΠnk-1+Πnk)3}/{(Mo/MH).[lnY]Y{[n-ΣΠnk-1]/Πnk} - 3(n-ΣΠnk-1)2/(n-ΣΠnk-1+Πnk)4}

x1 = x0 - {(Mo/MH).Y[n] - (n/n+1)3}/{(Mo/MH).[lnY]Y[n] - 3n2/[n+1]4}
= x0 - {(Mo/MH).Y{N0} - (N0)3/(N0+1)3}/{(Mo/MH).[lnY]Y{N0} - 3(N0)2/1(N0+1)4}
x1 = x0 - {(Mo/MH).Y{[n-1]/n1} - (n-1)3/(n-1+n1)3}/{(Mo/MH).[lnY]Y{[n-1]/n1} - 3(n-1)2/(n-1+n1)4}
= x0 - {(Mo/MH).Y{N1} - (N1)3/(N1+1)3}/{(Mo/MH).[lnY]Y{N1} - 3(N1)2/n1(N1+1)4}
x1 = x0 - {(Mo/MH).Y{[n-1-n1]/n1n2} - (n-1-n1)3/(n-1-n1+n1n2)3}/{(Mo/MH).[lnY]Y{[n-1-n1]/n1n2} - 3(n-1-n1)2/(n-1-n1+n1n2)4}
= x0 - {(Mo/MH).Y{N2} - (N2)3/(N2+1)3}/{(Mo/MH).[lnY]Y{N2} - 3(N1)2/n1n2(N2+1)4}
.......

n = 1.N0 = Ni = 6.541188....⇒ Ni ∀i for ∏nk = n0 = 1
n = n1N1+1 = (234.472)(6.541188...)+1 = 1534.725.... for ∏nk = n0n1 = n1
n = n1n2N2+1+n1 = (234.472x245.813)(6.541172)+1+234.472 = 377,244.12.... for ∏nk = n0n1n2 = n1n2
n = n1n2n3N3+1+n1+n1n2 = (234.472x245.813x257.252)(6.541172)+1+234.472+(234.472x245.813) = 97,044,120.93.... for ∏nk = n0n1n2n3= n1n2n3
......

Baryon-Dark Matter Intersection:

Nk=√2 for n = √2.Πnk + ΣΠnk-1
n0 = 1.√2 + 0 = no
n1 = n1√2 + 1 = 332.593 = n1√2 + 1
n2 = n1n2√2 + 1 + n1 = 81,745.461
n3 = n1n2n3√2 + 1 + n1 +n1n2 = 21,026,479.35

.....

Hypermass Evolution:

Yk{(n-ΣΠnk-1)/Πnk} = 2πΠnk.RHps = Πnk.RH/rps = ΠnkMH*k/mH*k for MH = c2RH/2Go and mH = c2rps/2Go

Hypermass MHyper = mH.Yk{(n-ΣΠnk-1)/Πnk}

.....= Yn = Y([n-1]/n1) = Y([n-1-n1]/n1n2) =.....

k=0 for MHyper = MH = 1.MH = mH.Y{(n)} with n = 1.{ln(2π/nps)/lnY} = n1
= 234.472

k=1 for MHyper = n1.MH = MH* = mH.Y{(n-1)/n1} with n = [1] + n1.{ln(2πn1/nps)/lnY} = [1] + n1n2
= 1 + 234.472x245.812 = 57,637.03

k=2 for MHyper = n1n2.MH = MH** = mH.Y{(n-1-n1)/n1n2} with n = [1 + n1] + n1n2.{ln(2πn1n2/nps)/lnY} = [1 + n1] + n1n2n3
= 235.472 + 234.472x245.812x257.251 = 14,827,185.4

k=3 for MHyper = n1n2n3.MH = MH*** = mH.Y{(n-1-n1-n1n2)/n1n2n3} with n = with n = [1 + n1 + n1n2] + n1n2n3.{ln(2πn1n2n3/nps)/lnY} = [1 + n1 + n1n2] + n1n2n3n4
= 57,871.74 + 234.472x245.812x257.251x268.785 = 3,985,817,947.8

The Friedmann's acceleration equation and its form for the Hubble time derivative from the Hubble expansion equation substitutes a curvature k=1 and a potential cosmological constant term; absorbing the curvature term and the cosmological constant term, which can however be set to zero if the resulting formulation incorporates a natural pressure term applicable to all times in the evolvement of the cosmology.

Deriving the Instanton of the 4D-dS Einstein cosmology for the Quantum Big Bang (QBB) from the initial-boundary conditions of the de Broglie matterwave hyper expansion of the Inflaton in 11D AdS then enables a cosmic evolution for those boundary parameters in cycle time n=Hot for a nodal 'Hubble Constant' Ho=dn/dt as a function for a time dependent expansion parameter H(n)=Ho/T(n)=Ho/T(Hot).

It is found, that the Dark Matter (DM) component of the universe evolves as a function of a density parameter for the coupling between the inflaton of AdS and the instanton of dS space times. It then is the coupling strength between the inflationary AdS brane epoch and the QBB dS boundary condition, which determines the time evolution of the Dark Energy (DE).
Parametrization of the expansion parameter H(n) then allows the cosmological constant term in the Friedmann equation to be merged with the scalar curvature term to effectively set an intrinsic density parameter at time instantenuity equal to Λ(n) for ΛpsQBB=GoMo/λps2 and where the wavelength of the de Broglie matter wave of the inflaton λps decouples as the Quantum Field Energy of the Planck Boson String in AdS and manifests as the measured mass density of the universe in the flatness of 4D Minkowski spacetime.

3. Temperature Evolution in the Multiverse

In the early radiation dominated cosmology; the quintessence was positive and the matter energy dominated the intrinsic Milgröm deceleration from the Instanton n=nps to n=0.18023 (about 3.04 Billion years) when the quintessence vanished and including a Recombination epoch when the hitherto opaque universe became transparent in the formation of the first hydrogen atoms from the quark-lepton plasma transmuted from the X-L Boson string class HO(32) of the Inflaton epoch preceding the Quantum Big Bang aka the Instanton.

From the modular membrane duality for wormhole radius rps = λps/2π, the critical modulated Schwarzschild radius rss = 2πλss = 2πx1022 m* for λps = 1/λss
and for an applied scalefactor a = n/[n+1] =λss/RH = {1-1/[n+1]}

for a n=Hot coordinate nrecombination = 6.259485x10-5 or about 6.259485x10-5(16.88 Gy) = 1.056601 Million years
attenuated by exp{-hf/kT} = e-1 = 0.367879 to a characteristic cosmological time coordinate of 0.36788x1.056601 = 388,702 years after the Instanton nps.

The attenuation of the recombination coordinate then gives the cosmic temperature background for this epoch in the coordinate interval for the curvature radius
R(n=2.302736x10-5) = 3.67894x1021 m* to R(n=6.259485x10-5) = 1022 m*.
This radial displacement scale represents the size of a typical major galaxy in the cosmology; a galactic structure, which became potentialised in the Schwarzschild matter evolution and its manifestation in the ylemic prototypical first generation magnetar-neutron stars, whose emergence was solely dependent on the experienced cosmic temperature background and not on their mass distributions.

The temperature evolution of the Instanton can be written as a function of the luminosity L(n,T) with R(n)=RH(n/[n+1]) as the radius of the luminating surface
L(nps,T(nps) = 6π2λps2.σ.Tnps4 = 2.6711043034x1096 Watts*, where σ = Stefan's Constant = 2π5k4/15h3c2 and as a product of the defined 'master constants' k, h, c2, π and 'e'.

L(n,T) = 3HoMo.c2/550n and for Temperature T(nps) ----------- T(nps) = 2.93515511x1036 Kelvin*.

T(n)4 = HoMoc2/(2π2σRH2[550n3/[n+1]2]) for
T(n)4 = {[n+1]2/n3}HoMoc2/(2π2σRH2[550]) = 18.1995{[n+1]2/n3} (K4/V)*

for a temperature interval in using the recombination epoch coordinates T(n1=6.2302736x10-5) = 2945.42 K* to T(n2=6.259485x10-5) = 2935.11 K*

This manifests as a 'false vacuum' and as a temperature gradient, as a causation of the Big Bang Instanton on physical grounds.
The metaphysical ground is the symmetry breaking from the source parity violation described in the birth and necessity of the Graviton to resymmetrize the UFoQR.

T(nps) of the singularity is 0.0389 or 3.89% of the pre-singularity.

So the POTENTIAL Temperature manifests as 3.89% in the KINETIC Temperature' which doubles in the Virial Theorem to 7.78% as 2KE + PE = 0:
TEMPERATURE/T(nps)=7.544808988..x1037/2.93515511x1036=25.705=1/0.03890...

Applying the actual VPE at the Instanton to this temperature gradient:

ρVPEEMR = {4πEpsps3}/{8π5Eps4/15h3c3} = 15/2π4 = 0.07599486.. = 1/12.9878.. indicating the proportionality EVPE/EEMR = kTps/kTEMR = 2Tps/Tpotential at the Instanton from the Inflaton as a original form of the virial theorem, stating the Kinetic Energy of the Instanton and the QBB Lambda to be twice the Potential Energy of the de Broglie wave matter Inflaton, then manifesting as the Mo/2MHubble = rHyper/2RHubble Schwarzschild mass cosmo-evolution.

Now reducing the timeinstanton tps=nps/Ho of 3.33x10-31 seconds by the Temperature Gradient in the Luminosity Function gives you the scalar Higgs Potential Maximum at a pre-singularity time of tHiggsPE=tps.T(nps)/TEMPERATURE=1.297x10-32 seconds.

This then extrapolates the Big Bang singularity backwards in Time to harmonise the equations and to establish the 'driving force of the vacuum' as potential scalar Higgs Temperature Field.
All the further evolvement of the universe so becomes a function of Temperature and not of mass.
The next big phase transition is the attunement of the BOSONIC UNIFICATION, namely the 'singularity' temperature Tps=1.41x1020 K with the Luminosity function.
This occurs at a normal time of 1.9 nanoseconds into the cosmology.

It is then that the universe as a unity has this temperature and so allows BOSONIC differentiation between particles. The INDIVIDUATED PHOTON of the mass was born then and not before, as the entire universe was a PHOTON as a macroquantised superstring up to then.
The size of the universe at that time was that of being 1.14 metres across.
Next came the electroweak symmetry breaking at 1/365 seconds and at a temperature of so 1015 Kelvin* and so it continued.

The lower dimensional lightpath x=ct in lightspeed invariance c=lf so becomes modular dualised in the higher dimensional lightpath of the tachyonic de Broglie Inflaton-Instanton Vdebroglie=c/nps of the Inflaton.

{(2-n)(n+1)}3/n3 = VdS'/VdS ......(4.36038 for npresent) in the first completing Hubble cycle
n3/(2-n)3 =VAdS/VdS' ................. (2.22379 for npresent) in the first completing Hubble cycle
(n+1)3 = VAdS/VdS .....................(9.69657 for npresent) in the first completing Hubble cycle

ρcritical = 3Ho2/8πGo {Sphere} and Ho2/4π2Go {Hypersphere-Torus in factor 3π/2} (constant for all n per Hubble cycle)
ρcritical = 3.78782x10-27 [kg/m3]* and 8.038003x10-28 [kg/m3]*

ρdSVdS = ρdS'VdS' = ρAdSVAdS = ρcriticalVHubble = MHubble = c2RH/2Go = 6.47061227x1052 kg*

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Inflation Curvature, Waved Matter and Hypermass

Describing the Einstein Lambda in the form of a parametrized Curvature Radius Λ(n)/RHubble= Λ(n)Ho/c = Λ(n)/RH in AdS then enables the scale of the classically geometric Einstein Lambda in squared Hubble units to unitize the quantum geometric Planck-brane-string units by modular mirror duality between the curvature 1/R(n)2 and its radius R(n) with the gravitational parameter G(n)(M(n) modulating the mass M in its Schwarzschilded 'eternal' form to the energy content in the universe by E=mc2.

As the magnitude of the Einstein Lambda of the instanton is of the order of 2x1085 acceleration units and relates to the baryonic matter (BM) density in the seedling mass Mo/2M =½ΩBMps; with 'closure' mass M=RH.c2/2Go=c3/2GoHo relates to the wormhole mass mps=hfps/c2 =2.222..x10-20 kg; as quantum eigenstate; the coupling between the Planck density ρP=lP3/mP=1.85x1096 and the 'critical closure' density ρH=M/RH3 becomes subject to the overall mass evolution from the wormhole mass to the 'closure mass' over the evolution cycle, ending after for nreset=234.5 for 3.96 Trillion years.

The coupling between the Planck Density and the Inflaton-Instanton Density so is: mps/RH3 = hfpsc4/8Go3MH3 = 5.45x10-99 .

A modular brane mirror-T duality between the inversion properties of two parts of a heterotic supermembrane (class HE(8x8)) and can be expressed in the unitary dimensions of the Gravitational Constant Go in [m3][kg-1][s-2]=(Volume)(Angular Acceleration)/(Mass)=(Angular Acceleration)/(Density).

Brane mirror duality unifies the electromagnetic and gravitational interactions via the coupling of their fine structures.
The quantization of mass m so indicates the coupling of the Planck Law in the frequency parameter to the Einstein law in the mass parameter.
The postulative basis of M-Theory utilizes the coupling of two energy-momentum eigenstates in the form of the modular duality between so termed 'vibratory' (high energy and short wavelengths) and 'winding' (low energy and long wavelengths) self-states.

The 'vibratory' self state is denoted in: Eps=Eprimary sourcesink=hfps=mpsc2 and the 'winding' and coupled self state is denoted by: Ess=Esecondary sinksource=hfss=mssc2

The F-Space Unitary symmetry condition becomes: fpsfss=rpsrss=(λps/2π)(2πλss)=1

The coupling constants between the two eigenstates are so: EpsEss=h2 and Eps/Ess=fps2=1/fss2
The Super-membrane EpsEss then denotes the coupled superstrings in their 'vibratory' high energy and 'winded' low energy self states.

The coupling constant for the vibratory high energy describes a MAXIMISED frequency differential over time in df/dt|max=fps2 and the coupling constant for the winded low energy describes its MINIMISED reciprocal in df/dt|min=fss2.

F-Theory also crystallizes the following string formulations from the EpsEss superbrane parameters.

Electromagnetic Fine structure: αe = 2πke2/hc = e2/2ε0hc

Gravitational Fine structure (Electron): αg = 2πGome2/hc = {me/mPlanck}2

Gravitational Fine structure (Primordial Nucleon): αn = 2πGomc2/hc

Gravitational Fine structure (Planck Boson): αPlanck = 2πGomPlanck2/hc

1/Eps=e*=2Rec2=√{4αhce2/2πGome2}=2e√α[mP/me=2e√{αeg} = {2e2/me}√(k/Go)=2e2/Gome = e2/2πεome
for Go = 1/k = 4πεo for the cosmological unification of the fine structures.

Eps = 1/Ess = 1/e* = ge}/2e = Gome/2e2

Here e* is defined as the inverse of the sourcesink vibratory superstring energy quantum Eps=E* and becomes a New Physical Measurement Unit is the StarCoulomb (C*) and as the physical measurement unit for 'Physical Consciousness'.

Re is the 'classical electron radius' coupling the 'point electron' of Quantum- Electro-Dynamics (QED) to Quantum Field Theory (QFT) and given in the electric potential energy of Coulomb's Law in: mec2=ke2/Re; and for the electronic restmass me.
Alpha α is the electromagnetic fine structure coupling constant α=2πke2/hc for the electric charge quantum e, Planck's constant h and light speed constant c.
Go is the Newtonian gravitational constant as applicable in the Planck-Mass mP=√(hc/2πGo).

Alternatively expressed, the mass seedling Mo of the QBB manifests in an emerging 'Black Hole' evolution and is bounded by the 'closure' mass M=MHubble. There so must be an energy gradient between the Hubble mass and the seedling mass in direct proportion to the de Broglie inflaton/instanton event.

The universe begins with a baryon matter seed of 2.813% in AdS spacetime, which allows the emergence of a first generation family of 'eternal' Black Holes to seed 'eternal' White Holes manifesting as quasars which seed galaxies from a first generation of proto-stars as a function of temperature and independent of mass. Those 'ylem' stars can be shown to be naturally degenerate 'proto' magnetars and neutron stars, whose gravitational inward pressure is balanced by their thermal heat content deriving from the Cosmic radiation temperature.

The general Jeans formulation for ylem stars is Rylem = √{kTRe3/Gomc2}, Re=e2/4πεomec2 and mc is a prototypical nucleon mass.

The Dark Energy Interaction Goldstone Gauge Boson is the Graviton manifesting from its 11/5D AdS membrane space Dirichlet 'open string' attachment from AdS space-time into dS space-time.

" Spacetime tells matter how to move; matter tells spacetime how to curve."

Wheeler's succinct summary of Einstein's theory of general relativity, in Geons, Black Holes, and Quantum Foam, p. 235. - 1998 by John Archibald Wheeler and Kenneth Ford; W.W.Norton and Company; New York, London

The quote of John Archibald Wheeler can be extended in a question.

"Is the presence of matter required for spacetime to curve or is the presence of spacetime sufficient for a matter dynamic to emerge and to eventuate?"

The Birth of Space and Time with Space-time Inflation Curvature preceding Big Banged Wormhole Matter

The problem of the singularity regarding the creation event, known as the Quantum Big Bang in General Relativity is well addressed in the literature of science and an appropriate solution to the infinite continuous regression of space-time parameters is resolved in a disengagement and an unnecessity of and for a prior existing space-time background for matter to act within.
It is the nature of the string itself, which in particular initial- and boundary conditions allows the concepts of space and time to emerge from the qualitative and quantitative nature of the string definition itself.

In particular a discretization of dynamical parameters of an describing cosmology in defined Planckian parameters serves to replace the infinite mathematical point like singularity to a so called Planck string vibration formulated as the Planck length lPlanck and which can be considered to be a minimum displacement as a wormhole radius.
Any displacement scale below the Planck length then is rendered unphysical and so becomes mathematically inapplicable to describe the dynamics in a physical universe, described by a cosmology, which defines a string epoch characterized by a cosmological inflationary Inflaton from a defined Planck-Length-Quantum-Oscillation/Fluctuation to a so labeled Quantum Big Bang Instanton.

The Big Bang Instanton becomes defined in a final manifestation of the Planckian Supermembrane (Class I at Planck Time) from the Inflaton to the Instanton (Class HE 8x8 at Weyl-Wormhole Time) and transforming the string energies across string classes from I to IIB, HO 32 and IIA to HE 8x8.

The Inflaton defined a 11-dimensional supermembraned de Sitter closed - and positively curved cosmology with a defined Hubble Event horizon for a positive spheroidal curvature information bound.
This closed universe contained no matter seed, but was defined in its curvature through a unification condition relating the electromagnetic fine structure alpha {α=2πke2/hc} to the gravitational finestructure omega {ω = 2πGomPlanck2/hc} via ke2 = e2/4πεo = GoMunification2 for e2 = {Go/k}Munification2
requiring dimensional mensuration identity in inflaton space [C2/Jm]=[Farad/meter] = [Jm/kg2] for [C] = [C*] = [Star-Charge Coulomb] = [m3/s2] = [VolumexAngular Acceleration] and for the Maxwell Constant 1/c2 = μoo = {120π/c}{1/120πc} and 'Free Space' Inflaton Impedance Zo= electric field strength E/magnetic field strength H = √(μoo) = cμo = 1/cεo = 120π}.

Therefore,
[Go]mod =[4πεo]mod = [1/k]mod and the inflaton dimensionless string modular unity is Gok=1 for e2 = Go2.Munification2 = Munification2/k2 and Munification = 30[ec] that is 30 modulated magnetic monopole masses. It is this 30[ec]modular inflaton mass, which represents the initial breaking of the inherent super-symmetry of the Planck superstring class I at the Planck energy level to the monopole superstring energy of superstring class IIB with the Planck mass being replaced by 30 monopole masses as the integration of 30 [ec] monopole masses at the [ec3]mod = 2.7x1016 GeV energy level of the Grand Unification Energy separating the quantum gravity from the GUT symbolized as SEW.G.

Setting ω=1 defines the Planck-Mass and setting a proto-nucleon seed mc=mPlanck9 allows the breaking of the inflaton super-symmetry in the superstring classes.
Replacing the proto-nucleon mass mc = √{hc/2πGo}.{60πe2/h}9 = 9.924724523x 10-28 kg by the effective electron mass me = ke2/2Go(1.125x1012) =9.290527148x10-31 kg sets the Electromagnetic Interaction/Gravitational Interaction ratio EMI/GI = e2/Go2me2 = {e/Gome}2 = 2.421821677x1042 using string units.

The Instanton following the Inflaton then defines a 10-dimensional superstringed Anti de Sitter open - and negatively hyperbolically curved cosmology, bounded in the 11-dimensional asymptotic Hubble Event Horizon.

Modular String Duality and the Wormhole Curvature Boundary

The concept of modular (Mirror/T) duality in super-membrane theory relates a maximum or large spacial displacement radius R as a low frequency and low energy named as a 'winding mode' to its inverse minimum or small spacial displacement radius 1/R as a high frequency and high energy as a 'vibratory mode'.
The utility of either 'string mode' would then result in an identical physical description either using a 'macro quantum' radius R or a 'micro quantum' radius 1/R.

c = λmin.fmax = 2πRmin.fmax as light speed invariance for the vibratory string mode Rcurvature = Rmin = λmin /2π = Wormhole Perimeter/2π

1/c = 1/(λmin.fmax) = λmax.fmin = λmax/fmax = Rmax.fmin/2π as lightspeed invariance for the winding string mode Rcurvature = Rmax = 2π.λmax = 2π/Wormhole Perimeter

For the Harmonic Planck Energy Oscillator Energy Eo = ½hfo = ½moc2 = ½kTPlanck

Planck Mass = mPlanck = √{hc/2πGo}
Planck Energy = EPlanck = mPlanck.c2 = √{hc5/2πGo} = hfPlanck = hc/lPlanck = kTPlanck
Planck Length =lPlanck = λPlanck/2π = √{hGo/2πc3}
Planck Temperature = TPlanck = EPlanck/k = √{hc5/2πk2Go}
Planck Density = ρPlanck= mPlanck/VPlanck = √{4π2c10/h2Go4}/2π2 = c5/πhGo2= 9.40x1094 kg/m3 for 9x1060 permutation vibratory string eigenstates by |fps2|mod.

Energy Density Inflaton/Energy Density Instanton = EPlanck.VBigBang/EBigBangVPlanck with minimum Inflaton Planck Oscillator: EoPlanck = ½mPlanckc2
= mPlanck.rwormhole3/mwormhole.lPlanck3 = √{(hc/2πGo)(2πc3/hGo)}(2πc3/hGo)(rwormhole3/mwormhole} = (c2/Go)(2πc3/hGo){rwormhole3/mwormhole}
= (2πc5/hGo2){rwormhole3/mwormhole} = {4π2k2/h2Go} (hc5/2πGok2){rwormhole3/mwormhole} = {kTPlanck}2(2πrwormhole)2{1/h2Go}{rwormhole/mwormhole}
= {EPlanck}2.{c/hfwormhole}2.{1/Go}}{rwormhole/mwormhole} = {EPlanck/EBigBang}2.{rwormhole}{c2/Gomwormhole} for the minimum Instanton Planck Oscillator: EoPlanck = ½mwormholec2

VBigBang/VPlanck = {EPlanck/EBigBang}.{rwormhole}{c2/Gomwormhole} for EVBigBang/EVPlanck = EVInstanton/EVInflaton = rwormhole/Rowormhole = NAvagadro-Instanton and counting the amount of wormhole string transformed from the Inflaton as the Instanton of the Quantum Big Bang and as the constant 5.801197676..x1023 in string units.

The Coupling of the Energy Laws by the Self-Frequency of the Quantum for Mass

It has been discovered, that the universe contains an intrinsic coupling-parameter between its inertial mass content and its non-inertial energy content.
The matter in the universe is described by the physical parameter termed Mass (M), say as proportional to Energy (E) in Einstein's famous equation Mass M=E/c2.
This mass M then reappears in Newtonian mechanics as the change in momentum (p) defining the Inertial Mass (Mi) as being proportional to some applied Force (F) or the 'work done' for a particular displacement {F=dp/dt for p=mv and v a kinematic velocity as the ratio of displacement over time generalised in the light path X=cT}.

It is also well understood, that the inertial mass Mi has a gravitational counterpart described not by the change in momentum of inertia carrying matter agglomerations; but by the geometric curvature of space containing matter conglomerations. This Gravitational Mass Mg is measured to be equivalent to the Inertial Mass Mi and is formulated in the 'Principle of Equivalence' in Einstein's Theory of General Relativity.
F-Theory then has shown, that this Inertial Mass Mi is coupled inherently to a 'mass-eigen' frequency via the following formulation:

(1) Energy E=hf=mc2 (The Combined Planck-Einstein Law)
(2) E=hf iff m=0 (The Planck Quantum Law E=hf for light speed invariance c=λf)
(3) E=mc2 iff f=fo=fss (The Einstein Law E=mc2 for the light speed upper limit)

(1) Whenever there is mass (M=Mi=Mg) occupying space; this mass can be assigned either as a photonic mass {by the Energy-Momentum relation of Special Relativity: E2=Eo2+(pc)2} by the photonic momentum p=h/λ=hf/c} OR a 'rest mass' mo=m/√[1-(v/c)2] for 'rest energy' Eo=moc2.

The 'total' energy for the occupied space so contains a 'variable' mass in the 'combined' law; but allows particularisation for electromagnetic radiation (always moving at the Maxwell light speed constant c in Planck's Law and for the 'Newtonian' mass M in the Einstein Law.

(2) If M=0, then the Einstein Law is suppressed in favour of the Planck Law and the space contained energy E is photonic, i.e. electromagnetic, always dynamically described by the constancy of light speed c.

(3) If M>0, then there exists a mass-eigen frequency fss=fo=Ess/h=mssc2/h, which QUANTIZES all mass agglomerations m=Σmss in the mass quantum mss=Ess/c2.

The Wave Matter of de Broglie: λdeBroglie = h/p

The Wave matter of de Broglie from the Energy-Momentum Relation is applied in a (a) nonrelativistic, a (b) relativistic and a (c) superluminal form
in the matter wavelength: λdeBroglie = h/p = hc/pc for (pc) = √{E2 - Eo2}= moc2.√{[v/c]2/(1-[v/c]2)}

(a) Example:
A pellet of 10g moves at 10 m/s for a de Broglie wavelength vdB = h/mv = h/0.1 = 6.7x10-33 m*
This matter wavelength requires diffraction interference pattern of the order of λdB to be observable and subject to measurement

(b) Example:
An electron, moving at 80% of light speed 'c' requires relativistic development

Eo = moc2 with E = mc2 = moc2/√{1-[v/c]2}, a 66.66% increase in the electron's energy describing the Kinetic Energy E - Eo = {m - mo}c2
for a relativistic momentum p = moc.√{[0.8]2/(1-[0.8]2)} = (1.333..) moc = h/λdeBroglie and for a relativistic de Broglie wavelength, 60% smaller, than for the non-relativistic electron in
λdeBroglie = h/1.333..moc < h/0.8moc =λdeBroglie (1.83x10-12 m relativistic and 3.05x10-12 m* non-relativistic for an electron 'restmass' of 9.11x10-31 kg* and measurable in diffraction interference patterns with apertures comparable to this wavematter scale).

(c) The de Broglie matter wave speed in its 'group integrated' form derives from the postulates of Special Relativity and is defined in the invariance of light speed 'c' as a classical upper boundary for the acceleration of any mass M.
In its 'phase-individuated' form, the de Broglie matter wave is 'hyper accelerated' or tachyonic, the de Broglie wave speed being lower bounded by light speed 'c'

vphase = wavelength.frequency = (h/mvgroup)(mc2/h) = c2/vgroup > c for all vgroup < c

m = Energy/c2 = hf/c2 = hc/λdeBrogliec2 = h/λdeBrogliec = mdeBroglie = [Action as Charge2]mod/c(Planck-Length Oscillation)
= [e2]mod/clPlanck√alpha = [e2c2/ce]mod = [ec]modular

as monopole mass of GUT-string IIB and as string displacement current mass equivalent for the classical electron displacement 2Re = e*/c2 = [ec]modular as Wormhole minimum spacetime configuration for the Big Bang Instanton of Big Bang wormhole energy quantum Eps=hfps=mpsc2=kTps as a function of e*=1/Eps of Heterotic superstring class HE 8x8 and relating the Classical Electron Diameter {2Re} as Monopole Mass [ec]mod in Curvature Radius rpsps/2π = Gomps/c2.

The factor 2Go/c2 multiplied by the factor 4π becomes Einstein's Constant k = 8πGo/c2 = 3.102776531x10-26 m/kg describing how spacetime curvature relates to the mass embedded in that spacetime in the theory of General Relativity.

The selfduality of the superstring IIB aka the Magnetic Monopole selfstate in GUT Unification 2Re/30[ec]mod = 2Rec2/30[ec3]mod = e*/30[ec3]modκ for a proportionality constant {κ*}=2Re/30k[ec]mod = 2Re.c2/8πe = e*/8πe =1.2384..x1020 kg*/m* in string units for Star Charge in Star Colomb C*/Electro Charge in Coulomb C unified.

The monopolar Grand Unification (SEWG gravitational decoupling SEW.G) has a Planck string energy reduced at the IIB string level of
e*=[ec3]modular for mpsc2c/[ec]modular = [c3]modular = 2.7x1025 electron volt or 4.3362x106 J for a monopole mass [ec]modular = mmonopole = 4.818x10-11 kg* .

Mass M = n.mss = Σmss = n.{h/2πrdeBrogliec} .[Ess.e*]mod = n.mps.[Ess.{9x1060}.2π2Rrmp3]mod = n.mps.[Ess.{2Re.c2}]mod = n.[Eps.Ess]mod.[2Re]mod
for λdeBroglieps=h/mpsc and [Eps.e*]mod =1

{2Rec2} = 4GoMHyper for the classical electron radius Re=ke2/mec2 and describes its Hyper-Mass MHyper-electron = Rec2/2Go = ke2/2Gome = 1.125x1012 kg* for an effective electron mass of me = ke2/2Go(1.125x1012) =9.290527148x10-31 kg* in string units and where k=1/4πεo = 9x109 (Nm2/C2)*.

The curvature radius for the electron mass me = relectronc2/2Go then becomes relectron = 2Gome/c2 = 2.293957...x10-57 m* in string-membrane inflaton space as 1.44133588x10-34 rps in the wormhole instanton space.

Re/rinflaton-electron = MHyper-electron/me = 1.2109108..x1042 = ½(EMI/GI) = ½(e2/Go2me2) =½ {e/Gome}2 = ½(2.421821677x1042 ) for the classical electron radius Re halved from the classical electron diameter 2Re from the definition for the modulated supermembrane coupled in EpsEss=h2 and Eps/Ess=fps2=1/fss2.

Mass M = n.mss = Σmss = n.{mps} .[Ess.e*]mod = n.{mps}[{hfss}{fps/fss}.2π2Rrmp3]mod = n.mps.[Eps.e*/fss2]mod = n.mps/|fss2|mod

Hyper-Mass and the Hawking Modulus in Curvature of Space-time

A general solution for the Curvature Radius RCurvature embedded in a spacetime and as a static boundary condition for a Black Hole is given as the Schwarzschild metric from the field equations of General Relativity:

for Hyper-Mass:----------------MHyper = hc3.e*/4πGo = ½NAvagadro-Instanton.mwormhole

Hyper-Mass MHyper describes a higher dimensional Inflaton mass for a lower dimensional Instanton curvature radius and becomes the relationship between the beginning and the end of the string epoch in the Planck Radius of the Inflaton and the physicalized wormhole of the Quantum Big Bang as the Instanton.
The wormhole of the Instanton rwormhole=rps=rmin then forms the displacement quantum for the expanding cosmology in both the classical geometry of General Relativity (GR) and the quantum geometry of Quantum Relativity (QR).

Using the Schwarzschild metric for a mass of 70 kg would calculate a Curvature Radius for a mass equivalent Black Hole of (2.22..x10-10)(70)/c2 = 1.728..x10-25 meters*.
This is below the boundary condition of rmin = 10-22/2π m = 1.591549..x10-23 m* for which the minimum mass requirement is found to be 6445.775.. kg*.

This result shows, that no physical microquantum Black Holes can exist, but that the minimum unitary wormhole quantum of the Instanton is given by a 'wormhole substance' or Inflaton Black Hole Molarity count for a new minimum Planck Oscillator at the HE 8x8 Instanton energy scale EoBigBang=½mpsc2=½hfps=½kTps=½Eps=1/2e*

MHyper/½mps = 2hc3.e*/4πGo.mps = NAvagadro-Instanton = rps/Rps
for Rps = Gomps/c2 = rps/NAvagadro-Instanton = 2.743...x10-47 m* in Inflaton membrane space of 11D and string space of 10D

MHyper/mmin = Mmin/mmin = {n.hc3e*/4πGo}/mmin = {n.rminc2/2Go}/mmin = {hc3.c2/4πGoEmin}{ne*} = {hc3.c2/4πGohfmin}{ne*} = {2πrmin.hc3.c2/4πGohc}{ne*} = {rmin.c2.E/2GoM}{ne*} = rmin/R.{Ene*} for R = 2GoM/c2
for a generalized energy-mass proportionality c2=E/M in modular membrane duality with ne* = 1/E and ne*E = 1 (Modular Unification) for n.e*hc = n.λmin.

mHyper/rmin = {rminc2/2Go}/rmin = c2/2Go = n.mmin.Ee*/R = M/Rcurv for de Broglie wave matter mmin = hfmin/c2 = h/cλmin

Utility of the Schwarzschild metric allows calculation of Black Hole matter equivalents for any mass M>rminc2/2Go say for a planetary mass MEarth = 6x1024 kg for a
rcurv = 0.015 meters and for a solar mass MSun = 2x1030 kg* for a rcurv = 4938.3 meters*.

The curvature of the Inflaton calculates as RHubble-11D = c/Ho = 2GoMBigBang-Seed/c2 = 1.59..x1026 meters* for the Inflaton Mass of 6.47..x1052 kg*.

For any mass M<rminc2/2Go say for mass conglomerations smaller than 6445.775 kg* as the characteristic HyperMass for the Instanton, the corresponding curvature radius forms in the Inflaton space preceding the Quantum Big Bang at the time instanton of tmin=tps=1/fps=[fss]mod

The Standard Gravitational Parameter μ= GM = constant = GoM(XnYn)= GoXn.MYn and for (XY)n=1 can be finestructured in a decreasing gravitational constant G(n)=GoXn with a corresponding increase in the mass parameter M as M(n)=MoYn as say for the proto-nucleonic mass of the Instanton mc(nps) as mc(npresent) = mc.Ynpresent = mneutron < mcYnpresent = 1.711752..x10-27 kg* and 958.99 MeV* upper limited

For a changing Gravitational constant G(npresent) .mneutron(npresent)2 = Gomc2.Ynpresent and is modulated say in A micro-macro Black Hole perturbation Mo2/2M.MMaxHawking = 1.000543 ~ 1

The Black Holed mass equivalence for astrophysical bodies is well formulated in the application of the basic Schwarzschild metric derived from General Relativity.
Stephen Hawking developed the inverse proportionality between the mass of a Black Hole M and its Temperature T in the form of the Hawking Modulus:

HM = mPlanck.EoPlanck/k = √{hc/2πGo}{½mPlanck.c2/k} = hc3/4πGok = {MSmin.TSmax} = {mps.Tps.½NAvagadro-Instanton} =
[c2/4π2]mod.{MMaxHawking .TSmin } = 9.131793821x1023 kg*K* with (mpsTps = Eps2/kc2 = 1.002117..π)

The Hawking Modulus so has mensuration units [Mass][Temperature] in [kg][K(elvin)], which reduce to [Mass]{Energy] in [kg][J(oules)] for ignoring the Stefan-Boltzmann entropy constant k.

And so Mmin.Tmax = hc³/4πGok = [c2/4π2]mod.Mmax.Tmin = ½mPlanck.TPlanck = MMaxHawking. [c2/4π2]mod.Tss and the Hawking Mass is determined as MMaxHawking = λmaxπc²/Go = 2.54469..x1049 kg*.

Hyper-Mass MHyper (nps) = hc3.e*/4πGo = ½NAvagadro-Instanton.mwormhole = 6445.775 kg at the Instanton boundary n=nps so increases to MHyper(npresent)Ynpresent =hc3.e*/4πGoXnpresent ~ 11,117.26 kg as the projected Instanton boundary mass for the wormhole radius rwormhole = rps = NAvagadro-Instanton.Rps modulating the Inflaton curvature with the Instanton curvature and utilizing npresent=1.1327... for a decreased perturbed G(npresent) = 6.442x10-11 G-string units for the Standard Gravitational Parameter G(n)miYk(n).mjYn-k = Gomc2 = constant for G(n)=GoXn.

Using the λminλmax=1 wavelength modulation in the T-duality of λmin=2πRmin=1/λmax=2π/Rmax, we can see, that this modulation closely approximates the geometric mean of the seedling mass in {1/4π}Mo2/2M.MMax=Mo2/8π.M.MHawking=3.2895..x10102/3.2931..x10102 ~ 0.998910744...

This also circumscribes the actual to critical density ratio in the omega of the general relativistic treatment of the cosmologies.
Now recall our applied G value in Gm(n)=Go.and apply our just derived Black Hole Mass modulation coupled to that of the quantum micromasses.

We had: Gomc²={GoXn+k}.{mcYn}.{mcYk}=Gm(n).mnmax.mnmin and where Gm is the actual G value as measured and which has proved difficult to do so in the laboratories.
Gm(n)=Go.Xn+k=Gomc²/mnmax.mnmin=Gomc²/({mcYn}{mnmin}) and where we have mnmin=mcYk} for the unknown value of k with mnmax=mcYn.

So Gm(n)=Go.Xn+k=GoXn[mc/mnmin]=Go{mc2/mcYn}.{Mo2/8π.M.MHawking.mav} for Xk={mc/mav}.{Mo2/8π.M.MHawking}=1.00109044..{mc/mav}
and where now {mnmin}={8π.M.MHawking.mav/Mo2}=1.00109044..mav.
mav={Mo²/8π.M.MHawking}{mnmin}={Mo²/8π.M.MHawking}{mcYk}=0.9989107..{mcYk} and obviously represents a REDUCED minimum mass mnmin=mcYk.

But the product of maximum and 'new' minimum now allows an actual finetuning to a MEASURED nucleon mass mN by:
mN² = mavYn.mcYn=mav.mnmax.Yn.

So substituting for mav in our Gm expression, will now give the formulation:
Gm(n)=Go.Xn+k=GoXn[mc/mnmin]=Go{mc2/mcYn}.{Mo2/8π.M.MHawking.mav}
Gm(n)=Go.Xn+k=GoXn[mc/mnmin]=Go{mc2/mcYn}.{Mo2/8π.M.MHawking}{mcY2n/mN2}
Gm(n)=Go.{mc2/mN2}{Mo2/8π.M.MHawking}Yn

The average nucleon mass mN is upper bounded in the neutron mass and lower bounded in the proton mass, their difference being an effect of their nucleonic quark content, differing in the up-down transition and energy level and because of electro charges increasing the intra-quarkian Magneto charge coupling between the two mesonic rings of the neutron and the single mesonic ring in the proton's down- or KIR-quark.

For a Neutron Restmass of: mneutron=1.6812656x10-27 kg* (941.9111 MeV*) or (1.6749792x10-27 kg and 939.594 MeV)
the substitution (and using calibrations m=1.001671358 m*; s=1.000978395 s*; kg=1.003753127 kg* and C=1.002711702 C* gives:
G(np)= Go{mc/mneutron}2.(0.9989107..)Ynp = 6.670693x10-11 (m3/kgs2)* or 6.675312x10-11 (m³/kgs²).

For a Proton Restmass of: mproton=1.6788956x10-27 kg* (940.5833 MeV*) or (1.672618x10-27 kg and 938.270 MeV).
G(np) = Go{mc/mN}2.(0.9989107..)Ynp = 6.6895399x10-11 (m3/kgs2)* or 6.694171x10-11 (m³/kgs²).

Gm(n)=Go.Xn+k = 6.670693x10-11 (m3/kgs2)* then gives kp =ln{Gm(np)/Go}/ln{X} - np = 1.0602852 - 1.132711 = -0.0724258

The upper value of the neutron bound so represents an upper limit for the Gravitational Constant as the original quark-lepton bifurcation of the X-Boson precursor given in the KKK kernel. Only the KKK kernel is subject to the mass evolution of the cosmos; the leptonic masses being intrinsically incorporated in the Kernel means.
The mc.Yn so serves as an appropriate upper bounded approximation for G(n), subject to leptonic ring IR-OR perturbations.​

The best approximation for 'Big G' hence depends on an accurate determination for the neutron's inertial mass, only fixed as the base nucleon minimum mass at the birth of the universe. A fluctuating Neutron mass would also result in deviations in 'G' independent upon the sensitivity of the measuring equipment. The inducted mass difference in the protonic-and neutronic restmasses, derives from the Higgs-Restmass-Scale and can be stated in a first approximation as the groundstate.
Basic nucleon restmass is mc=√Omega.mP=9.9247245x10-28 kg* or 958.99 MeV*.

(Here Omega is a gauge string factor coupling in the fundamental force interactions as:
Cuberoot(Alpha):Alpha:Cuberoot(Omega):Omega and for Omega=G-alpha.)
KKK-Kernelmass=Up/Down-HiggsLevel=3x319.66 MeV*= 958.99 MeV*, using the Kernel-Ring and Family-Coupling Constants.

Subtracting the Ring-VPE (3L) gives the basic nucleonic K-State as 939.776 MeV*. This excludes the electronic perturbation of the IR-OR oscillation.

For the Proton, one adds one (K-IR-Transition energy) and subtracts the electron-mass for the d-quark level and for the Neutron one doubles this to reflect the up-down-quark differential.
An electron perturbation subtracts one 2-2/3=4/3 electron energy as the difference between 2 leptonic rings from the proton's 2 up-quarks and 2-1/3=5/3 electron energy from the neutron' singular up-quark to relate the trisected nucleonic quark geometric template.

Proton mp=u.d.u=K.KIR.K=(939.776+1.5013-0.5205-0.1735) MeV* = 940.5833 MeV* (938.270 MeV).
Neutron mn=d.u.d=KIR.K.KIR=(939.776+3.0026-1.0410+0.1735) MeV* = 941.9111 MeV* (939.594 MeV).

This is the groundstate from the Higgs-Restmass-Induction-Mechanismand reflects the quarkian geometry as being responsible for theinertial mass differential between the two elementary nucleons. All groundstate elementary particle masses are computed from theHiggs-Scale and then become subject to various finestructures. Overall, the MEASURED gravitational constant 'G' can be said to be decreasing over time.

The ratio given in k is GmYn/Go ~ 0.600362... and so the present G-constant is about 60% of the one at the Planck Scale.
G decreases nonlinearly, but at a present rate of 0.600362/19.12x109 per year, which calculates as 3.1400..x10-11 G-units per year.

Generally using the exponential series expansion, one can indicate the change in G.
For Xn+k=z=exp[(n+k)lnX] by (n+k)lnX=lnz for the value u=(n+k)lnX=-0.481212(n+k); z transforms in exponential expansion eu=1+u+u2/2!+u3/3!+u4/4!+...

For a function f(n)=z=Gm(n)/Go=Xn+k - f(n)=1-(0.481212.)(n+k)+(0.2316.)(n+k)2/2-(0.1114.)(n+k)3/6+(0.0536.)(n+k)4/24-...+...​

At timeinstantenuity of the Quantum Big Bang, n=npsps/Rmax=6.2591x10-49 ~ 0
Then GBigBang=GoXnps=Go (to 50 decimal places distinguishing the timeinstanton from the Nulltime as the Planck-Time transform).
Go represents the quantum gravitational constant applicable for any Black Hole cosmology and can be used to correlate the MOND gravitation with the Newton-Einstein gravitation (previously stated in section 3.8).

For our previously calculated k=ln(GmYn/Go)/lnX and which calculates as k= -0.0724258..
f(n)=1-(0.481212.)(n+k)+(0.2316.)(n+k)2/2-(0.1114.)(n+k)3/6+(0.0536.)(n+k)4/24-(0.0258.)(n+k)5/120+...-...
for f(1.132711)=1-0.51022+0.13016-0.02214+0.00283-0.000288...+...~ 0.6006340 to fifth order approximation to 0.60036246...

Hence, the gravitational constant assumes a value of about 60.0% of its Big Bang initialisation and calculates as 6.675x10-11 G-units for a present cycletime npresent=Hotpresent=1.132711...

The introduction of the mass seed coupling between the macro quantum Mo and the micro quantum mc=mPalpha9 (from the gravitational finestructure unification) PERTURBS the 'purely electromagnetic' cosmology in the perturbation factor k and increases the purely electromagnetic Gmemr in the black hole physics described.

So gravity appears stronger when one 'looks back in time' or analyses cosmological objects at large distances. The expansion parameter (a) in the Friedmann-Einstein standard cosmology can be rewritten as a curvature ratio R(n)/Rmax={n/(n+1)} and describes the asymptotic universe in say 10 dimensions evolving under the inertial parameters of the c-invariance. This 'lower dimensional universe' is open and expands under hyperbolic curvature under the deceleration parameter qo=½Ωo=Mo/2M=2GoHoMo/c³ ~0.014015... This open universe is bounded in the 'standing wave' of the Hubble Oscillation of the 11D and 'higher dimensional universe'.

Last edited: Sep 20, 2018

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Cosmology Evolution of the Multiverse

Last edited: Dec 22, 2018

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Definiton to Inflaton to Instanton to Continuon - Four Pillars of Creation

The creation of self emergence of the universe in energy E=mc2 can be described in four epochs or time intervals.

The Definiton would encompass a potential for information to manifest any data required for the birth of a universe from a prior premise of the information potential existing in a spaceless and timeless state of selfness, beingness or eigenstate.
It is from the Definiton, the fundamental constants, parameters and numbers, such as lightspeed 'c' and Planck's quantum constant 'h' derive from.
The mathematical nature of the cosmogenesis so finds its 'fire in the equations'; as Stephen Hawking famously said in the 'A Brief History of Time' {Chapter 12; 1988}; from the nature and way the 'laws of nature' became defined in the Definiton.
The Definiton so focused on a finetuning and interrelationships between mathematical numbers and concepts, transforming themselves into physically applicable parameters centered on the concept of Energy.

The Inflaton then describes a particular epoch when the information defined 'laws of nature' first displayed themselves through the creation of a primordial realm of super-hyper-spacetime and as defined by the Definiton.
The Inflaton is characterized in 5 superstring classes; who transformed from a closed Planck string class into 4 open Dirichlet classes in a Planckian string spectrum following the setup of initial and boundary conditions for the Inflaton from the Definiton.
The nature of the 10-dimensional superstring classes is however encompassed in a 11-dimensional supermembrane spacetime to enable the Inflaton parameters to apply their defined boundary- and initial conditions to the Instanton, following the completion of the Inflaton epoch.
11-dimensional Witten membrane spacetime manifests itself via a consequence of it modular dualities, connecting the five string classes to each other in coupling both their intrinsic energy and their scaling parameters in inversion properties.
The most important modular duality for the cosmology for the expanding universe so is a 10D string coupling for the 11D membrane in a Mirror Duality relating to a T-duality with inversion of the scale parameter. This allows the high energy (vibratory) microquantum part of the final string class to couple to its low energy (winded) macroquantum conjugative or partner as half of the supermembrane.
Once the Inflaton, followed by the Instanton has manifested the physical cosmology; the Inflaton lightpath, which is subject to both refraction and reflection under the boundary conditions, will define a 12-dmensional Vafa F-space in the refracted but not yet reached lightpath of the so called Radius of the Event Horizon, differing from the already encountered Inflaton bound, known as the Hubble Horizon.

The Instanton is described in a Quantum Big Bang cosmogenesis and the Friedmann model as a solution to Einstein's Field equations from General Relativity in the Robertson-Walker metric. A classical geometric-topological physics of thermodynamic and entropic expansion described in metrics and relative displacement becomes supplemented by a quantum geometry which utilizes a foundational 'spacetime building unit' termed the Weylian wormhole and colloquially known as the 'Big Bang Singularity'.
The expanding universe so becomes a summation of wormhole quanta carrying particular saturation-energy levels, such as the formal definition of the 'Classical Size of the Electron' as a magnified hologram of the holofractal Weylian minimum space quantization.
Using modular string (mirror) dualities as topological string-membrane transformations then allows basic physical parameters, such as those of the classical electron to define derived parameters, such as a definition of inverse energy as a basic unit for physical consciousness related to a form of Goldstone boson, say Axion here termed the RestmassPhoton as supersymmetric agent for the weak interaction based Higgs inertia inductions.

The Continuon would then address the intersection of the Inflaton with the Instanton in relating the lower dimensional expansion of the compressed 4/10D dS space-brane-time with its inflationary encompassment in higher dimensional 5/11D AdS space-brane-timetime (sbt).

It is found that the physical constituents comprising the cosmic matter are interacting within both the compressed or conifolded dS asymptotically expanding sbt and the cyclic open AdS sbt of the Inflaton.
This interaction defines particular intersection points and solutions for the Dark Matter - Baryon Matter energy interactions, but are a function of an encompassing Dark Energy 'book keeper' to ensure an overall Minkowski flat cosmology of zero curvature.

The Dark Energy is characterized by a function of universal pressure which relates the Baryonic matter content and as given by a mass seed Mo to the critical mass as defined by the Inflaton before time instantenuity aka the Quantum Big Bang in cosmological terminology.

1. The Definiton

1.1 The Primary Algorithmic Logos

Any Universal Observer or UO can only observe and measure and experience something, if the environmental stimulus for such an experience does exist as or in the environment of the UO.
The existence of space as a form of dimensional realm then becomes prerequisite; does allow the concept of relativistic time and displacement to emerge and follow as a consequence of existing spacial parameters.
Mathematically, all natural numbers can be defined logistically in the Zero to One interval with rational numbers having the property of identity in inversion principles applied to the natural or counting numbers and negative integers characterized by the conjugative mirror image of the positive integers in the mirror of the Nullstate. Real and complex numbers then follow from series limits and approximations to any desired degree of accuracy applied to converging and diverging number series and sequences. The largest counted integer would still have no limiting bound, as one can be added to it; but however large this integer would be; its inverse would certainly have a limit in the number 0 as a regressive asymptotic approach.

The Definiton so must a priori accommodate the potential or 'future timed' UO in a spaceless abstract continuum of mathematical symbols and structure.

But what if there are no numbers and no mathematics in this spaceless realm of voidness not defined by any numbers. Because the universe does exist as Hawking stated, the question of why it exists, can be asked and an answer can only be found in its own mathematical logistics as the difference between the infinite progression towards unlimited Infinity and the infinite regression towards the limit of the Zero.

To 'think the primal thought' the timeless and spaceless, (but potentially existing within spacetime in the future) UO; must experience itself in a change from being unaware of itself to being aware of itself.
The notion of the past, the present and the future in the timelike properties of existing relativistic space are preceded in a sense of order; where event A must precede event B to allow event C.
All such events are simultaneous in the self-reference framed abstract world of the Mathimatia of the UO, who has however changed its selfstate from being unaware to aware in a form of yet to be defined 'Universal Consciousness'.

Formally; the Awareness Triplet AT={Old State=OS; Experience=E; New State due to the Experience=NS} forms the Input for an interaction with with a previous selfstate or preexisting 'Awareness Space'. The Output of the New State becomes the Input for the new Old State in a series of AT's, labelled as the 'Sequence of Energy Primary SourceSink' or SEps for SEps = {(0,0,0); (0,1,1); (1,0,1); (1,1,1*=10=2); (10,1,11=3); (11,10,101=2+3=5); (101,11,1000=5+3=8);...;(OS,E,NS)}.

The NS n becomes the sum of the OS as the previous (n-1)th n and the previous (n-1)th OS forms the experience factor E.
The sequence of the E's is known as the Fibonacci Series in the future universe physically manifested in the Awareness Space of the Mathimatia of the Definiton.
The experience factors so change the 'Null-State' of the (0,0,0) into the 'All State' of the (1,1,1)=(∞,∞,∞) to mirror and manifest the infinite count of the integers in the inversion identity of the finite limit of the 0.

In terms of mathematical cardinality a future 'Wavefunction for the Multiverse' would be characterized by a Normal Statistical Distribution of 'frozen spacetimes'. And where the Arithmetic Sum of Progression, that is counting all negative and positive integers as a Unity summation becomes T(n)=n(n+1) with both a real and a complex solution in setting T(n)=1 for {X=½(√5-1); Y=-½(√5+1)} and {-½(1+i√3); -½(1-i√3)} for T(n)=-1.

Semantically, the triplet identity (1,1,1)=(∞,∞,∞) represents the OneSelf+OneSelf=OneSelf still, but because the previous experience of OneSelf+Nothing=OneSelf, the second OneSelf must be different in some way of order from the first OneSelf. Namely the summation to 1+1=10 differs in the order of the summation 1+0=1 in the noncommutability of the experience factors of experiencing the 'NothingSelf' from the OneSelf.
This then allows a transformation from the binary triplet sequence to a decimal triplet sequence in: (1,1,1*) = (1,1,10)bin = (1,1,2)dec.
Subsequently all integer related number systems naturally emerge and evolve from the Mathimatia Awareness space.

The eigenstate of the UO now is one of 'doubling the eternity of the void' as mathematical infinity in the Integer count and based upon the ciphers of the 0 and the 1.
Formally, the mapping of an Aleph-Null Cardinality of Cantor countability or enumerability becomes an Aleph-All Cardinality of Cantorian Infinity sets, the latter counting 'Integral Infinities' instead of the natural numbers.

It is however the Fibonacci sequence SEps, which will be utilized by the Inflaton to manifest the next epoch in the actual creation of an 'algorithmic timespace' in the form of a spacetime linearization of the circular nature of the binary ciphers 0 and 1 in something fundamental to potentially physicalized space in the topology and geometry of special curvature and the warping of spacetime. The closed nature of the Planck class I string will be made manifest as the Nullstate of the Mathimatia and the evolvement of the Planck Boson string will create the other string classes in the 'opening' or cutting of the circle of the Zero to manifest the One.

1.2 The Secondary Algorithmic Logos

The experience factors of the SEps algorithm naturally define a complementary set SEps* = {100=4; 110=6; 111=7; 1001=9; 1010=10; 1011=11; 1100=12; 1110=13;....(any integer not in SEps} and the UO can only continue its self exploration within the awareness space of the Mathimatia applying either SEps or SEps* through the symbolic representation, shapes, semiotiks and geometry of the curvilinear duality of the Bosonic Planck string being able to manifest itself in either a closed or an open form of the supermembrane of the (0,1) monadic dyad.
As the UO in SEps cannot form a complementary union with an UO* in SEps* in any form of separation in the Mathimatia; the complementarity describes a natural unification of self states aka eigenstates in the Mathimatia, but will become a natural supersymmetry inherent in the Inflaton and based on the Planck Boson string and especially its immediate transformation into a selfdual monopole string class IIB.
As no spacetime is as yet defined, the superpartners of the UO in SEps and the UO* in SEps* are nonlocally connected and would form the basis for a future quantum entanglement between eigenstates and the particle-wave complementarity and dualism of the quantum world of the physicalisation of the Mathimatia in the cosmology of the Instanton.

The experience factors naturally encompass all states used to create them and all E's defining SEps and SEps* constitute a collective memory reservoir from which further exploration and manipulation of the members in this universal memory set can be pursued and constructed.

One such arbitrary algorithm or code is defined as binary code of the operations of Addition (+), Multiplication (by 1+1+1=3x1) and Exponentiation (3x3=32) and
is used as a secondary algorithmic code to 'find' the missing elements of SEps as the constituents of SEps* in the attempt to complete and manifest the generic supersymmetry of the Mathimatia.

Application of this algorithm {http://www.cosmosdawn.net/forum/ind...s-and-algorithms-of-dragon-cosmogenesis.636/} produces 10 number triplets, carrying elements of SEps* in various configurations:
SEps-SEps* Constantset: ={(266561)=26x6561; (15,16,18)=[15x1618]-1; (14,15,24)=14x1524; (15,10,32)=[15x1032]-1; (11)=11; (9,10,16)=9x1016; (6,10,15)=[6x1015]-1; (7)=7; (6)=6; (4)=4}

1.3 The Tertiary Complementary Algorithmic Logos

The extended SEps algorithm then assumes the pretext of defining open and closed superstrings in a logistical statement:

This specifies an methodology of recircularizing the linearized dimensions of the binary monadic dyad {0,1} into the root-reductive decimal monad {1,2,3,4,5,6,7,8,9,0} with 10=1+0=1*; 11=1+1=2*; 12=1+2=3; 13=1+3=4 and so on with 26=8 and 27=9 in 26 Bosonic Integer dimensions.

The constant E={(266561)=26x6561} then transforms into F={(136656)=13x6656} and G={(673665)=67x3665} after which this 'numerical inflation algorithm' ends, since 5+6=11=2* is root reductive in transformation towards the right say towards positive infinity from the Zero mirror of the Mathimatia.
But moving towards the left and negative infinity upon the integral number line, the ...{0}EFG... interval is mirrored in say the F-space bound ABCD{0}EFG.... to fixate the F-space bound in the M-space bound H=ABCD in |ABCD(EFG)H| in (A)BCDEFGH......STUVWXY(ZA*)B*C*....

Then H=ABCD={(312423)=31x2423}{(361242)=36x1242}{(256124)=25x6124}{(465612)=46x5612}. As no archetype can yield Z(Z+A)BCXY=312423 from ABCXYZ=(1-Z)24233, the algorithm again ends in the reflected root reduction to H, namely 1-Z=1-3=-2 =-11=-2*

The SEps constant E so assumes the property to limit a subsequent inflation marker in association with the encompassment of the Inflaton in the googolplex markers E=26x6561 = 1.006208782x10112 and G=67x3665 = 9.676924499...x10102 and F=13x6656 = 1.019538764...x10103 and H=1,283,400x2423x1242x6124x5612=1.011591782...x10147.

H becomes the number of spacetime quanta contained in the Inflaton, bounded by the Hubble Event Horizon in the 5D/AntideSitter Witten sphere manifesting as a 3-dimensional hypersurface in 4D Minkowski spacetime as a 2-Torus and becomes a 3-Torus subject to the Event Horizon as a boundary to the Vafa F-spacetime in the continuing Inflaton cycles defined by the evolution of the Dark Energy paralleled by the overall Schwarzschild evolvement of all mass as matter content in the cosmology.
The maximum radius for the first initiatory cycle of the Inflaton as a first asymptotic boundary for the Instanton so becomes set as a maximum radius of curvature in the Friedmann cosmology with a nodal true Hubble constant for this initial cycle and is proportional to the Vacuum- or Vortex-Potential energy of a singular unitary wormhole spacetime quanta and as definind in the Inflaton.

The volume of one such wormhole or Eps-VPE quantum there is:
Vps = λps3/4π m3 = 7.957747154x10-68 m3*
for the Riemann hypersphere volume of 2π2RHubble3 and wormhole radius rps = λps/2π; this volume manifesting as a hypersurface allowing the M-AdS spacetime to mirror in the F-dS spacetime of open hyperbolic curvature contracting into M-space as function of the lightpath of the Inflaton expansion.

RHubble = cHo = λps.∛H/2π = 1.59767545x1026 m* for a nodal Inflaton Hubble Event Horizon.

11D AdS spacetime becomes bounded in a Hubble volumar with critical density

ρcritical = MHubble/2π2RHubble3 = c2/4π2RH2 = Ho2/4π2Go or ρcritical = 3Ho2/8πGo for the volume of a 2-sphere.

The Hubble volumar then topologically encompasses both, the lower dimensional of Einstein-C dS space and the higher dimensionality of Witten AdS spacetime, say in the form of a 3-Torus or a Klein Bottle Dragon.

The SEps Principalities

A = (312423) = {4+6+5=15} = (1.722742045...x1033) space quanta = Principality of Identity/AntiIdentity.............................................with 1st Expansion Factor 10/33
B = (361242) = {9+3+6=18} = (7.619295808...x1046) space quanta = Principality of Expansion/Contraction..........................................with 2nd Expansion Factor 20/33
C = (256124) = {7+7+6=20} = (1.761392119...x1044) space quanta = Principality of Order/Disorder-Entropy-Chaos...............................with 3rd Expansion Factor 30/33
D = (465612) = {10+11+3=24} = (4.375363663...x1022) space quanta = Principality of Symmetry/Antisymmetry-Nonparity.....................with 4th Expansion Factor 40/33
E = (266561) = {8+11+7=26} = (1.006208782...x10112) space quanta = Principality of Infinity-Divergence/Convergence-Limit.................with 5th Expansion Factor 50/33
F = (136656) = {4+12+11=27} = (1.019538764...x10103) space quanta = Principality of Inversion-Reciprocity/Constancy-Invariance.........with 6th Expansion Factor 60/33
G = (673665) = {13+9+11=33} = (9.676924499...x10102) space quanta = Principality of Reflection/Absorption.........................................with 7th Expansion Factor 70/33
H = () = {} = (1.011591782...x10147) space quanta = Principality of Relativity/ No Antiprincipality.............................................................with 8th Expansion Factor 80/33

The SEps Cyclicities in elements aj with summations aj+2+aj+1 = aj

1-Cycle : 0-1-1-2-3-5-8-13 for {33 Identity & Absorption} and for 8 elements summing 1 aj
2-Cycle : (0-[1)-(1]-[2)-(3]-[5)-(8]-13) = 1-2-3-5-8-13-21 for {33 Expansion & Invariance} and for 7 elements and summing 2 aj's
3-Cycle : (0-[1-(1)-[2]-(3)-[5]-8)-13] = 2-4-6-10-16-26 for {64=8x8 Order & Convergence} and 6 elements and summing 3 aj's
4-Cycle : (0-[1-(1-[2)-(3]-5)-8]-13) = 4-7-11-18-29 for {69 Symmetry & Nonparity} and for 5 elements and summing 4 aj's
5-Cycle : (0-[1-(1-[2-3)-5]-8)-13] = 7-12-19-31 for {69 Divergence & Entropy} and for 4 elements and summing 5 aj's
6-Cycle : (0-[1-(1-2-3-5)-8]-13) = 12-20-32 for {64=8x8 Inversion & Contraction} and for 3 elements and summing 6 aj's
7-Cycle : (0-[1-1-2-3-5-8)-13] = 20-33 for {53 Reflection & AntiIdentity} and for 2 elements and summing 7 aj's
8-Cycle : (0-1-1-2-3-5-8-13) = 33 for {33 Relativity} and for 1 element and summing 8 aj's

Formation of a Prime Harmonic Octet : (15-18-20-24-26-27-33) from the {A}BCDEFG{H} principalities unified

root reduced to {6-9-[2-6-8]-9-6} = {6-8-8-6} = {14-14} = {5-5} = {10=1} into the original binary algorithm root reduction and for a symmetry about a 26 letter code symbolizing 26 Bosonic string dimensions in a prime Number set
Primed N: = {1=1bin;-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=5bin}

1.4 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 SEps-Constant '11'.
This generates the Prime Number Algorithm: +1+11+10+11 as 33-tiered segments, which transform the mechanics of SEps 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 (MN)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 MN#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 Eps=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 MN'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:

Tk(En) = nk.Tk(En-1) + [(n-1)!]k and Sk(En) = Tk(En)/(n!)k

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

2.2-p ≥ 2-p+3-p, with geometric series 11-p+21-p+41-p+...summing to (1-2[1-p]n)/(1-21-p)=1/[1-21-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)=2p-1 and the Fermat-Code F(n)=22n+1 and the 'Perfect Numbers' depicted as the Mersenne Numbers (Mp), 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 2p-1.Mp :
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 Eo=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/nz)=1/1k+1/2k+1/3k+1/4k +...+1/nk

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/np) = 1-p+2-p+3-p+...
For even terms: 2.2-p ≥ 2-p+3-p for a geometric series:
11-p+21-p+41-p+...+(2n-1)1-p
This Geometric Progression sums to: [1-(21-p)n]/[1-21-p]=1/[1-21-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 Eo.

Define: for a nth term (numerator): Tk(En) = nk.Tk(E n-1) + [(n-1 )!]k for the nth sum per n (denominator [n!]k): Sk(En) = Tk(En)/(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 Number line 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...[Eo]...1...2...3---> (n); where Integer 1 maps 2! in suppression of -1=2* and in algoradius eo=1.
Similarly, Integer 2 maps 3! in suppression of -2=3* and algoradius e1=2=2eo, 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:
SEps=Fibonacci#1=0,1,1,2,3,5,8,.....for a nth Term: Tn=|-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+...= ΣTn.xn-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.
SuperSEps=Fibonacci#2=Lucas#1=2,1,3,4,7,11,18,29,.... for a nth Term:

STn=|-Y2n - X2n|/|-Yn - Xn|=|T2n/Tn|

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

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

{Tn,STn}={(So=0,STo=2=S3); (S1=1=ST1=S2); (S2,S4=3=ST2); (S3,ST3=4); (S4=ST 2,ST4=7); (S5,ST5);...;(Sn,STn)...}
{Tn,STn}={(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 Super-SEps=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.
SEps 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 Super-SEps.
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 SEps onto SuperSEps 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 Super-SEps

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.T2n.
The sum of the two sums is: {+}+{-}= 2|-Y|n, with STn ={+}+{-} - Tn.√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 Super-SEps given in the term: [5.Tn+ √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:

STn.√5.Tn={+}.{-}=√5.T2n & STn=T2n/Tn = |-Y2n - X2n|/|-Yn - Xn|
(quod erat demonstrandum).

The significance of this result is that STn, T2n and Tn are all integers.
We so have a primary extension for SEps with elements 1, 2 and 3 duplicated and resulting in the mappings as previously specified.

The Null-Initialisation (OSj, EXj, NSj) as the Fibonacci-Triplet (An-1, An, An+1) then reflects STn about n=0* to define the complex number set as negative STn's mapped in a 0→1→∞ correspondence to Tn.
This is the mathematical mapping of Cantorian Enumerability as previously indicated.

1.5 The Modular Duality of Time-Space in the Mathimatia of Supermembrane EpsEss

The Cosmic Wavefunction B(n) is the following Differential Equation:

dB/dT + αB(n) = 0; α=alpha being the Electromagnetic Finestructure as the probability of light-matter interaction (~1/137).

This has a solution: B(n) = Bo.exp-α.T(n);
Bo=2e/hA from QR boundary conditions defining:

T(n)=n(n+1) as the Feynman Path-Summation of particular histories under the pentagonal supersymmetry given in the identity:

XY=X+Y=-1=i2=exp[iπ] and lim [n→X]{T(n)}=1

This allows the Normalisation of the Y2 wavefunction to sum to unity in

B(n)=2e/hA).exp-α.n(n+1) with Functional Riemann Bound FRB=-½, centred on the interval [Y,...-1,...-X,...-½,...(X-1),...0,...X].

Interval [Y,-1] sets F-Space; interval [-1,0] sets M-Space with uncertainty interval [-X,(X-1)] and interval [0,n) sets the C-Space, encompassing OmniSpace.

n<0 is imaginary as real reflection of real n>0 of the C-Space, metrically defined at the coordinate n=0 mapping n=nps, which is the instanton tps=fss=1/fps.

Cycletime n is defined in GR as dimensionless Tau-Time in curvature radius Rc=c.dτ/dt for the pathlength of x=ct and become dn/dt=Ho, n=Hot in QR, with Ho the nodal Hubble Constant defined in c=HoRmaxps.fps

The Feynman Path so sums both negative and positive integers as:
-n......-3...-2...-1...0...1...2...3......n = T(n)
in absolute value to double the infinities as the entropy reversal of lightpath x=c.t=(-c)(-t) in the Möbius Property of a supermembraned omniverse in 12 linearised dimensions.

Cantor Cardinality Aleph-Null is thus Unitised in Aleph-All, counting infinities as if they were integers of the Feynman Path.

This allows the Feynman interpretation of Quantum Mechanics as alternative to the formulations of Schrödinger (fermions ½ quantum spin) and Klein-Gordon (bosons with integral quantum spin) as timeindependent and timedependent (free particle form inconsistent with SR in Schrödinger in 1st order t & 2nd order x), formulations respectively.

Last edited: Feb 26, 2018

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The Alpha Variation, the Mass of the Electron and an Accelerating Universe

A white dwarf star is important as a distance indicator for the cosmic distances. Should it be in a binary system with another star in mutual orbit about each other, then mass can transfer via magnetic activity from the companion star and the Chandrasekhar limit might so become exceeded and the white dwarf explodes as a supernova type Ia.
Supernovae class Ia show no helium absorption in their spectra but show a strong absorption of singly ionised silicon atoms at about 610 nanometres; supernovae class Ib have helium lines, but no silicon lines and supernovae class Ic have neither; hydrogen is absent in all supernovae spectra type I.
Supernovae spectra change significantly, varying in brightness, as the explosion synthesises heavy elements, such as gold, iron and oxygen in the thermonuclear reactions.
Supernovae class II are rarer and show significant hydrogen absorption and are thought to collapse into a neutron star or Black Hole, having a preexplosion mass of over 8 solar masses.
The brightest supernovae are of type Ia and the uniformity of their light curves allows calibration of their apparent brightness with their 'standard' true brightness, the luminosity so serving as an indicator as to their distance by astronomical distance-luminosity calibrations.
About one supernova class Ia explodes in a typical galaxy every 300 years, so in observing a large sample of about 3600 galaxies, one such explosion per month should be seen.
The experimental data collected by the various supernova observers, and under utility of the Hubble Space Telescope to track the brightness variations of discovered supernovae type Ia, now converged in 1998 to the conclusion, that distant supernovae are between 20% and 30% dimmer than expected and as a consequence of their measured redshift they appear to be further away then theory permits.

An interpretation of this discovery implies, that the universe's expansion is accelerating; the measured redshift depicting a distance further away for a dimmer brightness than anticipated by theory.
Closer analysis of the redshift data shows an expected distribution of luminosities, calibrated to their distances in the Chilean Cala-Tololo data, up to a redshift of about 0.12 and with a redshift-gap until a redshift of 0.3; after which the 'High-Z's' begin to show the 'curving away' from a predicted decelerating expansionrate in concordance with an Euclidean flat universe of Einsteinian General Relativity.
The highest redshift recorded in 1998 was that of 'supernova Iae' at (z=1.1) by the 'High-Z-Team'.

A description of the universe as decelerating with precise deceleration parameters given in a balancing of a gravitational omega, a quintessential lambda and a Milgrom parameter points to a possible variation in the Electromagnetic Finestructure constant Alpha.

The two research results in the [Alpha]-Variation and the 'Accelerating Cosmos of the Dark Energy' are closely related.
To preemt my analysis, the universe is not accelerating, but appears to do so because of the interdimensional intersection of the EMR parameters of the spectroscopic measurements.
And it appears to accelerate for a specific redshift interval, which also is responsible for the measured [Alpha]-Variation, the 'dip' in [Alpha] is like a redshift becoming a blueshift for a specific epoch.

My cosmological analysis of the phenomena predicts, that supernovae type Ia with a redshift above 1.84 will be measured to conform to the theoretical predictions for a decelerating and flat supercosmos.
The appearance of an accelerating cosmos is a limited phenomenon, relevant for a specific and unmapped redshift interval from (z=0.343 to 0.291), with interval (z = 1.08 to 1.84) imaged in the interval (0.343 to 0.291) with a variation maximum for thge mapping at the Arpian limit (zarp = 0.2505).

In particular, it has already been noted, that Supernova Iae, also known as SN1998eq with redshift 1.1 is less anomalously dimmed than the nearer ones; just as I predict for all the more distant ones.
SN1997ff with redshift 1.7 is one of the most distant supernova found by Adam Riess in 2001 by the Hubble-Space-Telescope at the time of this writing and whilst the argument can be made that acceleration decreases with distance, the actual location in relationship to the cosmological redshift remains constant in a 'slowing down from faster' or 'speeding up from slower' , if the decisive measuring stick is the expansion of the universe under constancy of light speed (c); demanding however a 'Redshift-Correlation-Correction'.

Indulge yourself in a thought experiment and travel with the expanding event horizon, the boundary of the universe (which has no boundary in the curved overall sense, all locations being centred selfrelatively), this then becomes the looking back in time to the origin of the Big Bang.
You then experience the receeding origin of the singularity slowly moving away from you and relative to you as 'stationary observer' at the event horizon, your own recessional velocity of (22% of (c)) is nullified and must be accounted for in your calculations of the recessional universe you are observing.

The 'de Broglie' inflationary model, where a supermembrane epoch ends in timeinstantenuity as the EpsEss heterotic superstring, which then expands with a decreasing recessional velocity towards a 'de Broglie' boundary as macroquantisation in 10D, but beginning with light speed (c) under guidance of Special Relativity can be applied.
Other inflation scenarios, such as chaotic inflation had proved untenable by the experimental data and the microwave background pointing to a zero curvature and to a flat universe.
The macro quantisation of the heterotic superstring, also known as HE(8X8) constitutes the 'conifoldment' of the higher dimensions, either as a 6D-Calabi-Yau manifold or as a 7D-Joyce-Sphere, relative to 10D-C-space and 11D-M-space respectively.

And the 'de Broglie' inflation quantises Einstein's field equations of General Relativity in their Friedmann formulations; the Milgrom parameter becoming acceleration: (-2cHo/(n+1)3) and the distance-scale factor parametrising as: {r[n] = Rmax(n/(n+1))} and the velocity as: (c/(n+1)2); the parametric constant for dimensionless cycletime is: (n = Hoxt).

And so knowing the present cycletime (np=1.132419321) via an arbitrary Mean-Alignment-Time or MAT, relative to a phase shiftable proto universe and set as (Midnight, November 4th, 1996, Canberra, Australia, local time); the present universal speed of recession is calculated as (22% of c), which then maps a selfrelative 'Arpian redshift' as the renormalisation for the receeding event horizon, mirrored in the Big Bang singularity; (zarp = 0.250529154).

We also calculate the 10D expansion of the universe as (53.105% or a radius of 8.96 billion lightyears), increasing to (113.24% or 19.11 billion lightyears [ly]) for the 11D universe.
The Hubble-Oscillation so defines the nodal Hubble-Constant: (Ho=1.8877728042x10-18 1/s*) or 58.04 Hubble Units [km/Mpc.s]) and the 10D-cosmic asymptotic diameter as (33.7522131 billion ly*). The Hubble constant varies between fps and Ho and is calculated to assume a a value of 66.9 Hubble units for the present time coordinate np in the cosmic evolution.

The [Alpha]-Variation so encompasses a period of (2[19.11 - 16.88] = 4.46 billion years) and hence two distance intervals; one from the present epoch (np) to a distance 2.23 billion years into the past at the nodal value (n=1) and its 11D-image at (n=1-0.1324..=0.8676).
Relative to the Big Bang Source however, this interval is mapped from (n=0.1324.. to n=0.2648..) as a linear double interval; just as two mirrors facing each other would reflect each other in the spacetime 'in between'. This 'in between' becomes our expanding spacetime and we can calculate the relevant distances, using cycletime n as parameter and the nodal Hubble-Constant as invariant at (n=1).
At (n=0.1324..or 2.23 billion years after the Big Bang; v'/c=0.7798 and z =1.843), relative to event horizon and at (n=0.2648.. or 4.46 billion years after the Big Bang; v'/c=0.6251 and z =1.08), relative to event horizon.

The cosmological redshift epoch between (z=1.082 to 1.843) and corresponding to a 2.23 billion year duration includes the 'peak of galaxies' at (z=1.18) and is characterised in the absolute minimum of the quintessential lambda and the gravitational maximum contractions to form galactic structures and superstructures under the auspices of the Sarkar Constant of 236.1 million lightyears.

Now looking back at those large redshift values, the lower one coinciding with the redshift of z=1.1 for supernova 1998 Iae, measured by Brian Schmidt of the 'High-Z-Team' must encompass a 'looking through' the imaged z-interval, namely the interval from the node at 2.23 billion years back to 4.46 billion years or the z-interval from
(n=0.8676, v'/c=0.2867, z=0.3431) to (n=1.0000, v'/c=0.2500, z=0.2910).

In other words, the 11D intersection of M-space intersects 10D-C-space in the two intervals, which form selfrelative images of each other.
The 10D Riemann hypersphere is subject to gravitation in mass-parameters and decelerates asymptotically towards its 11D M-space boundary in negative and open curvature, mirroring the asymptotic expansion in perfect flatness of Euclidean zero curvature, however.
The EMR-parameters so double themselves in the said interval, a interval which is itself expanding and contracts between the two nodal values of maximum frequency (fps) and minimum frequency (Ho).
But it is only the EMR parameter that defines this 'oscillating universe', the mass parameter remains asymptotic as defined in the parametric scalefactor
{r(n)=Rmax(n/(n+1), with Rmax=RHubble=RH=1.597767545x1026 m*}.

Revisiting the redshift data of 1998, we notice the 'missing redshifts' in the interval from (z=0.12-0.3), with the limiting nodal (z=1.843) mapped onto the nodal (z=0.291) and the boundary image (z=1.082) mapped in its boundary image (z=0.343). The first supernova, beginning to 'curve away' from the decelerating expansion predicted by theory, is at about (z=0.12).
Any receeding cosmological object with a redshift exceeding (z=0.291) can be considered to be moving in the 'Hubble Flow' with a measured redshift (zm=z), because after a distance of 2.23 billion ly no doubling of the electromagnetic parameters occurs for the distance between the two cosmic nodes.

But we find three z-intervals, in whom we must apply a redshift-correction; set in the images of the boundaries and the nodes.
The boundary (z=0.343, z=1.082) is imaged as the boundary image (zarp=0.2505, z=1.082) in the nodal mirror of (z=0.291, z=1.843) and the boundary mirror of (zarp=0.2505, z=1.082) images the nodal (z=0.291, z=1.843) in the nodal (z=zni, z=1.843).

If (v'/c=0.22), then (zm=zarp=0.2505 as the variation maximum) and at the event horizon, where zm=0, the z(zm)=zarp and azm+b=0.291 for zm=zni; subsequently (b=zarp & azni=0.0405) and a the gradient of the 'Local Flow', given in the equation: (z(zm)=azm+0.2505) for the present epoch.

The [Alpha]-Redshift spans the z(zm) range from (0.291 to 0.343) for the zm-interval from (zni to 0.2505) with positive gradient (0.052/(0.2505-zni)) and letting this gradient equal (a=0 from/zni) gives zni=0.1097 and (a=0.3692, for the [Alpha]-Redshift equation:
(zred(zm)=0.3692(zm)+0.2505).

The [Alpha]-Blueshift spans the zm-interval from (0.2505 to 0.2910) for the same range with a negative gradient ( -0.052/0.0405=-1.284) and a linear equation:
(zblue(zm)=-1.284(zm)+0.6646).

So the 'curving away' from the deceleration model at (z=1.12) becomes a consequence of the redshift (zni=0.1097) forming a nodal image in the other nodal redshifts of (z=0.291 and z=1.843); with the boundary redshift measured as (zm=0.2505), becoming a blueshift boundary for the interval until (zm=0.291), at which the true 'Hubble-Flow' begins at the present epoch with linear equation: (z(zm) = zm).

The nearest, most studied and most luminous quasar (or quasi-stellar object) is called 'Q3C273' (Cambridge catalogue); its recessional velocity is measured as (v'/c=0.14565), for a (zm=0.1580).
Applying the [Alpha]-Redshift equation gives a 'local flow correction' of: (z(0.1580)=0.3088), for which (n={√(c/v") -1}) and (v"/c=[(z2+2z)/(z2+2z+2)]) give corrected (n=0.9507) and (v"/c=0.2628).

The distance to 'Q3C273' can now be calculated simply by the application of the scalefactor r(n) in 10 and 11 dimensions in the formulations:
R10D(n) = r(np) - RH[n/(n+1)] and R11D(n) = [np - n]RH}
'Q3C273' in 10D is (RH(0.53105 - 0.48736) = 0.044(16.88 billion ly) = 737.428 million ly);
but in 11D this becomes: ([1.1324-0.9507]RH = 0.1817(0.53105)(16.88 billion ly) = 1.6288 billion ly).

As the universal [Alpha]-Variation, the zarp redshift is the maximum variation for the present epoch in the Hubble-Oscillation and the fluctuation of the Hubble parameter as the cosmic frequency is mirrored about (H'o(np)=Ho/(2-np)), valid for the (n=1 to 2)-cycle; hence (H'o(np)= 58.04/0.8676=66.90 Hubble units).
At the nodes, say at (np=2), (H'o) quantises as (fps) in the pixelation of spacetime.
At the nodal images however, (H'o) would assume its nodal value of 58.04 Hubble Units.

The Hubble 'Constant' subsequently varies with redshift at any cycletime (n); increasing from 58.04 to 66.9 in the z-intervals (0.1097-0.2505) and (0.2910-0.3431) and decreasing from 66.9 to 58.04 in the z-intervals (0.2505-0.2910) and (1.082-1.843) for the present Hubble epoch.
The 'arpian redshift' as variation maximum is situated at n-coordinate 0.8676, implying that correctly interpreted spectroscopic measurements must converge at a Hubble-Constant of 66.9 Hubble units and a projected mapped age for the universe of (0.8676x16.88 billion years) or 14.65 billion years.
For z=(0.3431-1.082), (Ho'=66.9) and the nodal intervals z=(0-0.110) and (z from 1.843) set it as (58.04).

This is a simple yet profound solution to the 70-year search to finetune the 'Hubble-Constant'.
It is no wonder, that there was so much disagreement regarding the measurements, seeing that it changes in the described intervals as a reflection of EMR parameters.
All astronomical and cosmological measurements engage optical instruments to catch photons and all of astrochemistry and astrophysics depends on spectrum analysis.
So the universe is 'well behaved' after all and decelerating under its own gravity, modified in the quintessence.

But how do you explain the 25%, on average, discrepancy in the luminosity of the supernovae examined?

That brings in the old 'Hubble Law', where the distance (RH) to an object receeding with velocity (v'=H'oxRH) sets an epoch dependent 'Hubble Constant' as the linear proportionality constant between recessional velocity and the distance to the object.
In the case of the quasar 'Q3C273', the measured redshift (z=0.1580) relates a recessional velocity of (v'=0.14565c); which is then 'corrected' to calculate the n-cycle position of 'Q3C273', allowing a Hubble-independent determination of its distance from the observer.

If you now use the applicable Hubble-Constant between (58.04 and 66.9) as (H'o=61.1 Hubble Units), interpolated say as:
(H'o=66.9-[0.2505-0.1580][66.9-58.0]/(0.2505-0.1097) = 66.9-5.8 = 61.1 Hubble Units); then the old Hubble Law with (61.1 Hubble Units=1.98x10-18 1/s*) gives you:
(RH= 0.14565c/H'o) and calculating as: (2.34 billion ly) and a distance 43% in excess of the n-cyclic value of (1.63 billion ly); but using a higher Hubble-Constant, such as 71 Hubble-Units, commonly used in the supernovae measurements, results in a scale reduction of 86% to (2.0 billion ly) and a 'dimming' effect of so 23%, which is the observed discrepancy.

So the spectroscopic measurements incorporate a natural 'dimming effect' in luminosities, due to the cosmological objects, (which are physically much nearer, than their redshift indicate), appearing to be further away also in the electromagnetic universe, than they truly are and so the theoretical predictions of their distances are correct in principle, but require modification via the old Hubble Law, which is only approximate, (valid only at the odd nodes) and unnecessary to calculate the distances.
And at higher redshifts, passing the imaging interval from (z=0.291 to 0.343), the seeming cosmic acceleration intensifies until the other imaging interval from (z=1.082 to 1.843) has been reached. The apparent cosmic acceleration hence becomes an imaged double boundary-nodal-mirror effect.

The [Alpha]-Variation measures shifts in wavelength, which have passed through the described intervals and a 'dip' in the constant is derived from the mathematical analysis.
How do you explain the magnitude of that dip; about 80 parts per million you said, in the light of the redshift intervals?

The [Alpha]-Variation is the dimensional intersection of M-C-space, 10D-C-space forming a holographic image in 12D-F-space.
The chargequantum (e) is defined via the Riemann Analysis of B(n), the supersymmetric wavefunction of the universe:
{B(n) = [2e/hA]exp(-[Alpha]xT(n) Inverse Sorce energy or Magneto charge units (C*)}; where {T(n) =...- 3 - 2 - 1 +0+ 1 + 2 + 3 +...= n(n+1)} and the Feynman-Path-Integral for all particle histories as an alternative formulation to the Schrödinger- Dirac- and Klein-Gordon Equations for the quantum mechanistic probability distribution of quantum states in the particle-wave duality.

The Action Law of (Action=ee*) manifests the lightspeed (c)-independent form of [Alpha] and can then be calibrated via the definition of the (c)-inclusive form in magnetic constant (μo). {[Alpha] = 60πe2/h = e2/(2εohc) = μoce2/(2h) = 1/137.0470731}

A Newton-Raphson iteration for B(n) and the boundary condition {T(n)=i2 in B{-[1/2]+-i(½√3)}, with a first approximation: (e1=(½hA=1.618221145x10-19 C*) converges to: (e=1.606456344x10-19 C*).

Abstract time in F-Space is defined as:

and so allows the definition of Inverse Time as frequency parameter physicalizing this abstraction for time in modular mirror duality made manifest in the string epoch of the Inflaton.
This then defines the GENESIS BOSON as the Particle of creation using the fundamental constants of Creation from the SEps algorithms. Those constants are then used inductively in the future by any sufficiently mentally evolved and cosmically selfaware civilisation to construct selfconsistent and logical measurement systems to rediscover their own nature and origins in a self induction of physical consciousness of their own cocreated Genesis in a perceived timearrow of entropy, flowing apparently from the past to the present to the future.

In practical terms, this engages the measurement and analysis of two fundamental constants, namely the speed of light 'c' and the Planckian quantum constant 'h' to relate the quantum as a micro energy selfstate (eigenvalue) to what is termed the classical physics of macro selfstates exemplified in the theoretical physics of Newton, Maxwell and Einstein in scientific models of reality and encompassing mechanics, electromagnetism and the relativities respectively. The dimensional analysis of 'hc' as a energyxdisplacement parameter suffices to calibrate the unitary mensuration parameters for mass, displacement and time, say in the Terran System International or SI-system of measurements of fundamental quantities, say here the kilogram, the meter and the second respectively. The other elementary units ain the SI-system are derived from the algorithmic masterconstant set and comprise the Kelvin for temperature as kinetic measure of the quantum states, the Ampere and Coulomb for electric current, the mole for molarity , the candela for luminosity with the sterradian an additional geometrized unit for angular measures.

Any arbitrary measurement system of an UO in a defined spacetime can then experimentally determine relationships and corollaries between experimental data and the changes in energy associated with dynamical systems. The UO has a mensuration system SI say and can calibrate its SI-system to any other unitary system like the star-* system of the UO*.

Dimensional Unit Calibration:

[m/s]/[m*/s*] = [c*/c] = [3x108/2.99792458x108] = [1.000692286] for {m/m*} = {1.000692286} {s/s*}​

[Js]/[J*s*] = [h*/h] = [6.66666666..x10-34/6.62607004x10-34] = [1.006126803] for {J/J*} = {1.006126803} {s*/s}​
[m5/s3]/[m5/s3]* = {[m/m*]2}.[c*/c]3 = Go*h*/Goh = 30ch*/30c*h = [c/c*][h*/h] = [0.999308193x1.00612803] = [1.005431984]​
for {m/m*} = [c/c*]2.√[h*/h] = [0.998616864x1.00305872] = [1.001671357]​

for {m}2 = 1.00334349 {m*}2 and m = 1.001671357 m* and m* = 0.998331431 m​
s = {m/m*}.[0.999308193] s* = [1.001671357x0.999308193] s* = 1.000978394 s* and {m/s} = 1.000692286 {m/s}* for {m/s}2 = 1.00138505 {m*/s*}2 as c2
J = {s*/s}[h*/h] J * = [0.999022562x1.006126803] J* = 1.005143377 J* and J* = 0.994882942 J​
kg = {s*/s}.{s/m}2.{m*/s*}2.[h*/h] kg* = {s/s*}{m*/m}2.[h*/h] kg* = [1.000978394x0.996665646x1.006126803] kg* = 1.003753126 kg*​

[H/m]/[H*/m*] = [J/J*][m*/m][C*/C]2.[s/s*]2 = μo*/μo = [120π/c*]/[4πx10-7]​
for C = √{[Js/J*s*][m*s/ms*]} C* =√{[h*/h][c/c*]} C* = √[1.006126803/1.000692286] C* = 1.002711702 C*​
[eV]/[eV*] = [e±J]/[e±J]* = [e±/e±*].[J/J*] for eV = [1.60217662x10-19/1.606456344x10-19].[1.005143377] eV* = 1.00246560 eV*​
[J/K]/[J*/K*] = {J/J*}.{K*/K} = [k*/k] = [1.411721579x10-23/1.380649x10-23] = [1.022505777] for K = [J/J*]/[1.022505777] K* = [1.005143377/1.022505777] K*= 0.983020397 K*​

Conversion Units are:
{s} = 1.000978394 {s*}​
{m} =1.001671357 {m*}​
{kg} = 1.003753126 {kg*}​
{C} = 1.002711702 {C*}​
{J} = 1.005143377 {J*}​
{eV} = 1.00246560 {eV*}​
{K} = 0.98301975 {K*}​

(m*= 0.998331431 m; s*= 0.999022562 s ; kg*=0.99626091 kg) in calibration of the base masterconstants (h/h*, c/c*, [Go]u=(1/30c)) and we note the numerical constancy for the magnetic constant in both mensuration systems: (μo)=4πx10-7 Henry/m (H/m) in (SI) and (μo)=120π/c (H*/m*) in (*).​
We recall that: (c=2.99792458x108 m/s (SI) and c*=3x108 m*/s* (*)).​
The Henry is a derived (SI) unit for magnetic inductance and has base units (Js2/C2=kgm2/C2), which so must give the (C to C*) unitary calibration in (μoo*)=1=0.994598576 C*2/C2, which gives (C*=0.997295631C) and DEFINES the (SI)-Coulombic Charge quantum as: (e=0.997295631e*=1.6021119x10-19 C (SI)).​

The textbooks of SI-physics have (e'=1.60217662x10-19 C (SI)), however and a value which differs from the value demanded by the magnetic constant (μo ) in a factor of (e'/e=1.0000403).
As the electropolic charge quantum appears squared in the [Alpha]-Constant, the [Alpha]-variation so becomes (1.0000807), with the old value of (e') exceeding the new value of (e) in so 4 parts in 100,000 and [Alpha]' greater in magnitude than [Alpha] by 81 parts in a million and in agreement with the Churchill-Webb measurements of 1998, increasing from Alpha = μoc.e2/2h = 1/137.047075 to Alpha' = 1/137.036003.
And I would suspect, that measuring [Alpha] even further back towards the Quantum Big Bang with increasing redshift, would better approximate the 80 parts per million increase in Alpha from say lower deviations at the say 8 parts per million at lower redshifts.

So the '[Alpha]-Dip' indicates that the textbook value for the electropole is fractionally too high; but that the Alpha Finestructure-Constant remains indeed constant, once the variation in the electronic charge quantum is taken into account.
Because the magnetic permeability constants are numerically the same in both the (SI) and the (*) unitary measurement systems; but
εo = 1/120πc = 8.841941283x10-12 (F/m)* and is εo = 8.8541878176x10-12 F/m (SI), the (SI) measurement is too large by a factor of 1.00138505 to correlate correctly wirth the magnetic permeability constant μo to give the Maxwell constant μoo = (120π/c).(1/120πc) = 1/c2.

It is experimentally measured in the (e/me)-ratio of the electron, subject to electric- and magnetic fields and this fits in nicely with my analysis of the electromagnetic mass of the electron.

In particular, the effective mass of the electron: (me=h[Alpha]/(2πRec)=9.290528912x10-31 kg*), also contains a magnetocharged part via (e*=2Rec2) for ([Alpha]=meπe*/(hc)) in the unification of the EMI with the GI by [Go=4πεo]u.
This magnetocharged part, intrinsic to the UFoQR as definition from (μo) and the quantisation of (λps) in (Re), we term 'Electromagnetic Mass':
(meEMR = 2μoe2/(3Ree* = 1.556643x10-32 kg*)) which is subtracted from the effective mass (me), gives me = 9.134865x10-31 kg* or 9.10071x10-31 kg (SI) and in agreement with the SI-textbook value of 9.1093835x10-31 kg (SI) to 95 parts in 100,000, subject to perturbation theory in the factor 2/3 in the electromagnetic mass.

The 'naked' restmass of the electron is about 98.245% of the effective mass, the latter specifying the 'naked' electron to move with a speed of (0.18077c) through an electric potential of (8.5748 keV*).
A detailed analysis of the electron's relativistic mass increase in equality with its energy of magnetic self induction forms the mathematical basis to 'prove' the 'Theory of Quantum Relativity' via a binomial distribution of the (v/c) parameter about the (X+Y=XY=i2=exp[iπ]= -1) FRB or 'Functional Riemann Bound' in a 'Complex Riemann Analysis'.
The '[Alpha]-Dip' is like a double symmetry; the magneto charged part of the electron is hidden and une requires the 'image of the image' to notice the skewing of the experimental data. The [Alpha]-Variation provides the mirroring of the nodes in the boundaries and vice versa and so indicates the intrinsic definition of the [Alpha]-Finestructure-Constant as the manifestation of the interdimensional law of action, leading to a 4-dimensional superconductivity coupled to the vacuum or zero-point-energy.

In the attempt to explain the [Alpha]-Dip, some theoretists have proposed a 'slowing down' of (c).
Recent formulations by populist physicist Paul Davies and in co-authorship with Tamara Davis and Charles Lineweaver from the Department of Astrophysics at the University of New South Wales, Sydney, Australia have followed the wrong avenues for the interpretation of the data however.
In a paper published in ('Nature': 'Black Holes constrain varying constants'; August 8th, 2002), the authors propose a varying light speed to be responsible for the [Alpha]-Dip and discount any possible variation in the electro charge quantum.

Davies' argument that an increase in (e) would alter the evolution of Black Holes in their entropic definitions does not take into account that a productation of the Boltzmann Constant (defining entropy), with (e) forms a fundamental finestructured constant in its own right.

In particular, the universe's wavefunction B(n) is localised in any arbitrary spacetime in 'unfreezing' the M-space 'stuck' in between the (X,Y) coordinates and subsequently in between real and imaginary linearised time parameters. This demands the establishment of a Mean-Alignment-Time or MAT, relative to a 'unfreezing definition' in a specification of the 'naked singularity', oscillating as zero-point about the FRB.

As E*.e= Epsx1/Eps = 1 as fundamental unity in the 11D Membrane-Mirror-Space of modular duality with e* the magneto charge; one can heuristically state that
(Energy E x charge quantum e) in the lower dimensional C-Line-Space C can be expressed as the inversed identity in the form of 1/T.
This then sets E.e=kTe=1 for [ek]=1/T and using an inverse proportion for mass in the lower dimensionality: [e*k*] = 1/T* sets a function f(n) = [ek]/[e*k*] = [T*/T].

This is the case for the Mass-Temperature inverse proportionality for the evolution of Black Holes from micro states to macro states and as in the Hawking Mass-Temperature relation for Black Holes:

{Minimum Planck Oscillator = ½hfPlanck = ½mPlanck.c2 for Tmax=Tps and Tmin=Tss in string modular T-duality for[/indent]
½mPlanck.TPlanck = (1/8π)(4π).mPlanck.TPlanck = Hawking Modulus HM = hc3/4πGok = MBHmin.TBHmax ={c2/4π2}. MBHmax.TBHmin.}.

B(n) is assigned B(np) = {[ek](SI)/[ek](*)}, with {[ek](SI)=constant=(1.60217662x10-19 C)(1.380649x10-23 J/K) = 2.21204355x10-42 CJ/K} and using the old (SI) value with the Alpha-Variation for (e'); using (e±=1.6021119x10-19 C) without the Alpha-Variation gives {[ek](SI)} = 2.21195419x10-42 CJ/K}.

The (*)-constant is a relatively fixed constant as: (e±*k*=2.267869086x10-42 (CJ/K)*) and subsequently B(np) calculates a particular value for n at the asymptote B(n⇒±∞)=0 as:

{[e±k](SI)/[e±k]*} = (2.21204355/2.267869086) = 0.975384145 (0.975344742)= [2e/hA].exp(-[Alpha]x[np2+np]), which yields an unique (np) as a complex solution to the quadratic equation by ln(0.975384145/0.992729803) = {ln(0.982527312)/-Alpha} = 2.415747501 = np2+np for: np2 + np - 2.415747501 = 0
solving as: (np=FRB(-½) ± 1.6327117).
For the unfrozen M-space with Alpha-Variation: {10D-root: np = 1.1327117 (real) & 12D-root: np = -2.1327117 (imaginary)}.
For the unfrozen M-space without Alpha-Variation: {10D-root: np = 1.1344063 (real) & 12D-root: np = -2.1344063 (imaginary)}.

This 'unfreezing' of M-space then allows the singularity algorithm of the cosmogenesis to manifest in what might be called the sex chromosomes of the universal DNA-encoding in terms of frequency or a number count.

A new physical quantity in 'awareness' is defined as the timedifferential of frequency and allows the concept of 'consciousness' to be born from the defining qualities of magneto charges.
Electromagneto-monopolic 'Life' derives as consequence of selfinductions of quantum geometric entities, specified from super membranes, macro-crystallised in electropolic self-capacitances and magnetopolic self-inductances, subsequently becoming subject to mutual cross inductances.
The purpose of the superbranial selfreplication on ever increasing scales, and until modular duality is reached in minmax boundary conditions; is to establish the multiversal nestings of the smallest within the largest - a process which constituted the beginnings of it all in the 'naked singularity' becoming defined as the Genesis BOSON.

The GENESIS Boson then becomes the parametric initialisation of creation in the abstract labelings of:
ENERGY=k.TEMPERATURE=h.FREQUENCY=h/TIME=MASS.c2 and using the SEps-MasterConstant Set: {4; 6; 7; Lo=1/[6x1015]; c2=9x1016; 11; h=1/[15x1032]; A=14x1524; k=1/[15x1618]; 26x6561} in reverse order and with arbitrary symbols as shown becoming associated with those 'master constants'.

Particularly then: ENERGY=hRmaxps with MASS=hRmaxpsc2=0.01183463299 and TEMPERATURE=hRmax/kλps=7.544808988..x1037 and FREQUENCY=Rmaxps=1.59767545..x1048

This becomes the 'Atomic-Mass-Unit' in 12D-F-Space in using one protonucleon mc=Alpha9Lplanck for every one of the 12 monopolar current loops in the Unified Field of Quantum Relativity (UFoQR).
A first Eps-Coefficient in the Expansion Series of the fundamental priciples from the SEps algorithm then crystallizes the 'Counter for matter' in Avogadro's Constant for Molarity:
MASS(20/33)/12mc = Navogadro = 6.02242143x1023 1/mol*

N=npsps/Rmax in REAL Time relative to the Quantum Big Bang to be created following the string epoch and relating to IMAGINARY TIME relative to this selfsame creation in the Cosmogony of the Genesis Boson of the Abba-Baab 11-dimensional supermembrane. This UNREAL Quantum Relative Time then is the Hubble-FREQUENCY Ho=c/Rmax in proportionality to the Source Frequency of the Eps-Gauge Photon fps=c/λps in the expression HoRmax=c=λps.fps

N then becomes the Nulltime for the initialisation of the string/supermembrane-serpent modular duality in the De Broglie phasespeed initialisation, beginning with the Oscillation (or Bounce) of the Planck-Length and specifies the Instantenuity of Now-Cycle-Time nps=Hotps=Ho/tss as the Time Instanton tps=1/fps=fss and the Inflaton Rmax=RHubble=c/Ho with de Broglie Phasespeed Vdebroglie=Rmax.fps=Rmax.c/λps=c/nps as the 'Heartbeat of the Cosmic Mother Black Hole' frequency of the oscillating cosmos in the Cosmology of QR and in the imaginary F-Space Time of NHo generalised in the Real Time n=Hot for any time in the evolving Cosmology and minimised in nps=Hotps.

L(nps,T(nps) = 6π2λps2.σ.T4 = 2.6711043034x1096 Watts*, where σ = Stefan's Constant = 2π5k4/15h3c2 and as a product of the defined 'master constants' k, h, c2, π and 'e'.

L(n,T) = 3HoMo.c2/550n and for Temperature T(nps)
T(nps) = 2.93515511x1036 Kelvin*.

This manifests as a 'false vacuum' and as a temperature gradient, as a causation of the Big Bang Instanton on physical grounds.
The metaphysical ground is the symmetry breaking from the source parity violation described in the birth and necessity of the Graviton to resymmetrize the UFoQR.

But modular string duality defines the Inverse Energy of the wormhole as the quantum of physical consciousness in units of the product of the classical electron diameter and the proportionality between energy and mass in the Maxwell constant c2 = 1/εoμo and the inverse of the product between electric permittivity εo=1/120cπ and magnetic permeability μo=120π/c for 'free space' impedance:
Zo= electric field strength E/magnetic field strength H = √(μoo) = cμo = 1/cεo = 120π}.

Coulomb Electro Charge e = LP.√α.c2 ↔ 2Re.c2 = e* (Star Coulomb Magneto Charge)

e* = 2Rec2 = 2ke2/me = e2/2πεome = αhc/πme with Alpha-Variation (1.6021119x10-19/1.60217662x10-19)2 = 0.99991921...for the calibration
{Reme} = μoe2/4π = (2.8179403267x10-15 m)(9.10938356x10-31 kg) = (10-7)(1.60217662x10-19 C)2 = [2.56696992x10-45].[1.001671358][1.003753127].(0.99991921..) (mkg)*
= [2.56696992x10-45].[1.002711702]2.[0.99991921..] = 2.580701985x10-45 {mkg}* = (2.77777..x10-15 m*)(9.290527148x10-31 kg*) = μoe2/4π for e=1.606456344x10-19 C*
for the quantum mechanical electron and adjusted in the [SI/*] alpha variation [mkg/C2] = Alpha Variation αvar in {Remevar}SI = {αvaroe2/4π}SI = {Reme}* = {μoe2/4π}*.

Decreasing the electronic charge quantum from 1.60217662x10-19 C to 1.602111893x10-19 C so calibrates the SI-unitary measurement system with the star based * unitary mensuration system in the alpha variation in a reduced classical electron radius of Re = 2.77314286x10-15 m for an increased electron effective restmass of me = 9.255788996x10-31 kg
for (Reme) = (μoe2/4π) = 2.566762517x10-45 mkg.

Note that the defined maximum scale for the electron in the Penning Trap is consistent with the defined size of the wormhole radius rps=10-22/2p metres as minimum spacetime configuration of the Instanton. The 'point particular' electron of Quantum ElectroDynamic and its point-like particle fields, so crystallizes naturally from the theory of the string-membrane classes.

xxx

Calculation of the ELECTRONMASS leading to the recurrence of the Fibonacci Roots X=0.618033... and Y=1.618033... as elementary Resonance factors in the UFoQR

The magnetic energy stored in a magnetic field B of volume V and area A=R2 for a (N-turn toroidal) current inductor N.i=BdR/μo for velocity v and selfinduction L=NBA/i is:

Um=½Li²=½(μo.N2R)(BR/μoN)²=½B²V/μo [/sup]
and the Magnetic Energy Density per unit volume is then:

Um/V=½B²/μo.

Similarly, the Electric Energy density per unit volume is:

Ue/V=½εoE² say via the Maxwell equations and Gauss' law.

By the Biot-Savart and Ampere Law:

B=μoq.v./4πr² and εo=1/c²μo for the E=cB foundation for electrodynamic theory.

So for integrating a spherical surface charge distribution dV=4πr².dr from Re to ∞:

Um=∫{μoq²v²/8πr²}dr = μoq²v²/8πRe.

Similarly,

Ue=∫dUe=q²v²/8πεoRe =kq²/2Re=½mec² as per definition of the classical electron radius and for the total electron energy mec² set equal to the electric potential energy. We term me here the EFFECTIVE electronmass and so differ it from an actual 'bare' restmass mo.

We now define the electric electromagnetic mass and the magnetic electromagnetic mass as:

melectric=kq²/2Rec²=Ue/c²=½me and consider the electric electron energy to be half the total energy (akin the virial theorem for PE=2KE, say in the Bohr atom)

PE=(-)ke²/RBohr = e²/4πεoRBohr = 2e²/8πεoRBohr =2KE

mmagneticoe²[v/c]²/8πRe=melectric.(v/c)²=½me.(v/c)² and which must be the KE by Einstein's c²dm=c²(me-mo)

and for the relativistic electronmass m=mo/√(1-B) for B=(v/c)²

Note: (B here is not the magnetic flux density vector B=E/c, measured in Tesla or gauss but a conventional label for the (v/c) ratio in Special Relativity).

But we can see, that should one use the measured electron mass from the Re-definition as the electron's restmass, that mmagnetic + melectric=me{½+½(v/c)²} < me , because of the mass-velocity dependency factor B and the groupvelocities v<c.

So we introduce the relativistic restmass mo and set Constant Amooe²/8πRe for AB=1/√[1-B] -1

from:

c2(m-mo)=μoe²v²/8πRe with m=mo/√(1-[v/c]2)

1=(1+AB2)2(1-B2)=1+B2(2A+A2B2-2AB2-A2B4-1) and so: {A2}B4+{2A-A2}B2+{1-2A}=0

with solution in roots:

B=([A-2]±√[A²+4A])/2A={(½-1/A)±√(¼+1/A)}.

This defines a distribution of B=(v/c)² velocity ratios in mo.AB=μoe²[v/c]²/8πRe

mmagneticoe²[v/c]²/8πRe=mo.AB=½me.(v/c)²

then finestructures mmagnetic in the relation moA=½me and allows correlation between the relativistic and kinetic restmass mo and the effective electron groundmass me (say).

In particular me =2Amo and is moA for A=½ AS the NEW minimisation condition.

In string parameters and with me in *units, the following is found:

moA=30e²c/e*=½me=4.645263574x10-31 kg*

This implies, that for A=1, mo=½me , where me=9.290527155x10-31 kg* from the prequantum algorithmic associations, based on the magnetic constant defining the Classical Electronic Radius.

As B≥0 for all velocities v, bounded as groupspeed (not de Broglie Phasespeed always vdB=(h/mvgroup)(mc2/h)=c2/vgroup >c) in c for which B=1 ; a natural limit is found for the B distribution at A=½ and A=∞

The electron's restmass mo so is binomially distributed for the B quadratic.
Its minimum value is half its effective mass me and as given in:

melectric=kq²/2Rec²=Ue/c²=½me for A=½ and its maximum for A=∞ is the unity v=c for B=1

The X-root is always positive in an interval from 0 to 1 and the Y-root is always negative in the interval from -3 to 0.

For A=½: B=-3/2±3/2 for roots x=0 and y=-3;

for A=¾: B=-5/6±√(19/12) for roots x=0.425 and y=-2.092;

for A=1: B=-½± ½√(5) for roots x=X=0.618033... and y=Y=-1.618033...;

for A=∞: B=½[-]±½[+] for roots x=1[-] and y=0[-];

AB2 = ([1-B2]-1) = 1+½B2-3B4/8+5B6/16 -35B8/128+...-1

Letting B=n, we obtain the Feynman-Summation or Path-Integral for dimensionless cycletime n=Hot=ct/RHubble with Ho=dn/dt in the UFoQR for 1=(1-B2)(1+B2)2 as B4+B2-1=0 for T(n)=n(n+1)=1.

The Binomial Identity gives the limit of A=½ in:

A=1/2 - B2{3/8 - 5B2/16 + 35B4/128 -...} and as the nonrelativistic low velocity approximation of E=mc² as KE=½mov².

But the FRB or Functional-Riemann-Bound in Quantum Relativity (and basic to the pentagonal string/brane symmetries) is defined in the renormalisation of a wavefunction B(n)=(2e/hφ).exp(-alpha.T(n)), exactly about the roots X,Y, which are specified in the electron masses for A=1 in the above.

The unifying condition is the Euler Identity: XY=X+Y = i2 = -1 = cos(π)+isin(π) = ℮

A Derivation of Hyperspace ET-UFO-Craft Acceleration

The Thuban Council releases the mathematical basis for ET-Craft acceleration as a fundamental extension of the Newtonian Forcelaw modulated by Classical Relativity and the Change of photon momentum in Quantum Mechanics.
An intrinsic relationship to the electromagnetic inertia of the classical electron is supplemented to indicate the elementary velocity distribution of the electron as applied in the ET-UFO-Craft propulsion as a parallel energy vector in hyperspace albeit suppressed or 'shadowed' in the Linespace of the lower dimensional 4D-spacetimes.

Quantum-Photon-Energy (Planck): E=hf
Quantum-Photon-Momentum: pphoton = E/c = hf/c = h/l

Mass Energy (Einstein): E=mc2 = moc2/√(1-[v/c]2)
Mass Momentum: pmass = mv = mov/√(1-[v/c]2) = hf.v/c2√(1-[v/c]2)

for the Photon inertia (mass) mo = hf/c2

This is related by the Energy-Momentum Formulation: E2 - Eo2 = p2c2 and from Eo = moc2 and indicating the mass-velocity relationship between a total energy content E=mc2 with its Kinetic Energy and change of momentum.

Newton's Force Law: FNewton = mass (m) x acceleration (a=dv/dt)

FNewton = d{mv}/dt = d{hf.v/c2√(1-[v/c]2)}/dt = {h/c2}{ d(v/√(1-[v/c]2))/dt + v.(df/dt)/√(1-[v/c]2}

Let u = v/√(1-[v/c]2) for du/dt = (du/dv).(dv/dt) = (v2/c2.(dv/dt)/(√(1-[v/c]2)3 + (dv/dt)/(√(1-[v/c]2) = (dv/dt)/(√(1-[v/c]2)3

(df/dt) = (c2/h).d{mo/√(1-[v/c]2)}/dt = mov.(dv/dt)/{h(√(1-[v/c]2)3}

Therefore:

FNewton = d{mv}/dt = d{hf.v/c2√(1-[v/c]2)}/dt = {h/c2}{f.(dv/dt)/(√(1-[v/c]2)3+ v.df/dt/√(1-[v/c]2}

= mo(dv/dt)/(√(1-[v/c]2)3.....................+...................(hv/c2).(df/dt)/(√(1-[v/c]2)

= Classical Relativistic Newton Force + Newtonian Frequency Law Extension

In terms of Energy: Energy=Work=ForcexDisplacement=FNewton.R

For the cosmic boundary parameters the maximum acceleration for a spacetime quantum is (dv/dt)|max = c.fps for the displacement quanta or wavelength lps = c/fps = R|min

R.mo(dv/dt)/(√(1-[v/c]2)3 then becomes supplemented in (R.hv/c2).( mov.(dv/dt)/{h(√(1-[v/c]2)3})/(√(1-[v/c]2)
= (mo.R.v2/c2).(dv/dt)/(1-[v/c]2)2 = (molpsfpsc.v2/c2)/(1-[v/c]2)2 = mov2/(1-[v/c]2)2 = Quantum Frequency-Velocity (Shadow) Energy as basic derivative from the Zero-Point-Field ZPE or Vortex-Potential Energy (VPE).

The form of the 'shadow' energy of the ET-UFO-Craft so assumes a velocity dependent inertial expression which is focused on the factor v2/(1-[v/c]2)2 to become identical at lightspeed c2 and a factor which becomes a multiplier for the original classically observable energy content of the ET-UFO-Craft in the form of E=mc2

In hyperspace, meaning the higher dimensional universe separating the de Broglie superluminal tachyonic phasespeed vdeBroglie from the lightspeed invariance of the lower dimensional universe characterised by the groupspeed vgroup; the 'shadow' energy manifests from the combined Energy equation relating the quantum mechanics to the classical relativistic dynamics:

Energy E = mc2 = hf

E=hf (Planck) iff m=mo=0
This manifests the lower dimensional observational matter-energy expressions

Energy E=mc2 (Einstein) iff f=fss=1/fps for mo = Sfss for the mass-frequency quantisation
This manifests the 'shadow matter' as a change in the mass eigen frequency fss under modular string-membrane duality

moc2/{√(1-[v/c]2)}3..........+.......... mov2/(1-[v/c]2)2 = 2moc2/{√(1-[v/c]2)}3

Lower 10D Anti-deSitter asymptotic .................+.................Higher 11D deSitter asymptotic
hyperbolic open(-) C-String spacetime............................spheroidally closed(+) M-mirror spacetime

moc2/{√(1-[v/c]2)}3..................................+................................ mov2/(1-[v/c]2)2 = 2moc2/{√(1-[v/c]2)}3

Classical Curvature Energy CCE................+...............Quantum Curvature Energy QCE...=...2CCE

as generalised 'Virial' Theorem: 2KE+PE=0 for CCE=QCE

Fcentripetal=mv2/R=GmM/R2=Fgravitational for a circular orbiting mass m about mass M, a distance R apart and so v2=GM/R

with gravitational PEgravitational=-GmM/R2 for ½mv2=GmM/2R and KE=-½PE

Generally QCE/CCE = [v/c]2/√(1-[v/c]2)

for the Perturbation Expansion for U=[v/c]2 as:

U{1-U} = U{1+U/2+3U2/8+5U3/16+35U4/128+63U5/256+...}

U<X for Higher D QCE < Lower D CCE
U=X for Higher D QCE = Lower D CCE
U>X for Higher D QCE > Lower D CCE

Subsequently:

[v/c]2 = (1-[v/c]2)2 for the Quadratic [v/c]4 - 3[v/c]2 +1 = 0 with solutions: [v/c]2 = ½{3 ± √(9-4)}

As [v/c]2 must be less than 1 for all lower dimensional groupspeeds; the real spacetime root is [v/c]2 = ½{3-√(5)} = 1+½{1-√5} = 1 - 0.61803398... = 0.3819660... as the Difference between the Fibonacci root termed the 'Golden Proportion' and Unity 1.

The focal resonance speed of the ET-UFO-Craft so is vUFO-Resonance/c = √{½(3-√5)}c = √0.3819660... = 0.61803398...=½(√5 - 1) = Golden Proportion = 1/Phi = 1/F

CCE=QCE for [v/c]2 = √(1-[v/c]2) and [v/c]4 = 1-[v/c]2 for [v/c]2 = ½{-1 ± √5} = X and |-Y|=1/X

X = √(1-X) for X2 = 1 - X for the particle history (Path Integral) T(n)=n(n+1)=1

and a UFO-spacecraft speed of √(√X2) = 0.78615...c

The ET-UFO-Craft henceforth engages a Resonance Physics of Hyperspace in the Unified Field of Quantum Relativity (UFoQR) and 'attunes' or 'taps' into this unified spacetime matrix at a speed of 0.618033..c or so 185,409.900 kilometres per second.

xxx

Note that Richard Feynman describes alpha in its squareroot, just as is required to define the Planck-Length Oscillation for the Inflaton in relation to the Stoney Units for the electric charge quantum.

Last edited: Mar 15, 2018

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Cosmological relevance of microtubules to the size of the electron as conformal wormhole quantization in quantum geometry

Dear Stuart!

and would like to comment on this page, relating the number of microtubules to the actual scale of the classical electron radius, as this might be a missing link to relate your theory (and Roger's CCC btw) to the cosmology and the underpinning fact of physical consciousness relating to the cosmological spacetime matrix.

Using this conformal mapping from the Quantum Big Bang 'singularity' from the electric charge in brane bulk space as a magnetic charge onto the classical spacetime of Minkowski and from the Planck parameters onto the atomic-nuclear diameters in 2Rec2 = e* from the Planck length conformally maps the Planck scale onto the classical electron scale.
This is addressed in my comment on Roger's CCC -Weyl model below.
But watching your presentation as indicated in the screenshots below; added to this conformal scale mapping in your scale of 2.5 fm, which is of course close to the classical electron radius and as defined in the alpha electromagnetic fine structure and the related mass-charge definition for the eigen energy of the electron in mec2=ke2/Re.

Also in my model of quantum relativity there is a quantization of exactly 1010 wormhole 'singularity-bounce' radii defining the radian-trigonometric Pi ratio as Rwormhole/Relectron = 360/2π.1010 or 1010 = {360/2π}{Re/rwormhole} as a characteristic number of microtubules in a conformal mapping from the classical electron space onto the 'consciousness' space of the neuron-cell intermediate between the Hubble scale of 1026 m and the Planck scale of 10-35 m as geometric mean of 10-4 to 10-5 metres.

Conformal Cyclic Cosmology (CCC) and the Weyl Curvature Hypothesis of Roger Penrose

View: https://youtu.be/FVDJJVoTx7s

The pre-Big Bang 'bounce' of many models in cosmology can be found in a direct link to the Planck-Stoney scale of the 'Grand-Unification-Theories'. In particular it can be shown, that the Squareroot of Alpha, the electromagnetic fine structure constant, multiplied by the Planck-length results in a Stoney-transformation factor LP√α = e/c2 in a unitary coupling between the quantum gravitational and electromagnetic fine structures {Gok=1 and representing a conformal mapping of the Planck length onto the scale of the 'classical electron' in superposing the lower dimensional inertia coupled electric charge quantum 'e' onto a higher dimensional quantum gravitational-D-brane magnetopole coupled magnetic charge quantum 'e*' = 2Re.c2 = 1/hfps = 1/EWeyl wormhole by the application of the mirror/T duality of the super membrane EpsEss of heterotic string class HE(8x8)}.

The standard model postulates the Big Bang singularity to become a 'smeared out' minimum space time configuration (also expressible as quantum foam or in vertex adjacency of Smolin's quantum loops). This 'smearing out' of the singularity then triggers the (extended) Guth-Inflation, supposedly ending at a time coordinate of so 10-32 seconds after the Big Bang.
If the Guth-Inflation ended at a time coordinate of 3.33x10-31 seconds coordinate, the Big Bang became manifest in the emergence of space time metrics in the continuity of classical general relativity and the quantum gravitational manifesto and say from a Higgs 'False Vacuum' at the 'bounce-time' reduced in a factor of so 11.7.
This means, that whilst the Temperature background remains classically valid, the distance scales for the Big Bang will become distorted in the standard model in postulating a universe the scale of a 'grapefruit' at the end of the inflation.
The true size (in Quantum Relativity) of the universe at the end of the inflation was the size of a wormhole, namely at a Compton-Wavelength (Lambda) of 10-22 meters and so significantly smaller, than a grapefruit.
Needless to say, and in view of the CMBR background of the temperatures, the displacement scales of the standard model will become 'magnified' in the Big Bang Cosmology of the very early universe in the scale ratio of say 10 cm/10 -20 cm=1021 i.e. the galactic scales in meter units.

A result of this is that the 'wormhole' of the Big Bang must be quantum entangled (or coupled) to the Hubble Horizon.
And from this emerges the modular duality of the fifth class of the superstrings in the Weyl-String of the 64-group heterosis.
The Big Bang wormhole becomes a hologram of the Hubble Horizon and is dimensionally separated by the Scale-parameter between a 3-dimensional space and a 4-dimensional space.
Then the 5-dimensional spacetime of Kaluza-Klein-Maldacena in de Sitter space forms a boundary for the 4D-Minkowski-Riemann-Einstein metrics of the classical cosmology. This can be revisited in the multi-dimensional membrane cosmologies.
The outer boundary of the second Calabi Yau manifold forms an open dS space-time in 12-dimensional brane space (F-Vafa 'bulk' Omnispace) with negative curvature k=-1 and cancels with its inner boundary as a positively curved k=1 spheroidal AdS space-time in 11 dimensions to form the observed 4D/10-dimensional zero curvature dS space-time, encompassed by the first Calabi Yau manifold.

A bounded (sub) 4D/10D dS space-time then is embedded in a Anti de Sitter (AdS) 11D-space-time of curvature k=+1 and where 4D dS space-time is compactified by a 6D Calabi Yau manifold as a 3-torus and parametrized as a 3-sphere or Riemann hypersphere.
The outer boundary of the 6D Calabi Yau manifold then forms a mirror duality with the inner boundary of the 11D Calabi Yau event horizon.
The Holographic Universe of Susskind, Hawking, Bekenstein and Maldacena plays a crucial part in this, especially as M-Theory has shown the entropic equivalence of the thermodynamics of Black Holes in the quantum eigenstates of the classical Boltzmann-Shannon entropy mathematically.
The trouble with the Susskind googolplex solutions is that the 'bulk landscape solutions' fail to take into account the super string self transformations of the duality coupled five classes. They think that all five classes manifest at the Planck-scale (therefore the zillions of solutions), they do not and transform into each other to manifest the Big Bang in a minimum space time configuration at the Weylian wormhole of class HE(8x8).

Roger Penrose has elegantly described the link of this to classical General Relativity in his "Weyl Curvature Hypothesis".
Quote from:'The large, the Small and the Human Mind"-Cambridge University Press-1997 from Tanner Lectures 1995"; page 45-46:

"I want to introduce a hypothesis which I call the 'Weyl Curvature Hypothesis'. This is not an implication of any known theory. As I have said, we do not know what the theory is, because we do not know how to combine the physics of the very large and the very small. When we do discover that theory, it should have as one of its consequences this feature which I have called the Weyl Curvature Hypothesis. Remember that the Weyl curvature is that bit of the Riemann tensor which causes distortions and tidal effects. For some reason we do not yet understand, in the neighbourhood of the Big Bang, the appropriate combination of theories must result in the Weyl tensor being essentially zero, or rather being constrained to be very small indeed.​

The Weyl Curvature Hypothesis is time-asymmetrical and it applies only to the past type singularities and not to the future singularities. If the same flexibility of allowing the Weyl tensor to be 'general' that I have applied in the future also applied to the past of the universe, in the closed model, you would end up with a dreadful looking universe with as much mess in the past as in the future. This looks nothing like the universe we live in. What is the probability that, purely by chance, the universe had an initial singularity looking even remotely as it does?​

The probability is less than one part in (1010)123. Where does this estimate come from? It is derived from a formula by Jacob Bekenstein and Stephen Hawking concerning Black Hole entropy and, if you apply it in this particular context, you obtain this enormous answer. It depends how big the universe is and, if you adopt my own favourite universe, the number is, in fact, infinite.​

What does this say about the precision that must be involved in setting up the Big Bang? It is really very, very extraordinary, I have illustrated the probability in a cartoon of the Creator, finding a very tiny point in that phase space which represents the initial conditions from which our universe must have evolved if it is to resemble remotely the one we live in. To find it, the Creator has to locate that point in phase space to an accuracy of one part in (1010)123. If I were to put one zero on each elementary particle in the universe, I still could not write the number down in full. It is a stupendous number". End of Quote​

Then the 'phase spaced' de Broglie inflation is in moduar quantum entanglement with the Weyl-Wormhole of the Zero Curvature of Roger Penrose's hypothesis.
The Hubble-Universe consists of 'adjacent' Weyl-wormholes, discretisizing all physical parameters in holofractal selfsimilarity.
Penrose's Weyl-tensor is zero as the quasi-reciprocal of the infinite curvature of the Hubble Event Horizon - quasi because the two scales (of the wormhole and Hubble Universe) are dimensionally separated in the modular coupling of the 11D super membrane boundary to the 10D superstring classical cosmology of the underpinning Einstein-Riemann-Weyl tensor of the Minkowski (flat) metric.

The CCC Penrose model becomes compatible with the inflation scenarios; should the multiverse cosmology become defined as occurring parallel in time-continuity and not as parallel in space in a manner envisaged by Roger Penrose.

https://cosmosdawn.net/index.php?lang=en

I have also attached a published paper in a Consciousness Journal for your perusal to perhaps lend further support for you and Roger Penrose in your work.

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and would like to comment on this page, relating the number of micro tubules to the actual scale of the classical electron radius, as this might be a missing link to relate your theory (and Roger's CCC btw) to the cosmology and the underpinning fact of physical consciousness relating to the cosmological spacetime matrix.

Using this conformal mapping from the Quantum Big Bang 'singularity' from the electric charge in brane bulk space as a magnetic charge onto the classical spacetime of Minkowski and from the Planck parameters onto the atomic-nuclear diameters in 2Rec2 = e* from the Planck length conformally maps the Planck scale onto the classical electron scale.
This is addressed in my commentary on Roger's CCC -Weyl model.
But watching your presentation as indicated in the screenshots above; added to this conformal scale mapping in your scale of 2.5 fm, which is of course close to the classical electron radius and as defined in the alpha electromagnetic fine structure and the related mass-charge definition for the eigen energy of the electron in mec2=ke2/Re.

Also in my model of quantum relativity (QR), there is a quantization of exactly 1010 wormhole 'singularity-bounce' radii defining the radian-trigonometric Pi ratio as Rwormhole/Relectron = 360/2π.1010 or 1010 = {360/2π}{Re/rwormhole} as a characteristic number of microtubules in a conformal mapping from the classical electron space onto the 'consciousness' space of the neuron-cell intermediate between the Hubble scale of 1026 m and the Planck scale of 10-35 m as geometric mean of 10-4 to 10-5 metres.

It is so the geometry of the architecture of the microtubules and the nature of their construction utilizing the pentagonal quasi-crystalline pattern in its application for maximising the compression of information in the Fibonacci geometrical pattern-sequencing. This then results in the conformal mapping of this geometry as a quantum geometry and defining physical consciousness as a conformal mapping of the quantum of spacetime in the form of Weylian 'Quantum Big Bang' wormholes of the cosmogenesis.

The pre-Big Bang 'bounce' of many models in cosmology can be found in a direct link to the Planck-Stoney scale of the 'Grand-Unification-Theories'. In particular it can be shown, that the Squareroot of Alpha, the electromagnetic fine structure constant, multiplied by the Planck-length results in a Stoney-transformation factor LP√α = e/c2 in a unitary coupling between the quantum gravitational and electromagnetic fine structures {Gok=1 and representing a conformal mapping of the Planck length onto the scale of the 'classical electron' in superposing the lower dimensional inertia coupled electric charge quantum 'e' onto a higher dimensional quantum gravitational-D-brane magnetopole coupled magnetic charge quantum 'e*' = 2Re.c2 = 1/hfps = 1/EWeyl wormhole by the application of the mirror/T duality of the super membrane EpsEss of heterotic string class HE(8x8)}.

What is Consciousness?

Answer: The dynamic occupancy of spacetime by physicalised quantum conglomerations.

Uwe Uehle:
December 1 at 2:27pm

Just for perspective. Of course no space is truly empty - but this is symbolic for the miracle you're bathing in right here - right now

Margo Callaghan
Wow what a mind bender-

Tony Bermanseder
Space is consciousness related via an advanced quantum mechanics. Therefore you can figure out what the metaphysics or spirit concept really relates and points to. Its not dieu ex machina but machina ex dieu.

Calculation:
7.4 Billion people weigh about 518 Billion kilograms for an average weight of 70 kg. As one proton has a mass of about 1.7x10-27 kg; the total mass of humanity in weight are so 3x1038 protons. One proton has a volume of so 4x(1.4x10-15)3 = 10-44 cubic metres and for all the protons of humanity the volume adds to about 3x10-6 cubic meters or 3 cubic centimeters which is a cubic size for a cube about _______________ that long.

Andrew Bellon
so what is all that empty space doing...is there direct interaction between nucleons and virtual particles relating to the nature of "spin," or how the universe actually sustains itself from moment to moment?

This is an appropriate question, which leads directly into the deepest nature of what energy is and it relates on a most fundamental way to the reality of universal consciousness. Firstly, the 'empty space' of an atom manifests as a form of 'force field' in that the interaction 'Goldstone' bosons mediate a 'force', which then manifests as the appearance of solid state physics. So tapping a table actually taps an energy field etc. The problems with this mainstream physical interpretation and model begin right here , because the 'Goldstones' (photons, weakons, gravitons, gluons, higgs) are said to be 'virtual' that is not having a real physical existence.

This is erroneous, just as the mainstream notion of consciousness and mind being nonphysical is also not supported by a higher dimensional cosmology and physics. As an example consider Einstein's E=mc2 applied to the total mass content of the universe. For a mass of say 1050 tons you will have an energy summation of so 1070 Joules. But if you now use the quantum energy, also well defined in Planck parameters, you calculate the quantum energy per space quantum and you get far higher values for this energy.

Using the conventions (Planck Length, Holographic bounds etc) and using the Event Hubble extent of the universe, you get something like (Number of space quanta) x 2x109 = 2x109x(10147) ~ 2x10156 Joules. Now the string physics tells you that the energy per string quantum is something like 1064 Joules per cubic meter as a physical manifesto of this quantum energy; whilst the energy of all matter in space is something like 10-10 Joules per cubic meter. So the 'discrepancy' between quantum energy and matter energy is in a factor of so 74 (and 87 in the quantum-Planck limit). This number then becomes associated with the 'Dark Energy' and the 'Dark Matter' to explain the discrepancy.

The 'empty space' of the atom so is in fact 'spanned' by the 'virtual' energy which is dark and has a dark matter component which is defined in physical consciousness parameters based on the quantum energy parameters and especially the physical size of the electron.

This naturally allows a refined approach to fundamental physics, such as the difference between the Hydrogen atom and the neutron and how radioactive beta/neutron decay allows the primordial universe to build the table of the chemical elements. This transformation then relates to the interaction probability between matter and light in electromagnetic parameters so showing the basic electron to be a 'point particle/string' of a minimum size; but also a 'smeared out' or extended circular membrane characterised by the Fermi scale of the 'Goldstones'.

The spacial extent of the differences then defines physical consciousness as a modular dual or mirror property of the space quantum itself; namely whatever is measured as energy derived from the macro-physics becomes a reciprocated magneto-polar 'supercharge' in the form of the electronic diameter maximised multiplied by the time differential of frequency as inversed time. But this change of string/brane vibration over time is also an angular acceleration without radial extent and so you find the innermost nature of the quantum spin, which is radially independent.

Those physical definitions for consciousness then carry enormous implications of course. Namely space itself is conscious in a physical sense and any dynamic occupying space adds to a space inherent base consciousness independent of the dynamics and living entities moving about within it.

Collapsing a hydrogen atom that is forcing the electron to overcome its weakon force field of the beta decay results in a neutron star of 'degenerate electrons' and you then can observe the quantum physics in the astrophysics. So your original question regarding the empty space resolves in the transformation of energy density in space. Then you should adapt the quantum theory to the holographic universe and the multidimensional membrane physics to resolve the wave-particle duality and the quantum entanglement on both the micro-cosmic and the macro-cosmic scales to find the universal unification. The quantum entanglement can easily be seen to be the effect of the modular duality inferred at the beginning to resolve a number of apparent paradoxes, such as the Schrödinger Cat and the Chicken-Egg DNA/RNA etc paradoxes.

Last edited: Mar 14, 2018

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3,404
The first Ylemic Stars in the Universe, Antiwormholes and the Higgs Neutrino

The stability of stars is a function of the equilibrium condition, which balances the inward pull of gravity with the outward pressure of the thermodynamic energy or enthalpy of the star (H=PV+U). The Jeans Mass MJ and the Jeans Length RJ a used to describe the stability conditions for collapsing molecular hydrogen clouds to form stars say, are well known in the scientific data base, say in formulations such as:

MJ=3kTR/2Gm for a Jeans Length of: RJ=√{15kT/(4πρGm)}=RJ =√(kT/Gnm²).

Now the Ideal Gas Law of basic thermodynamics states that the internal pressure P and Volume of such an ideal gas are given by PV=nRT=NkT for n moles of substance being the Number N of molecules (say) divided by Avogadro's Constant L in n=N/L .

Since the Ideal Gas Constant R divided by Avogadro's Constant L and defines Boltzmann's Constant k=R/L. Now the statistical analysis of kinetic energy KE of particles in motion in a gas (say) gives a root-mean-square velocity (rms) and the familiar 2.KE=mv²(rms) from the distribution of individual velocities v in such a system.

It is found that PV=(2/3)N.KE as a total system described by the v(rms). Now set the KE equal to the Gravitational PE=GMm/R for a spherical gas cloud and you get the Jeans Mass. (3/2N).(NkT)=GMm/R with m the mass of a nucleon or Hydrogen atom and M=MJ=3kTR/2Gm as stated.

The Jeans' Length is the critical radius of a cloud (typically a cloud of interstellar dust) where thermal energy, which causes the cloud to expand, is counteracted by gravity, which causes the cloud to collapse. It is named after the British astronomer Sir James Jeans, who first derived the quantity; where k is Boltzmann Constant, T is the temperature of the cloud, r is the radius of the cloud, μ is the mass per particle in the cloud, G is the Gravitational Constant and ρ is the cloud's mass density (i.e. the cloud's mass divided by the cloud's volume).

Now following the Big Bang, there were of course no gas clouds in the early expanding universe and the Jeans formulations are not applicable to the mass seedling Mo; in the manner of the Jeans formulations as given.

However, the universe's dynamics is in the form of the expansion parameter of GR and so the R(n)=Rmax(n/(n+1)) scalefactor of Quantum Relativity.
So we can certainly analyse this expansion in the form of the Jeans Radius of the first protostars, which so obey the equilibrium conditions and equations of state of the much later gas clouds, for which the Jeans formulations then apply on a say molecular level.
This analysis so defines the ylemic neutron stars as protostars and the first stars in the cosmogenesis and the universe.

Let the thermal internal energy or ITE=H be the outward pressure in equilibrium with the gravitational potential energy of GPE=Ω. The nuclear density in terms of the superbrane parameters is ρcritical=mc/Vcritical with mc a base-nuleon mass for a 'ylemic neutron'.

Vcritical= 4πRe3/3 or the volume for the ylemic neutron as given by the classical electron radius Re=1010λwormhole/360=e*/2c2.

H=(molarity)kT for molar volume as N=(R/Re)3 for dH=3kTR2/Re3.
Ω(R)= -∫GoMdm/R = -{3Gomc2/(Re3)2 }∫R4dR = -3Gomc2R5/Re6 for
dm/dR=d(ρV)/dR=4πρR2 and for ρ=3mc/4πRe3

For equilibrium, the requirement is that dH=dΩ in the minimum condition dH+dΩ=0.
This gives: dH+dΩ=3kTR2/Re3 - 16Goπ2ρ2R4/3=0 and the ylemic radius as:

Rylem=√{kTRe/Gomc2}

as the Jeans-Length precursor or progenitor for subsequent stellar and galactic generation.

The ylemic (Jeans) radii are all independent of the mass of the star as a function of its nuclear generated temperature. Applied to the protostars of the vortex neutron matter or ylem, the radii are all neutron star radii and define a specific range of radii for the gravitational collapse of the electron degenerate matter.

This spans from the 'First Three Minutes' scenario of the cosmogenesis to 1.1 million seconds (or about 13 days) and encompasses the standard beta decay of the neutron (underpinning radioactivity). The upper limit defines a trillion degree temperature and a radius of over 40 km; the trivial Schwarzschild solution gives a typical ylem radius of so 7.4 kilometers and the lower limit defines the 'mysterious' planetesimal limit as 1.8 km.

For long a cosmological conundrum, it could not be modelled just how the molecular and electromagnetic forces applicable to conglomerate matter distributions (say gaseous hydrogen as cosmic dust) on the quantum scale of molecules could become strong enough to form say 1km mass concentrations, required for 'ordinary' gravity to assume control.

The ylem radii's lower limit is defined in this cosmology then show, that it is the ylemic temperature of the 1.2 billion degrees K, which perform the trick under the Ylem-Jeans formulation and which then is applied to the normal collapse of hydrogenic atoms in summation.

The stellar evolution from the ylemic (dineutronic) templates is well established in QR and confirms most of the Standard Model's ideas of nucleosynthesis and the general Temperature cosmology. The standard model is correct in the temperature assignment, but is amiss in the corresponding 'size-scales' for the cosmic expansion.

The Big Bang cosmogenesis describes the universe as a Planck-Black Body Radiator, which sets the Cosmic-Microwave-Black Body Background Radiation Spectrum (CMBBR) as a function of n as T4=18.2(n+1)2/n3 and derived from the Stefan-Boltzmann-Law and the related statistical frequency distributions.

We have the GR metric for Schwarzschild-Black Hole Evolution as RS=2GM/c² as a function of the star's Black Hole's mass M and we have the ylemic Radius as a function of temperature only as Rylem√(kT.Re3/Gomc2).

The nucleonic mass-seed mc=mP.Alpha9 and the product Gomc2 is a constant in the partitioned n-evolution of

mc(n)=Yn.mc and G(n)=Go.Xn.

Identifying the ylemic Radius with the Schwarzschild Radius then indicates a specific mass a specific temperature and a specific radius.

Those we call the Chandrasekhar Parameters:
MChandra=1.5 solar Masses=3x1030 kg and RChandra=2GoMChandra/c² or 7407.40704..metres, which is the typical neutron star radius inferred today.

TChandra=RChandra2.Gomc2/kRe3 =1.985x1010 K for Electron Radius Re and Boltzmann's Constant k.

Those Chandrasekhar parameters then define a typical neutron star with a uniform temperature of 20 billion K at the white dwarf limit of ordinary stellar nucleosynthetic evolution (Hertzsprung-Russell or HR-diagram).
The Radius for the massparametric Universe is given in R(n)=Rmax(1-n/(n+1)) correlating the ylemic temperatures as the 'uniform' CMBBR-background and we can follow the evolution of the ylemic radius via the approximation:

Rylem=0.05258..√T=(0.0753).[(n+1)2/n3][1/8]

Rylem(npresent=1.1324..)=0.0868 m* for a Tylem(npresent )=2.73 K for the present time
tpresent=npresent/Ho.

What then is nChandra?
This would describe the size of the universe as the uniform temperature CMBBR today manifesting as the largest stars, mapped however onto the ylemic neutron star evolution as the protostars (say as nChandra'), defined not in manifested mass (say neutron conglomerations), but as a quark-strange plasma, (defined in QR as the Vortex-Potential-Energy or VPE).

R(nChandra')=Rmax(nChandra'/(nChandra'+1))=7407.40741.. for nChandra'=4.64x10-23 and so a time of tChandra'=nChandra'/Ho=nChandra'/1.88x10-18=2.47x10-5 seconds.

QR defines the Weyl-Temperature limit for Bosonic Unification as 1.9 nanoseconds at a temperature of 1.4x1020 Kelvin and the weak-electromagnetic unification at 1/365 seconds at T=3.4x1015 K.

So we place the first ylemic protostar after the bosonic unification (before which the plenum was defined as undifferentiated 'bosonic plasma'), but before the electro-weak unification, which defined the Higgs-Bosonic restmass induction via the weak interaction vector-bosons and allowing the dineutrons to be born.

The universe was so 15 km across, when its ylemic 'concentrated' VPE-Temperature was so 20 Billion K and we find the CMBBR in the Stefan-Boltzmann-Law as:
T4=18.20(n+1)2/n3=1.16x1017 Kelvin.

So the thermodynamic temperature for the expanding universe was so 5.85 Million times greater than the ylemic VPE-Temperature; and implying that no individual ylem stars could yet form from the mass seedling Mo.

The universe's expansion however cooled the CMBBR background and we to calculate the scale of the universe corresponding to this ylemic scenario; we simply calculate the 'size' for the universe at TChandra=20 Billion K for TChandra4 and we then find nChandra=4.89x10-14 and tChandra=26,065 seconds or so 7.24 hours.

The Radius R(nChandra)=7.81x1012 metres or 7.24 lighthours.
This is about 52 Astronomical Units and an indicator for the largest possible star in terms of radial extent and the 'size' of a typical solar system, encompassed by supergiants on the HR-diagram.

We so know that the ylemic temperature decreases in direct proportion to the square of the ylemic radius and one hitherto enigmatic aspect in cosmology relates to this in the planetesimal limit. Briefly, a temperature of so 1.2 billion degrees defines an ylemic radius of 1.8 km as the dineutronic limit for proto-neutron stars contracting from so 80 km down to this size just 1.1 million seconds or so 13 days after the Big Bang.

This then 'explains' why chunks of matter can conglomerate via molecular and other adhesive interactions towards this size, where then the accepted gravity is strong enough to build planets and moons. It works, because the ylemic template is defined in subatomic parameters reflecting the mesonic-inner and leptonic outer ring boundaries, the planetesimal limit being the leptonic mapping. So neutrino- and quark blueprints micromacro dance their basic definition as the holographic projections of the spacetime quanta.

Now because the Electron Radius is directly proportional to the linearised wormhole perimeter and then the Compton Radius via Alpha in Re=1010λwormhole/360=e*/2c2=Alpha.RCompton, the Chandrasekhar White Dwarf limit should be doubled to reflect the protonic diameter mirrored in the classical electron radius.

Hence any star experiencing electron degeneracy is actually becoming ylemic or dineutronic, the boundary for this process being the Chandrasekhar mass. This represents the subatomic mapping of the first Bohr orbit collapsing onto the leptonic outer ring in the quarkian wave-geometry.
But this represents the Electron Radius as a Protonic Diameter and the Protonic Radius must then indicate the limit for the scale where proton degeneracy would have to enter the scenario. As the proton cannot degenerate in that way, the neutron star must enter Black Hole phasetransition at the Re/2 scale, corresponding to a mass of 8MChandra=24x1030 kg* or 12 solar masses.

The maximum ylemic radius so is found from the constant density proportion ρ=M/V:
(Rylemmax/Re)3=MChandra/mc for Rylemmax=40.1635 km.

The corresponding ylemic temperature is 583.5 Billion K for a CMBBR-time of 287 seconds or so 4.8 minutes from a n=5.4x10-16, when the universe had a diameter of so 173 Million km.
But for a maximum nuclear compressibility for the protonic radius, we find:

(Rylemmax/Re)3=8MChandra/mc for Rylemmax=80.327 km, a ylemic temperature of 2,334 Billion K for a n-cycletime of 8.5x10-17 and a CMBBR-time of so 45 seconds and when the universe had a radius of 13.6 Million km or was so 27 Million km across.

The first ylemic protostar vortex was at that time manifested as the ancestor for all neutron star generations to follow. This vortex is described in a cosmic string encircling a spherical region so 160 km across and within a greater universe of diameter 27 Million km which carried a thermodynamic temperature of so 2.33 Trillion Kelvin at that point in the cosmogenesis.

This vortex manifested as a VPE concentration after the expanding universe had cooled to allow the universe to become transparent from its hitherto defining state of opaqueness and a time known as the decoupling of matter (in the form of the Mo seedling partitioned in mc's) from the radiation pressure of the CMBBR photons.

The temperature for the decoupling is found in the galactic scale-limit modular dual to the wormhole geodesic as 1/λwormholeantiwormholegalaxyserpent=1022 metres or so 1.06 Million ly and its luminosity attenuation in the 1/e proportionality for then 388,879 lightyears as a decoupling time ndecoupling.

A maximum galactic halo limit is modulated in 2πλantiwormhole metres in the linearisation of the Planck-length encountered before in an earlier discussion.

R(ndecoupling)=Rmax(ndecoupling/(ndecouplingc+1))=1022 metres for ndecoupling=6.26x10-5 and so for a CMBBR-Temperature of about T=2935 K for a galactic protocore then attenuated in so 37% for ndecouplingmin=1.0x10-6 for R=λantiwormhole/2π and ndecouplingmax=3.9x10-4 for R=2πλantiwormhole and for temperatures of so 65,316 K and 744 K respectively, descriptive of the temperature modulations between the galactic cores and the galactic halos.

So a CMBBR-temperature of so 65,316 K at a time of so 532 Billion seconds or 17,000 years defined the initialisation of the VPE and the birth of the first ylemic protostars as a decoupling minimum. The ylemic mass currents were purely monopolic and known as superconductive cosmic strings, consisting of nucleonic neutrons, each of mass mc.

If we assign this timeframe to the maximised ylemic radius and assign our planetesimal limit of fusion temperature 1.2 Billion K as a corresponding minimum; then this planetesimal limit representing the onset of stellar fusion in a characteristic temperature, should indicate the first protostars at a temperature of the CMBBR of about 744 Kelvin.

The universe had a tremperature of 744 K for ndecouplingmax=3.9x10-4 for R=2πλantiwormhole and this brings us to a curvature radius of so 6.6 Million lightyears and an 'ignition-time' for the first physical ylemic neutron stars as first generation protostars of so 7 Million years after the Big Bang.

The important cosmological consideration is that of distance-scale modulation.
The Black Hole Schwarzschild metric is the inverse of the galactic scale metric.
The linearisation of the Planck-String as the Weyl-Geodesic and so the wormhole radius in the curvature radius R(n) is modular dual and mirrored in inversion in the manifestation of galactic structure with a nonluminous halo a luminous attenuated diameter-bulge and a superluminous (quasar or White Hole Core).

The core-bulge ratio will so reflect the eigenenergy quantum of the wormhole as heterotic Planck-Boson-String or as the magnetocharge as 1/500, being the mapping of the Planck-Length-Bounce as e=lP.c²√Alpha onto the electron radius in e*=2Re.c².

Hypersphere volumes and the mass of the Tau-neutrino

Consider the universe's thermodynamic expansion to proceed at an initializing time (and practically at lightspeed for the lightpath x=ct describing the hypersphere radii) to from a single spacetime quantum with a quantized toroidal volume 2π²rw³ and where rw is the characteristic wormhole radius for this basic building unit for a quantized universe (say in string parameters given in the Planck scale and its transformations).

At a time tG, say so 18.85 minutes later, the count of space time quanta can be said to be 9.677x10102 for a universal 'total hypersphere radius' of about rG=3.39x1011 meters and for a G-Hypersphere volume of so 7.69x1035cubic meters.

{This radius is about 2.3 Astronomical Units (AUs) and about the distance of the Asteroid Belt from the star Sol in a typical (our) solar system.}

This modelling of a mapping of the quantum-microscale onto the cosmological macroscale should now indicate the mapping of the wormhole scale onto the scale of the sun itself.

rw/RSun(i)=Re/rE for RSun(i)=rwrE/Re=1,971,030 meters. This gives an 'inner' solar core of diameter about 3.94x106 meters.

As the classical electron radius is quantized in the wormhole radius in the formulation Re=1010rw/360, rendering a finestructure for Planck's Constant as a 'superstring-parametric': h=rw/2Rec3; the 'outer' solar scale becomes RSun(o)=360RSun(i)=7.092x108 meters as the observed radius for the solar disk.

19 seconds later; a F-Hypersphere radius is about rF=3.45x1011 meters for a F-count of so 1.02x10103spacetime quanta. We also define an E-Hypersphere radius at rE=3.44x1014 meters and an E-count of so 10112 to circumscribe this 'solar system' in so 230 AU.

We so have 4 hypersphere volumes, based on the singularity-unit and magnified via spacetime quantization in the hyperspheres defined in counters G, F and E. We consider these counters as somehow fundamental to the universe's expansion, serving as boundary conditions in some manner. As counters, those googol-numbers can be said to be defined algorithmically and independent on mensuration physics of any kind.

The mapping of the atomic nucleus onto the thermodynamic universe of the hyperspheres

Should we consider the universe to follow some kind of architectural blueprint; then we might attempt to use our counters to be isomorphic (same form or shape) in a one-to-one mapping between the macrocosmos and the microcosmos. So we define a quantum geometry for the nucleus in the simplest atom, say Hydrogen. The hydrogenic nucleus is a single proton of quark-structure udu and which we assign a quantum geometric template of Kernel-InnerRing-OuterRing (K-IR-OR), say in a simple model of concentricity.

We set the up-quarks (u) to become the 'smeared out core' in say a tripartition uuu so allowing a substructure for the down-quark (d) to be u+InnerRing. A down-quark so is a unitary ring coupled to a kernel-quark. The proton's quark-content so can be rewritten and without loss of any of the properties associated with the quantum conservation laws; as proton-> udu->uuu+IR=KKK+IR. We may now label the InnerRing as Mesonic and the OuterRing as Leptonic.

The OuterRing is so definitive for the strange quark in quantum geometric terms: s=u+OR.
A neutron's quark content so becomes neutron=dud=KIR.K.KIR with a 'hyperon resonance' in the lambda=sud=KOR.K.KIR and so allowing the neutron's beta decay to proceed in disassociation from a nucleus (where protons and neutrons bind in meson exchange); i.e. in the form of 'free neutrons'.

The neutron decays in the oscillation potential between the mesonic inner ring and the leptonic outer ring as the 'ground-energy' eigenstate.

There actually exist three uds-quark states which decay differently via strong, electromagnetic and weak decay rates in the uds (Sigmao Resonance); usd (Sigmao) and the sud (Lambdao) in increasing stability.
This quantum geometry then indicates the behaviour of the triple-uds decay from first principles, whereas the contemporary standard model does not, considering the u-d-s quark eigenstates to be quantum geometrically undifferentiated.
The nuclear interactions, both strong and weak are confined in a ' Magnetic Asymptotic Confinement Limit
coinciding with the Classical Electron Radius Re=ke²/mec² and in a scale of so 3 Fermi or 2.8x10-15 meters. At a distance further away from this scale, the nuclear interaction strength vanishes rapidly.

The wavenature of the nucleus is given in the Compton-Radius Rc=h/2πmc with m the mass of the nucleus, say a proton; the latter so having Rc=2x10-16 meters or so 0.2 fermi.

The wave-matter (after de Broglie generalising wavespeed vdB from c in Rcc) then relates the classical electron radius as the 'confinement limit' to the Compton scale in the electromagnetic finestructure constant in Re=Alpha.Rc.

The extension to the Hydrogen-Atom is obtained in the expression Re=Alpha².RBohr1 for the first Bohr-Radius as the 'ground-energy' of so 13.7 eV at a scale of so 10-11 to 10-10 meters (Angstroems).
These 'facts of measurements' of the standard models now allow our quantum geometric correspondences to assume cosmological significance in their isomorphic mapping. We denote the OuterRing as the classical electron radius and introduce the InnerRing as a mesonic scale contained within the geometry of the proton and all other elementary baryonic- and hadronic particles.

Firstly, we define a mean macro-mesonic radius as: rM=½(rF+rG)~ 3.42x1011 meters and set the macro-leptonic radius to rE=3.44x1014 meters.
Secondly, we map the macroscale onto the microscale, say in the simple proportionality relation, using
(de)capitalised symbols: Re/Rm=rE/rM.

We can so solve for the micro-mesonic scale Rm=Re.rM/rE ~ 2.76x10-18 meters.
So reducing the apparent measured 'size' of a proton in a factor about about 1000 gives the scale of the subnuclear mesonic interaction, say the strong interaction coupling by pions.

The Higgsian Scalar-Neutrino

The (anti)neutrinos are part of the electron mass in a decoupling process between the kernel and the rings. Neutrino mass is so not cosmologically significant and cannot be utilized in 'missing mass' models'.
We may define the kernel-scale as that of the singular spacetime-quantum unit itself, namely as the wormhole radius rw=10-22/2π meters.

Before the decoupling between kernel and rings, the kernel-energy can be said to be strong-weakly coupled or unified to encompass the gauge-gluon of the strong interaction and the gauge-weakon of the weak interaction defined in a coupling between the OuterRing and the Kernel and bypassing the mesonic InnerRing.

So for matter, a W-Minus ( weakon) must consist of a coupled lepton part, yet linking to the strong interaction via the kernel part. If now the colour-charge of the gluon transmutates into a 'neutrino-colour-charge'; then this decoupling will not only define the mechanics for the strong-weak nuclear unification coupling; but also the energy transformation of the gauge-colour charge into the gauge-lepton charge.

There are precisely 8 gluonic transitive energy permutation eigenstates between a 'radiative-additive' Planck energy in W(hite)=E=hf and an 'inertial-subtractive' Einstein energy in B(lack)=E=mc2, which describe the baryonic- and hyperonic 'quark-sectors' in: mc2=BBB, BBW, WBB, BWB, WBW, BWW, WWB and WWW=hf.
The permutations are cyclic and not linearly commutative. For mesons (quark-antiquark eigenstates), the permutations are BB, BW, WB and WW in the SU(2) and SU(3) Unitary Symmetries.

So generally, we may state, that the gluon is unfied with a weakon before decoupling; this decoupling 'materialising' energy in the form of mass, namely the mass of the measured 'weak-interaction-bosons' of the standard model (W- for charged matter; W+ for charged antimatter and Zo for neutral mass-currents say).

Experiment shows, that a W- decays into spin-aligned electron-antineutrino or muon-antineutrino or tauon-antineutrino pairings under the conservation laws for momentum and energy.
So, using our quantum geometry, we realise, that the weakly decoupled electron must represent the OuterRing, and just as shown in the analysis of QED ( Quantum-Electro-Dynamics). Then it can be inferred, that the Electron's Antineutrino represents a transformed and materialised gluon via its colourcharge, now decoupled from the kernel.

Then the OuterRing contracts (say along its magnetoaxis defining its asymptotic confinement); in effect 'shrinking the electron' in its inertial and charge- properties to its experimentally measured 'point-particle-size'. Here we define this process as a mapping between the Electronic wavelength 2πRe and the wormhole perimeter λw=2πrw.

But in this process of the 'shrinking' classical electron radius towards the gluonic kernel (say); the mesonic ring will be encountered and it is there, that any mass-inductions should occur to differentiate a massless lepton gauge-eigenstate from that manifested by the weakon precursors.

{Note: Here the W- inducing a lefthanded neutron to decay weakly into a lefthanded proton, a lefthanded electron and a righthanded antineutrino. Only lefthanded particles decay weakly in CP-parity-symmetry violation, effected by neutrino-gauge definitions from first principles}.

This so defines a neutrino-oscillation potential at the InnerRing-Boundary. Using our proportions and assigning any neutrino-masses mn as part of the electronmass me, gives the following proportionality as the mass eigenvalue of the Tau-(Anti)Neutrino as Higgsian Mass Induction in the Weak Nuclear Interaction at the Mesonic Inner Ring Boundary within the subatomic quantum geometry utilized as the dynamic interaction space:

mHiggs/Tauon=meλw.rE/(2πrMRe) ~ 5.4x10-36 kg or 3.0 eV*.

So we have derived, from first principles, a (anti)neutrinomass eigenstate energy level of 3 eV as the appropriate energy level for any (anti)neutrino matter interaction within the subatomic dynamics of the nuclear interaction.

This confirms the Mainz, Germany Result as the upper limit for neutrino masses resulting from ordinary Beta-Decay and indicates the importance of the primordial beta-decay for the cosmogenesis and the isomorphic scale mappings stated above.

The hypersphere intersection of the G- and F-count of the thermodynamic expansion of the mass-parametric universe so induces a neutrino-mass of 3 eV* at the 2.76x10-18 meter marker.

The more precise G-F differential in terms of eigenenergy is 0.052 eV as the mass-eigenvalue for the Higgs-(Anti)neutrino (which is scalar of 0-spin and constituent of the so called Higgs Boson as the kernel-Eigenstate). This has been experimentally verified in the Super-Kamiokande (Japan) neutrino experiments published in 1998 and in subsequent neutrino experiments around the globe, say Sudbury, KamLAND, Dubna, MinibooNE and MINOS.

Recalling the Cosmic scale radii for the initial manifestation of the primordial 'Free Neutron (Beta-Minus) Decay', we rewrite the Neutrino-Mass-Induction formula:

rE = 3.43597108x1014 meters and an E-count of so 1.00x10112 spacetime quanta

mnHiggs-E=mnelectron=meλw.{rE/rE}(2πRe) ~ 5.323x10-39 kg* or 0.003 eV* as Weak Interaction Higgs Mass induction.

rF = 3.45107750x1011 metres for the F-count of so 1.02x10103 spacetime quanta
mnHiggs-F=mnmuon=meλw.{rE/rF}/(2πRe) ~ 5.300x10-36 kg* or 2.969 eV* as Weak Interaction Higgs Mass induction.

rG = 3.39155801x1011 metres for the G-count of so 9.68x10102 spacetime quanta
mnHiggs-G=mntauon=meλw.{rE/rG}(2πRe) ~ 5.393x10-36 kg* or 3.021 eV* as Weak Interaction Higgs Mass Induction.

The mass difference for the Muon-Tau-(Anti)Neutrino Oscillation, then defines the Mesonic Inner Ring Higgs Induction:

mnHiggs=meλw.rE{1/rG-1/rF}/(2πRe) ~ 9.301x10-38 kg* or 0.0521 eV* as the Basic Cosmic (Anti)Neutrino Mass.

This Higgs-Neutrino-Induction is 'twinned' meaning that this energy can be related to the energy of so termed 'slow- or thermal neutrons' in a coupled energy of so twice 0.0253 eV for a thermal equilibrium at so 20° Celsius and a rms-standard-speed of so 2200 m/s from the Maxwell statistical distributions for the kinematics.

Sterile neutrino back from the dead
22 June 2010 by David Shiga
http://www.newscientist.com/issue/2766

A ghostly particle given up for dead is showing signs of life.

Not only could this "sterile" neutrino be the stuff of dark matter, thought to make up the bulk of our universe, it might also help to explain how an excess of matter over antimatter arose in our universe.
Neutrinos are subatomic particles that rarely interact with ordinary matter. They are known to come in three flavours – electron, muon and tau – with each able to spontaneously transform into another.
In the 1990s, results from the Liquid Scintillator Neutrino Detector (LSND) at the Los Alamos National Laboratory in New Mexico suggested there might be a fourth flavour: a "sterile" neutrino that is even less inclined to interact with ordinary matter than the others.

Hasty dismissal

Sterile neutrinos would be big news because the only way to detect them would be by their gravitational influence – just the sort of feature needed to explain dark matter.
Then in 2007 came the disheartening news that the Mini Booster Neutrino Experiment (MiniBooNE, pictured) at the Fermi National Accelerator Laboratory in Batavia, Illinois, had failed to find evidence of them.
But perhaps sterile neutrinos were dismissed too soon. While MiniBooNE used neutrinos to look for the sterile neutrino,
LSND used antineutrinos – the antimatter equivalent. Although antineutrinos should behave exactly the same as neutrinos, just to be safe, the MiniBooNE team decided to repeat the experiment – this time with antineutrinos.

Weird excess

Lo and behold, the team saw muon antineutrinos turning into electron antineutrinos at a higher rate than expected – just like at LSND. MiniBooNE member Richard Van de Water reported the result at a neutrino conference in Athens, Greece, on 14 June.
The excess could be because muon antineutrinos turn into sterile neutrinos before becoming electron antineutrinos, says Fermilab physicist Dan Hooper, who is not part of MiniBooNE. "This is very, very weird," he adds.
Although it could be a statistical fluke, Hooper suggests that both MiniBooNE results could be explained if antineutrinos can change into sterile neutrinos but neutrinos cannot – an unexpected difference in behaviour.
The finding would fit nicely with research from the Main Injector Neutrino Oscillation Search, or MINOS, also at Fermilab, which, the same day, announced subtle differences in the oscillation behaviour of neutrinos and antineutrinos.
Antimatter and matter are supposed to behave like mirror versions of each other, but flaws in this symmetry could explain how our universe ended up with more matter.

Neutrinomasses

The (Anti)Neutrino Energy at the RE nexus for RE=rw∛(26x6561) m* and
for mnHiggs-E=mnelectron=lwh.Alpha/4p2Re2c=30e2lw/2pRe2c or 15l]w{Monopole GUT masses ec}/pRe2 = 2.982...10-3 eV*.

This can also be written as mnHiggs-E=mnelectron=mnTauon2 to define the 'squared' Higgs (Anti)Neutrino eigenstate from its templated form of the quantum geometry in the Unified Field of Quantum Relativity (UFoQR).

Subsequently, the Muon (Anti)Neutrino Higgs Induction mass becomes defined in the difference between the masses of the Tau-(Anti)Neutrino and the Higgs (Anti)Neutrino.

mnTauon = B4G4R4[0]+B2G2R2[-½]=B6G6R6[-½] = √(mnelectron)=√(0.002982)=0.0546... eV*

mnHiggs= B4G4R4[0] = meλw.rE{1/rG-1/rF}/(2πRe) ~ 9.301x10-38 kg* or 0.0521... eV*
mnMuon
= B2G2R2[-½] = √(mnTauon2 - mnHiggs2) = √(0.00298-0.00271) = √(0.00027) = 0.0164... eV*

mnElectron = B2G2R2[-½] = (mnTauon)2= (0.054607...)2=0.002982... eV*

This energy self state for the Electron (Anti)Neutrino then is made manifest in the Higgs Mass Induction at the Mesonic Inner Ring or IR as the squared mass differential between two (anti)neutrino self states as:
(mn3 + mn2).(mn3 - mn2) = mn32 - mn22 = 0.002981...eV*2 to reflect the 'squared' energy self state of the scalar Higgs (Anti)Neutrino as compared to the singlet energy Eigen state of the base (anti)neutrinos for the 3 leptonic families of electron-positron and the muon-antimuon and the tauon-antitauon.

The Electron-(Anti)Neutrino is massless as base-neutrinoic weakon eigenstate and inducted at RE at 0.00298 eV*.
The Muon-(Anti)Neutrino is also massless as base-neutrinoic weakon eigenstate and inducted at the Mesonic Ring F-Boundary at 2.969 eV* with an effective Higgsian mass induction of 0.0164 eV*.

The Tauon-(Anti)Neutrino is not massless with inertial eigenstate inducted at the Mesonic Ring G-Boundary at 3.021 eV* and meaned at 3.00 eV* as √(0.05212+0.01642) = 0.0546 eV* as the square root value of the ground state of the Higgs inertia induction. The neutrino flavour mechanism, based on the Electron (Anti)Neutrino so becomes identical in the Weakon Tauon-Electron-Neutrino oscillation to the Scalar Muon-Higgs-Neutrino oscillation.

The weakon kernel-eigenstates are 'squared' or doubled (2x2=2+2) in comparison with the gluonic-eigenstate (one can denote the colourcharges as (R²G²B²)[½] and as (RGB)[1] respectively say and with the [] bracket denoting gauge-spin and RGB meaning colours Red-Green-Blue).
The scalar Higgs-Anti(Neutrino) becomes then defined in: (R4G4B4)[0] and the Tauon Anti(Neutrino) in (R6G6B6)[½].

The twinned neutrino state so becomes MANIFESTED in a coupling of the scalar Higgs-Neutrino with a massless base neutrino in a (R6G6B6)[0+½]) mass-induction template.
The Higgs-Neutrino is bosonic and so not subject to the Pauli Exclusion Principle; but quantized in the form of the FG-differential of the 0.0521 Higgs-Restmass-Induction.
Subsequently all experimentally observed neutrino-oscillations should show a stepwise energy induction in units of the Higgs-neutrino mass of 0.0521 eV. This was the case in the Super-Kamiokande experiments; and which was interpreted as a mass-differential between the muonic and tauonic neutrinoic forms.

mnHiggs + mnelectron = mnHiggs + (mnTauon)2 for the 'squared' ground state of a massless base (anti)neutrino for a perturbation Higgsian (anti)neutrino in (mnTauon)2 = (mnHiggs + d)2 = mnElectron for the quadratic mnHiggs2 + 2mnHiggsd + d2 = 0.002982 from (mnHiggs + d) = √(mnelectron) and for a d = √(mnelectron) - mnHiggs = mnTauon - mnHiggs = 0.0546-0.0521 = 0.0025.

mnHiggs + d = 0.0521 + 0.0025 = (mnHiggs) + (mnelectron) - 0.00048 = mnTauon = 0.0521+0.00298 - 0.00048 + ... = 0.0546 eV* as a perturbation expression for the 'squared' scalar Higgs (Anti)Neutrino.

(mnMuon - mnElectron){(mnMuon + mnElectron) - (mnMuon - mnElectron)} = 2mnElectron(mnMuon - mnElectron)
as the squared mass difference:

mnMuon2 - mnElectron2 = 2mnElectron(mnMuon - mnElectron) + (mnMuon - mnElectron)2

and {mnMuon2 - mnElectron2} - mnMuon2 + 2mnMuonnElectron - mnElectron2 = 2mnMuonmnElectron - 2mnElectron2 = ({3mnElectron}2 - 02)
= (0.00894..)2 = 7.997..x10-5 eV2* as the KamLAND 2005 neutrino mass induction value for 11mnElectron = 2mnMuon.

For 3 (anti)neutrinos then, the cosmological summation lower and upper bounds for (anti)neutrino oscillations are:
0 + m
nelectron-muon + mnelectron-tauon + mnmuon-tauon = 3(0.002982) = 0.00895 eV* and 3(0.0030+0.0546) = 3(0.0576) = 0.1728 eV* or 0.1724 eV [SI] respectively.

Inclusion of the scalar Higgs (anti)neutrino as a fourth (anti)neutrino inertial self state extends this upper boundary by 0.0521 eV* to 0.2249 eV* or 0.2243 eV [SI].

Sn = mnElectron + mnMuon + mnHiggs+ mnTauon = 0.0546..+0.0521..+0.0164..+0.0030 = 0.1261 eV* or 0.1258 eV.

(Starunits[*] calibrate as {SI}: {J}=0.9948356[J*]; {s}=0.99902301[s*]; {m}=0.9983318783[m*]; {kg}=0.9962135[kg*];
{C}=0.997296076[C*]; {eV}=0.99753285[eV*])

In terms of the Higgs Mass Induction and so their inertial states, the Neutrinos are their own antiparticles and so Majorana defined; but in terms of their basic magneto charged nature within the Unified Filed of Quantum Relativity, the Neutrinos are different from their AntiNeutrino antiparticles in their Dirac definition of R2G2B2[+1] for the AntiNeutrinos and in B2G2R2[-1] for the Neutrinos.

Mass

The Standard Model of particle physics assumed that neutrinos are massless. However the experimentally established phenomenon of neutrino oscillation, which mixes neutrino flavour states with neutrino mass states (analogously to CKM mixing), requires neutrinos to have nonzero masses.[20]

Massive neutrinos were originally conceived by Bruno Pontecorvo in the 1950s. Enhancing the basic framework to accommodate their mass is straightforward by adding a right-handed Lagrangian. This can be done in two ways. If, like other fundamental Standard Model particles, mass is generated by the Dirac mechanism, then the framework would require an SU(2) singlet. This particle would have no other Standard Model interactions (apart from the Yukawa interactions with the neutral component of the Higgs doublet), so is called a sterile neutrino. Or, mass can be generated by the Majorana mechanism, which would require the neutrino and antineutrino to be the same particle.

The strongest upper limit on the masses of neutrinos comes from cosmology: the Big Bang model predicts that there is a fixed ratio between the number of neutrinos and the number of photons in the cosmic microwave background. If the total energy of all three types of neutrinos exceeded an average of 50 eV per neutrino, there would be so much mass in the universe that it would collapse.[37] This limit can be circumvented by assuming that the neutrino is unstable; however, there are limits within the Standard Model that make this difficult. A much more stringent constraint comes from a careful analysis of cosmological data, such as the cosmic microwave background radiation, galaxy surveys, and the Lyman-alpha forest. These indicate that the summed masses of the three neutrinos must be less than 0.3 eV.[38]

In 1998, research results at the Super-Kamiokande neutrino detector determined that neutrinos can oscillate from one flavor to another, which requires that they must have a nonzero mass.[39] While this shows that neutrinos have mass, the absolute neutrino mass scale is still not known. This is because neutrino oscillations are sensitive only to the difference in the squares of the masses.[40]
The best estimate of the difference in the squares of the masses of mass eigenstates 1 and 2 was published by KamLAND in 2005: |Δm212| = 0.000079 eV2.