Symmetrical Breaking (spin 8)

124875 is a doubling circuit . By addition, all numbers reduce to the root number. The numbers all spiral around O, this spiral makes the 124875 doubling circuit and also correlates 369. 124875 is also a halving circuit. By addition every number will reduce to its own root number. (Vortex Math)

The pseudoscalar meson nonet. Members of the original meson “octet (8)” are shown in green, the singlet in magenta. Although these mesons are now grouped into a nonet (9), the Eightfold Way name derives from the patterns of eight for the mesons and baryons in the original classification scheme. (Wikipedia)

In geometry, an enneagram (🟙 U+1F7D9) is a nine-pointed plane figure. It is sometimes called a nonagram, nonangle, or enneagon.[1]

The word ‘enneagram’ combines the numeral prefix ennea- with the Greek suffix -gram. The gram suffix derives from γραμμῆ (grammē) meaning a line.

• A regular enneagram is a 9-sided star polygon. It is constructed using the same points as the regular enneagon, but the points are connected in fixed steps.
• Two forms of regular enneagram exist:
  • One form connects every second point and is represented by the Schläfli symbol {9/2}.
  • The other form connects every fourth point and is represented by the Schläfli symbol {9/4}.
• There is also a star figure, {9/3} or 3{3}, made from the regular enneagon points but connected as a compound of three equilateral triangles.[3][4] (If the triangles are alternately interlaced, this results in a Brunnian link.)
• From this perspective, there are twenty-seven (27) distinct personality patterns, because people of each of the nine (9) types also express themselves as one of the three (3) subtypes.

This star figure is sometimes known as the star of Goliath, after {6/2} or 2{3}, the star of David.[5] (Wikipedia)

Vortex Based Mathematics transcends our myopic quantitative understanding for the way Number operates in our holographic universe. Numbers are not just mere quantities. Each has its own unique quality, archetype, and behavior. Vortex Based Math (VBM) is the study of Number in and of itself. Numeronomy as opposed to Numerology. The bedrock of the Quadrivium, Number structures our conceptual waking reality. As Pythagoras once so aptly put it, “All is Number”. (JoeDubs)

The pattern of weak isospin T3, weak hypercharge YW, and color charge of all known elementary particles, rotated by the weak mixing angle to show electric charge Q, roughly along the vertical. The neutral Higgs field (gray square) breaks the electroweak symmetry and interacts with other particles to give them mass. (Wikipedia)

Explanatory diagram showing how symmetry breaking works. At a high enough energy level, a ball settled in the center (lowest point), and the result has symmetry. At lower energy levels, the center becomes unstable, the ball rolls to a lower point - but in doing so, it settles on an (arbitrary) position and the result is that symmetry is broken - the resulting position is not symmetrical (Wikipedia)

SU(5) fermions of standard model in 5+10 representations. The sterile neutrino singlet’s 1 representation is omitted. Neutral bosons are omitted, but would occupy diagonal entries in complex superpositions. X and Y bosons as shown are the opposite of the conventional definition

Researchers at the U.S. Department of Energy’s Ames Laboratory have discovered a new type of Weyl semimetal, a material that opens the way for further study of Weyl fermions, a type of massless elementary particle hypothesized by high-energy particle theory and potentially useful for creating high-speed electronic circuits and quantum computers.

• Researchers created a crystal of molybdenum and tellurium, one of only a few compounds that had been predicted to host a new and recently postulated type of Weyl state, where the hole and electron bands normally separated by an indirect gap touch at a few Weyl points. Those points are equivalent to magnetic monopoles in the momentum space and are connected by Fermi arcs.
• A combination of angle resolved photoemission spectroscopy (ARPES), modelling, density functional theory and careful calculations were used to confirm the existence of this new type of Weyl semimetal. This material provides an exciting new platform to study the properties of Weyl fermions, and may lead the way to more new materials with unusual transport properties.

“This an important, interdisciplinary discovery because it allows us to study many aspects of these exotic particles predicted by high energy physics theory in solid state, without need for extremely expensive particle accelerators,” said Adam Kaminsky, Ames Laboratory scientist and professor in the Department of Physics and Astronomy at Iowa State University. “From my perspective as solid state physicist it is absolutely extraordinary to observe two bands touching each other at certain points and being connected by Fermi arcs – objects that are prohibited to exist in “ordinary” materials.” (rdworldonline.com)

This proposition was first demonstrated by Edwin Hubble (1889-1953). The American astronomer discovered in 1929 that every galaxy is pulling away from us, and that the most distant galaxies are moving the most quickly. This suggests that there was a time in the past when all the galaxies were located at the same spot, a time that can only correspond to the Big Bang. (Hubble bubble)

Tensors may map between different objects such as vectors, scalars, even other tensors contained in a group of partitions.

Mathematically, they specify the decomposition of the tensor product of two irreducible representations into a direct sum of irreducible representations, where the type and the multiplicities of these irreducible representations are known abstractly. The name derives from the German mathematicians Alfred Clebsch (1833–1872) and Paul Gordan (1837–1912), who encountered an equivalent problem in invariant theory.

Generalization to SU(3) of Clebsch–Gordan coefficients is useful because of their utility in characterizing hadronic decays, where a flavor-SU(3) symmetry exists (the eightfold way) that connects the three light quarks: up, down, and strange. (Wikipedia)

In this short review, we have briefly described the structure of exceptional field theories (ExFT’s), which provide a (T)U-duality covariant approach to supergravity. These are based on symmetries of toroidally reduced supergravity; however are defined on a general background.

• From the point of view of ExFT the toroidal background is a maximally symmetric solution preserving all U-duality symmetries. In this sense the approach is similar to the embedding tensor technique, which is used to define gauge supergravity in a covariant and supersymmetry invariant form. Although any particular choice of gauging breaks certain amount of supersymmetry, the formalism itself is completely invariant. Similarly the U-duality covariant approach is transferred to dynamics of branes in both string and M-theory, whose construction has not been covered here.
• In the text, we described construction of the field content of exceptional field theories from fields of dimensionally reduced 11-dimensional supergravity, and local and global symmetries of the theories. Various solutions of the section constraint giving Type IIA/B, 11D and lower-dimensional gauged supergravities have been discussed without going deep into technical details. For readers’ convenience references for the original works are present.
• As a formalism exceptional field theory has found essential number of application, some of which have been described in this review in more details. In particular, we have covered generalized twist reductions of ExFTs, which reproduce lower-dimensional gauged supergravities, description of non-geometric brane backgrounds and an algorithm for generating deformations of supergravity backgrounds based on frame change inside DFT. However, many fascinating applications of the DFT and ExFT formalisms have been left aside.

Among these are non-abelian T-dualities in terms of Poisson-Lie transformations inside DFT [100,101]; generating supersymmetric vacua and consistent truncations of supergravity into lower dimensions [102,103,104] (for review see [105]); compactifications on non-geometric (Calabi-Yau) backgrounds and construction of cosmological models [54,55,106,107]. (U-Dualities in Type II and M-Theory)

The eigenvectors of the matrix (red lines) are the two special directions such that every point on them will just slide on them (Wikipedia).

From what we learned above about segregating twin prime candidates, we can demonstrate that they compile additively in perfect progression, completing an infinite sequence of circles (multiples of 30 and 360)