Modeling that predicts elementary particles and explains data about dark matter, early galaxies, and the cosmos

We try to solve three decades-old physics challenges. List all elementary particles. Describe dark matter. Describe mechanisms that govern the rate of expansion of the universe. We propose new modeling. The modeling uses extensions to harmonic oscillator mathematics. The modeling points to all known elementary particles. The modeling suggests new particles. Based on those results, we do the following. We explain observed ratios of dark matter amounts to ordinary matter amounts. We suggest details about galaxy formation. We suggest details about in ation. We suggest aspects regarding changes in the rate of expansion of the universe. We interrelate the masses of some elementary particles. We interrelate the strengths of electromagnetism and gravity. Our work seems to o er new insight regarding applications of harmonic oscillator mathematics. Our work seems to o er new insight regarding three branches of physics. The branches are elementary particles, astrophysics, and cosmology.


Introduction and summary
We oer modeling that may solve at least the following three physics challenges. List all elementary particles. Describe dark matter. Explain some seemingly unresolved aspects regarding the rate of expansion of the universe.
The modeling outputs the elementary particle Standard Model particle set and suggests additional elementary particles. The modeling suggests a well-specied description of dark matter particles. The modeling adds aspects to concordance cosmology.
This essay discusses relationships between data, so-called ongoing modeling, and so-called proposed modeling. The data features the domains of elementary particle physics, astrophysics, and cosmology.
Ongoing modeling denotes established physics modeling and unveried modeling that other people propose. Proposed modeling denotes our work.
Each of ongoing modeling and proposed modeling includes a core component and another component.
Core ongoing modeling includes established modeling regarding motion, the Standard Model particle set, and concordance cosmology. Ongoing modeling also includes unveried models such as supersymmetry.
Core proposed modeling outputs a set of elementary particles that includes and adds to the Standard Model elementary particle set. Supplementary proposed modeling includes modeling -regarding motion -that has some similarities to quantum eld theory. Table 1 lists some goals that we have for proposed modeling.
The core of this essay has bases in synergies between core ongoing modeling and core proposed modeling. For example, each one of core ongoing modeling and core proposed modeling embraces symmetries that correlate with, for example, conservation of momentum and conservation of angular momentum.
Our work progressed through three phases. Each later phase enriched methods and results from prior phases. Phase one pursued the following two goals. Explain three eras in the rate of expansion of the universe. Explain the ratio of dark matter density of the universe to ordinary matter density of the universe. Phase two pursued the following two goals. Develop and use a model that outputs the list of all known elementary particles and a set of well-specied suggested elementary particles. Describe dark matter. Phase three pursued the following goal. Explain ratios, that pertain to galaxy clusters and to galaxies, of dark matter amounts to ordinary matter amounts. Table 2 summarizes some of the results that our modeling produces. (Table 27b notes the new property -isomer or isomers -that pertains regarding elementary particles. Discussion regarding table 27 points to additional information about isomers.) Table 3 points to tables that summarize some results from proposed modeling. Table 4 discusses relationships between some aspects of ongoing modeling and some aspects of proposed modeling.
The following remarks provide perspective about this essay.
Reference [1] suggests standards regarding discussing modeling. Regarding individual models, we discuss correlations with data, limits of applicability, opportunities to make improvements, unresolved aspects, and alternatives. Regarding collections of models, we discuss possible synergies between models and possible discord between models.
This essay makes correlations between aspects of data, ongoing modeling, and proposed modeling.
Such correlations can consider that aspects of one model do not necessarily equal similar aspects of another model. Wording of the form AA correlates with BB does not necessarily imply concepts such as AA equals BB or AA implies BB. Table 1: Some goals for proposed modeling Goal • Explain data that ongoing modeling seems not to explain.
• Predict data that people can (at least eventually) verify or refute. • Develop and use models that are compatible with essentially all relevant currently known data. • Develop and use models that are compatible with core ongoing modeling. (The models might point to limits of applicability for some aspects of core ongoing modeling.) • Develop and use models that people might nd, based on notions such as preponderance of evidence, to be more compelling than aspects of current unveried ongoing modeling.
• Develop and use models -that people might nd to be compelling -regarding relevant topics that ongoing modeling seems not to address.  • Explaining observed ratios of dark matter to ordinary matter. • Explaining various astrophysics aspects and cosmology aspects. Table 87 lists aspects of cosmology and astrophysics for which proposed modeling seems to provide insight that augments insight that ongoing modeling suggests. This essay shows proposed modeling models that suggest the new insight.
• Interrelating properties of objects. properties. This essay shows relationships between masses of elementary particles. Table 4: Relationships between some aspects of ongoing modeling and some aspects of proposed modeling (a) Core ongoing modeling and core proposed modeling Aspect of core ongoing modeling -Discussion based on core proposed modeling • Dark matter -Proposed modeling suggests that much dark matter has some similarities to unveried ongoing modeling notions of so-called WIMPs (or, weakly interacting massive particles).
Unlike would-be WIMPs, this dark matter features hadron-like particles (which include elementary particles) that people would not consider to be elementary particles.
• Modeling regarding large-scale phenomena -People allude to possible problems regarding using the Hubble constant, models that compute pressures based on densities, and general relativity to model some of the largest-scale phenomena that people observe. Proposed modeling points to reasons why such modeling may not apply adequately accurately to some aspects of large-scale phenomena.
• Modeling regarding motion -People can use core proposed modeling with modeling regarding motion that comports with conservation of energy, conservation of angular momentum, and conservation of momentum. Each one of core ongoing modeling and supplementary proposed modeling includes such modeling regarding motion.
(b) Unveried ongoing modeling and core proposed modeling Aspect of unveried ongoing modeling -Discussion based on core proposed modeling • Quantum gravity -Proposed modeling outputs (rather straightforwardly) a model of quantum gravity. That modeling and other concepts that this essay discusses seem to point to diculties regarding trying to describe quantum gravity by quantizing aspects of general relativity.
• Supersymmetry -The proposed modeling list of elementary particles may suce to explain phenomena that led people to suggest supersymmetry. The list does not exhibit supersymmetry.
There may be little further physics need for people to explore supersymmetry.
(c) Core ongoing modeling and supplementary proposed modeling Aspect of core ongoing modeling -Discussion based on supplementary proposed modeling • Quantum eld theory -Supplementary proposed modeling suggests a somewhat parallel to ongoing modeling QFT (or, quantum eld theory). The two types of modeling dier from each other. For example, the proposed modeling parallel to QFT features modeling that is quadratic in energy, whereas ongoing modeling QFT features modeling that is linear in energy. Proposed modeling that somewhat parallels QFT might provide or point to useful bases for modeling, for example regarding anomalous magnetic moments or regarding nuclear physics. • Outputs information about properties of the elementary particles.
• Outputs information about interactions in which elementary particles participate.
• Embraces conservation laws pertaining to motion.
• Embraces core ongoing modeling regarding motion.
• Helps explain data that ongoing modeling seems not to explain. • Correlations exist between spins and numbers of similar particles.
• So-called PDE modeling, based on math that echoes those correlations, can be useful.
• PDE modeling uses partial dierential equations pertaining to harmonic oscillators.
• PDE modeling mathematically correlates allowed spins with three spatial dimensions.
• PDE modeling uses information about some particles to output aspects of other particles.
• So-called ALG modeling features ladder operators pertaining to harmonic oscillators.
• ALG modeling uses symmetries pertaining to harmonic oscillators.
• ALG modeling has bases in models that correlate with the excitement of boson states.
• ALG modeling outputs representations that correlate with particles.
• ALG modeling points to symmetries that correlate with properties of particles.
• ALG modeling proposes new property-centric conservation laws.
• ALG modeling points to symmetries that correlate with properties of interactions.
• ALG modeling embraces symmetries correlating with kinematics conservation laws.
• ALG modeling helps bridge between proposed modeling and ongoing modeling.
• ALG modeling bridging includes aspects correlating with motion.
This essay cites references regarding data. For some aspects of mathematics and modeling, this essay does not cite references. Perhaps, reference [2] points to precedent for not necessarily citing references regarding mathematics and modeling as well as to precedent for discussing context.

Methods
We provide perspective about our development and use of proposed modeling.

Goals, concepts, and steps
We use the four-word term proposed elementary particle modeling to describe a core of our work.
The acronym PEPM abbreviates the four-word term proposed elementary particle modeling. Table 5 suggests goals for PEPM. Interactions can change, regarding objects in general, each of internal properties and motion.
Our work contributes to each of the goals that table 5 lists.
Ongoing modeling does not necessarily achieve the rst few goals. Development of ongoing modeling has tended to produce modeling regarding motion without necessarily completely knowing the nature of objects that move or without necessarily completely cataloging types of objects that move.
Goals that table 5 lists correlate with potential synergy between proposed modeling and ongoing modeling. Together, proposed modeling and ongoing modeling seem to explain data that ongoing modeling seems not to explain. We provide perspective about harmonic oscillator mathematics.
Mathematics pertaining to harmonic oscillators includes two types of expressions. PDE modeling features solutions that feature sums of terms of the form that equation (1) shows. The symbol x denotes • The symbol Ψ(r) denotes a function of angular coordinates, as well as of r.
• The symbol Ω SA correlates with aspects correlating with angular coordinates.
• The symbol D correlates with a number of dimensions.
• The symbol ν SA might correlate with an energy level.
a continuous variable. ALG modeling features solutions that feature one or more terms, with each term being a product of one or more factors of the form that equation (2) shows. The occupation number n is an integer.

PDE mathematics
We explore mathematics underlying PDE modeling.
Equations (3) and (4) correlate with an isotropic quantum harmonic oscillator. Here, r denotes the radial coordinate and has dimensions of length. The parameter η SA has dimensions of length. The parameter η SA is a non-zero real number. The magnitude |η SA | correlates with a scale length. Each of ξ SA and ξ SA is a constant. The symbol Ψ(r) denotes a function of r. The symbol ∇ r 2 denotes a Laplacian operator. The symbol Ω SA is a constant. We associate the term SA-side with this use of symbols and mathematics. We anticipate that the symbols used correlate with spatial aspects of some physics modeling. We anticipate that TA-side symbols and mathematics pertain for -and correlate with temporal aspects of -some physics modeling.
Ψ(r)∝(r/η SA ) ν SA exp(−r 2 /(2(η SA ) 2 )), with (η SA ) 2 > 0 (6) Table 7 discusses possible values for and assumptions about Ψ(r), Ω SA , D, and ν SA . Our work does not necessarily automatically embrace assumptions that ongoing modeling tends to embrace. Table 8 provides details that lead to solutions that equations (7) and (8) characterize. We consider equations (3), (4), and (6). The table assumes, without loss of generality, that (ξ SA /2) = 1 and that η SA = 1. More generally, we assume that each of the four terms K _ and each of the two terms V _ includes appropriate appearances of (ξ SA /2) and η SA . The term V +2 correlates with the rightmost term in equation (3). The term V −2 correlates with the rightmost term in equation (4). The four K _ terms correlate with the other term to the right of the equals sign in equation (4). The sum of the two K 0_ terms correlates with the factor D + 2ν SA in equation (7). Equations (7) and (8) characterize solutions. The parameter η SA does not appear in these equations.
We explore the topic of normalization regarding Ψ(r).
∞ 0 (Ψ(r)) * Ψ(r)r D−1 dr < ∞ (9) Our work embraces somewhat the same concept -as ongoing modeling embraces -regarding normalization. The dierence in the domain for r (that is, 0 < r < ∞ for our work versus 0 ≤ r < ∞ for ongoing modeling) is not material for this essay. For essentially the entire remainder of this essay, we assume that equation (10) pertains. (For a complex number z, the expression z = (z + i (z) pertains.
The expression (z) denotes the real part of z. The expression (z) denotes the imaginary part of z. The symbol i denotes the positive square root of the number −1.) We take the liberty to assume that the normalization criterion that equation (9) denes pertains for any real number D.
(ν SA ) = 0 (11) Equation (12) correlates with the domains of D and ν SA for which normalization pertains for Ψ(r). For D + 2ν SA = 0, normalization pertains in the limit (η SA ) 2 → 0 + . Regarding mathematics relevant to normalization for D + 2ν SA = 0, the delta function that equation (13) shows pertains. Here, x 2 correlates with r 2 and 4 correlates with (η SA ) 2 . (Reference [3] provides equation (13).) The dierence in domains, between −∞ < x < ∞ and equation (5), is not material here. (Our use of this type of modeling features normalization. Considering normalization leads to de-emphasizing possible concerns, regarding singularities as r approaches zero, regarding some Ψ(r).) D + 2ν SA ≥ 0 (12) δ(x) = lim →0 + (1/(2 √ π ))e −x 2 /(4 ) We use the one-element term volume-like to describe solutions for which D + 2ν SA > 0. The term volume-like pertains regarding behavior with respect to the coordinate or coordinates that underlie modeling. (For ongoing modeling, generally, the word coordinates -as in r plus angular coordinates -can be appropriate.) We use the one-element term point-like to describe solutions for which D + 2ν SA = 0.
Here, Ψ(r) is eectively zero for all r > 0. The term point-like pertains regarding behavior with respect to the coordinate or coordinates that underlie modeling.
We explore some relationships regarding and between solutions.
• Develop appropriate modeling that correlates with at least one of the two sets of a pair of oscillators. Table 11: A process for transforming a solution that is appropriate for D 1 = D dimensions into a solution that is appropriate for D 2 = D SA dimensions Steps • Choose values of ν SA , σ SA , S SA , and D SA . • Determine (a rst value of ) D via equation (26). Let D 1 denote this value of D.
• Embrace the radial dependence of Ψ(r) that equation (6) implies and set any dependence on angular coordinates to a non-zero constant.
• Combine the radial dependence with an angular dependence appropriate to a solution (to equations (3) and (4)) for which (a second value of ) D (in equation (4)) satises D = D SA . Let D 2 denote this (second) value of D. (The value of D 2 is not necessarily the same as the value of D 1 .) • Thereby, produce a Ψ(r) that (may have angular dependence and) pertains regarding D SA dimensions. Table 10 list steps -other than deploying mathematics correlating with spinors -that proposed modeling suggests to avoid problems to which equation (22) seems to point.
We explore some modeling that considers angular coordinates. Regarding equation (8), we explore mathematics for which equation (24) pertains for some choice of σ SA , S SA , and D SA . Equation (25) restates equation (8). Combining equations (24) and (25) yields equation (26).  Table 11 shows a process for transforming a solution that is appropriate for D 1 = D dimensions into a solution that is appropriate for D 2 = D SA dimensions. (See equation (26).) Here, we deploy some concepts that ongoing modeling embraces. (See table 7.) We anticipate using PDE modeling that combines TA-side aspects and SA-side aspects. The following equations dene the operators A P DE T A and A P DE SA . The symbol Ψ(t, r) denotes a solution.

ALG mathematics
We explore mathematics underlying ALG modeling.
Equation (32) shows an ongoing modeling representation for states for a one-dimensional harmonic oscillator. The symbol |_ > correlates with the notion of quantum state. (See equation (2).) Equation (33) shows the ongoing modeling representation for a raising operator. Equation (34) shows the ongoing modeling representation for a lowering operator. In ongoing modeling, n is a nonnegative integer.
A ALG XA = (ξ XA /2) For ALG modeling, equation (38) pertains. Each of A ALG T A and A ALG SA correlates with the concept of an isotropic quantum harmonic oscillator. The word isotropic (or, the two-word term equally weighted) also pertains to the pair consisting of A ALG T A and A ALG SA . The one-element term double-entry pertains.
For example, increasing a TA-side excitation number by one requires either decreasing a dierent TAside excitation by one or increasing one SA-side excitation by one. The two-element term double-entry bookkeeping pertains.
For core proposed modeling, we assume that equation (38) pertains. Equation (38) provides an ALG analog to PDE equation (31). Table 12 provides ways to visualize solutions to equation (38). For each of TA and SA, one includes just the columns XA0 through XA(D XA − 1). Each relevant n XA_ is an integer. (Note equation (32). Also, for some applications, we assume the following. We assume that equation (38) implies that (ξ T A /2) = (ξ SA /2) = 0. We can assume, without loss of generality, that (ξ T A /2) = (ξ SA /2) > 0. Paralleling results that equations (7) and (8) show, we assume, without loss of generality for ALG modeling, that η T A = η SA = 1.) Equations (38) and (39) characterize all solutions that we include in ALG modeling that is based on isotropic harmonic oscillators.
b + |n >= n 1/2 |n + 1 > (42) b − |n >= (1 + n) 1/2 |n − 1 > We discuss symmetries that correlate with mathematics for isotropic harmonic oscillators. Table 13 shows symbols that this essay suggests and groups to which proposed modeling refers. Regarding information pertaining to groups, aside from rows (in the table) that show a negative contribution to A ALG XA or that show the symbol π @0,@−1 , information in the table comports with standard relationships between mathematics of group theory and mathematics for isotropic quantum harmonic oscillators. The leftmost column shows the relevant number of oscillators. For each row, the symbol XA can be TA, in which case all of the oscillators are TA-side oscillators, or SA, in which case all of the oscillators are SA-side oscillators. The symbol χ correlates with the concept of choice. The symbol χ a pertains to one oscillator and correlates with the equation n XA_ = a. The symbol S1G denotes a group with one generator. The number of generators for U (1) is two. One generator correlates with integer increases regarding the number of excitations that pertain for the oscillator for which the table shows n _ ≥ 0.
One generator correlates with integer decreases regarding the number of excitations that pertain for the oscillator for which the table shows n _ ≥ 0. The symbol π correlates with the concept of permutations. The symbol π a,b denotes two possibilities. Regarding the two oscillators, for one possibility, a pertains to the rst oscillator and b pertains to the second oscillator. For the other possibility, a pertains to the second oscillator and b pertains to the rst oscillator. Regarding the symbol π n,@−1 , the U (1) symmetry correlates with the n. Use of the symbol π @0,@−1 is sensitive to context. In some contexts, a U (1) symmetry pertains and correlates with the appearance of @ 0 . In some contexts, no U (1) symmetry pertains. The symbol A0+ denotes π @0,@0 . The symbol κ correlates with the concept of a continuous set of choices.
For example, regarding two oscillators XA1 and XA2, equations (44) and (45) describe the continuum of possibilities correlating with κ 0,−1 . Here, each of d and e is a complex number. The symbol [blank] denotes the concept that, in tables such as table 35, one can interpret a blank cell as correlating with κ 0,−1 . Regarding SU (j), each one of the symbols κ @−1,···,@−1 and κ @0,···,@0 correlates with a continuous set of choices involving amplitudes pertaining to j oscillators. The number of generators for SU (j) is j 2 − 1.
• Motion -Regarding the object, describe a trajectory (classical physics) or wave function (quantum physics).
• Measurements -Regarding an observer's measurements of the object, predict or explain measured values.
We note a relationship between SU (j) groups and the group U (1).
Equation (47) echoes mathematics and some ongoing modeling. Here, each of the positive integers j 1 and j 2 is at least two. The symbol ⊃ correlates with the notion that each group to the right of the symbol is a subgroup of the group to the left of the symbol. SU (j 1 + j 2 ) ⊃ SU (j 1 ) × SU (j 2 ) × U (1) (47) 2.4. Relationships between applications of various types of models Table 14 shows some aspects and objectives of physics modeling regarding an object. (This essay de-emphasizes discussing many notions regarding the completeness with which modeling does or could meet objectives that table 14 notes. For example, we do not necessarily adequately discuss the extent to which modeling regarding objects leads to modeling that sub-optimally describes nature. For example, we do not necessarily adequately discuss the extent to which models completely separate one object from the rest of the universe. Ongoing modeling devotes much attention to the notion of entanglement. For example, we do not necessarily adequately discuss the notion of how well modeling denes objects. In ongoing modeling, modeling based on the Dirac equation does not necessarily completely separate an electron from a correlated positron. And so forth.) This essay seeks to develop core proposed modeling -that models descriptions of objects -that complements core ongoing modeling models regarding motion and measurements. Table 15 discusses the terms KMS (or, kinematics modeling space), PFS (or, particle eld space), and UMS (or, united modeling space). Table 16 discusses uses for core proposed modeling ALG models. Table 17 characterizes applications -that this essay discusses -of various types of modeling based on harmonic oscillator mathematics. For each of the cases PFS PDE and KMS PDE, this essay uses symbols such as t and r to denote relevant coordinates. PFS PDE use of such a symbol does not necessarily completely correlate with KMS PDE use of the same symbol.
UMS modeling provides a basis to explore relationships between KMS modeling and core proposed modeling PFS models. This essay does not fully explore relationships between KMS modeling and core Table 15: KMS (or, kinematics modeling space), PFS (or, particle eld space), and UMS (or, united modeling space) Aspect • The term KMS abbreviates the three-word term kinematics modeling space. The term KMS refers to modeling that can -and, in ongoing modeling, often does -use coordinates that people use to model aspects that people correlate with notions of space-time. Ongoing modeling tends to use KMS modeling to address the topics of motion and measurements. (See table 14.) Core proposed modeling tends to embrace results from such ongoing modeling. Supplementary proposed modeling suggests new KMS modeling that might supplement such ongoing modeling.
• The term PFS abbreviates the three-word term particle eld space. The term PFS refers to modeling that generally does not correlate directly with space-time coordinates. Core proposed modeling tends to use PFS modeling to address the topic of objects (especially, elementary particles). (See table 14.) Core ongoing modeling seems not to include, for at least elementary particles, an analog to PFS modeling.
• The term UMS abbreviates the three-word term united modeling space. The term UMS refers to modeling that embraces aspects that correlate with, at least, KMS modeling and PFS modeling.
Core proposed modeling tends to use UMS ALG modeling to address topics regarding properties of objects and regarding conservation laws. Here, the two-word term conservation laws pertains regarding internal properties of objects and regarding motions of objects. (Perhaps, note table 14.) Unveried ongoing modeling seems to suggest -for example via the notion of a so-called theory of everything -possible desirability for people to explore notions such as UMS modeling.  suggest that people might use core proposed modeling ALG models as bases for exploring such concepts.
We provide additional perspective about modeling that this essay discusses.
Generally, core proposed modeling embraces motion via representations for motion-centric conservation laws and via relying on ongoing modeling models for motion. Hence, core proposed modeling uses, Proposed modeling associates the one-element term TA-side with modeling that correlates with the two-word term temporal aspects. The two-word term temporal aspects echoes notions of temporal aspects of ongoing modeling KMS modeling that uses space-time coordinates. We use the term temporal aspects in the context of PFS modeling and in the context of KMS modeling. Proposed modeling associates the one-element term SA-side with modeling that correlates with the two-word term spatial aspects. The two-word term spatial aspects echoes notions of spatial aspects of ongoing modeling KMS modeling that uses space-time coordinates. We use the term spatial aspects in the context of PFS modeling and in the context of KMS modeling.

A method that organizes properties of elementary particles and other objects
We discuss a method to organize and conceptualize aspects of modeling that we develop below. The method itself might point to insight about modeling and about nature. (See discussion related to table   111.) However, for the moment, we treat the method as, in essence, an organizational convenience.
The method has bases in the notion that SU (17) symmetry might be relevant. The method has bases in the notion that modeling based on 17 harmonic oscillators can correlate with SU (17) symmetry. (See   table 13.) The method has bases in table 12b. We label the 17 oscillators as HO1, HO2, ..., and HO17.
The method correlates with the two one-element terms UMS and ALG. Table 18 notes aspects pertaining to some types of symmetries and related conservation laws. Proposed modeling correlates these aspects with aspects regarding interactions between objects. The terms exact symmetry, approximate symmetry, and no symmetry correlate with mathematical modeling and with aspects of ongoing modeling. The following discussion reprises examples that table 18 shows. An electron, correlates with an exact symmetry regarding conservation of charge. An electron correlates with a rebuttable always conservation law that correlates with charge. For an interaction between the electron and other objects that all correlate with rebuttable always conservation of charge, the outgoing fermion that correlates with the incoming electron has the same charge as the electron. For that example, a notion of always conservation of charge -across the electron and the related outgoing fermion -pertains.
Suppose, however, that one of the incoming particles is a W boson. The W boson correlates with no symmetry and with not necessarily conservation of charge. If the W boson is a positively charged W boson, the interaction can transform the electron into a neutrino, which has zero charge. Here, in eect, the not necessarily conservation of charge correlating with the W boson rebuts the rebuttable always conservation of charge for the electron. Table 19 discusses aspects relevant to the method to organize properties of objects. Table 20 discusses the method and previews aspects of applications of the method.  • Symmetries rank as follows regarding exactness. An exact symmetry is more exact than an approximate symmetry. An exact symmetry is more exact than no symmetry. An approximate symmetry is more exact than no symmetry.
• Conservation laws interrelate as follows. Not necessarily takes precedence over rebuttable somewhat. Not necessarily takes precedence over rebuttable always. Rebuttable somewhat takes precedence over rebuttable always.
• For an interaction, the least exact symmetry that pertains regarding any incoming elementary particle or object pertains.
• For example, for an interaction between an electron and a photon, the following sentences pertain. The electron correlates with a π @0,@−1 exact symmetry, which correlates with rebuttable always conservation of fermion charge. The photon correlates with a π @0,@−1 exact symmetry, which correlates with rebuttable always conservation of fermion charge. The interaction correlates with rebuttable always conservation of fermion charge. The outgoing particle is a negatively charged lepton.
• For example, for an interaction between an electron and a positively charged W boson, the following sentences pertain. The electron correlates with a π @0,@−1 exact symmetry, which correlates with rebuttable always conservation of fermion charge. The W boson correlates with a κ @0,@−1 no symmetry, which correlates with not necessarily conservation of fermion charge. The interaction correlates with not necessarily conservation of fermion charge. The outgoing particle is a neutrino, which has zero charge. • An SU (2) symmetry might correlate with a trio of degrees of freedom for aspects that sum. For example, regarding charge, the three degrees of freedom correlate with negative charge, zero charge, and positive charge. One can sum -across components of an object -each of the three quantities. One can obtain a net charge for the object by combining the three sums. Regarding momentum and either proposed modeling or ongoing modeling, the three degrees of freedom correlate with the three components of a vector that can correlate with momentum or with three spatial dimensions. Regarding any one of the three components of momenta vectors, one can sumacross components of an object -that component of momentum.
• A U (1) symmetry might not correlate with a rebuttable always conservation law. An SU (2) symmetry might not correlate with a trio of degrees of freedom. A pairing of one such U (1) symmetry and one such SU (2) symmetry provides a symmetry that correlates with six generators and that can correlate with six isomers of a physics property. Such properties seem to include charge and may include mass.
• The symbol 3LB denotes the notion of three times the quantity lepton number minus baryon number. In each of proposed modeling and ongoing modeling, lepton number minus baryon number is a conserved quantity.
• The series of symbols 2G, 4G, 6G, and 8G denotes four elementary particles that proposed modeling suggests. The symbols correlate respectively with the (spin-one) photon (which correlates with each of core proposed modeling and core ongoing modeling), a (spin-two) graviton (which correlates with each of core proposed modeling and unveried ongoing modeling), a spin-three elementary particle (which correlates with core proposed modeling and not with ongoing modeling), and a spin-four elementary particle (which correlates with core proposed modeling and not with ongoing modeling). • Each multi-element item (deferred to k 1 -k 2 ) implies that a later row discusses the HO range k 1 -k 2 and that the U (1) symmetry pertains to the k 1 -k 2 HO range.
• Cons denotes the word conservation.
• Regarding the item 3-4 Mass, a property pertaining to all objects is rest mass (or -equivalentlyrest energy).
• Regarding the item 5-6 Generations, the property pertaining to all objects is freeable energy (or, energy above ground state).
• Conservation of energy -for an individual object -correlates with conservation of rest energy (or, rest mass times c 2 -in which c denotes the speed of light) minus freeable energy.
• The two-element abbreviation ang mom abbreviates the two-word phrase angular momentum.
• The one-element abbreviation mom abbreviates the word momentum.  • We say that the case PR1ISP correlates with -for each elementary particle -one isomer. Core ongoing modeling features a subset of the elementary particles that proposed modeling suggests.
Core ongoing modeling correlates with a subset of PR1ISP.
• We say that -regarding all elementary particles except G-family elementary particles -PR6ISP correlates with six isomers of PR1ISP. PR6ISP correlates with the notions of six isomers of charge and one isomer of mass. The one isomer of mass correlates with a notion of one isomer of gravity.
The six isomers of PR1ISP interact with each other via at least (one aspect of ) gravity.
(Technically, some aspects of gravity do not connect all six isomers to each other. See, for example, • We explore one possible way to invoke SM6b symmetry.
• We say that -regarding all elementary particles except G-family elementary particles -PR36ISP correlates with six isomers of PR6ISP. PR36ISP correlates with the notions of 36 isomers of charge and six isomers of mass. Each one of the isomers of mass correlates with its own isomer of gravity.
The six isomers of PR6ISP interact with each other via (some aspects of ) electromagnetism. The six isomers of PR6ISP do not interact with each other via gravity. Proposed modeling PR36ISP models might provide an (alternative to ongoing modeling) explanation for ratios of density of dark energy to density of dark matter plus ordinary matter.
• We explore another possible way to invoke SM6b symmetry.
• Six permutations of color charge: Table 20a correlates the three-oscillator HO range 9, 10, and 17 with an SU (3) symmetry that correlates with the strong interaction. Proposed modeling correlates, in eect, each one of the color charge red, the color charge blue, and the color charge green with a dierent one of three oscillators. (See discussion related to table 69.) Possibly, a permutation symmetry -π r,b,g -has physics relevance. (c) Policy regarding using the two-word term elementary particle Aspect • This essay uses the two-word term elementary particle so as to include proposed modeling aspects -such as the 0I, 0P, and 2J bosons -to which table 22b alludes.

Summary: a table of known and suggested elementary particles
We suggest that the notion of elementary particle might depend, to some extent, on modeling and vocabulary that people choose to use. Table 22 discusses use -in this essay -of the two-word term elementary particle.   (48) and equation (49).
We use the two-word term simple particle to pertain to each entry in table 23 other than G-family entries and U-family entries. We correlate the two-word term root force with each G-family entry in (b) Simple particles and root forces (with notation featuring names of elementary particles; with * denoting that people might have yet to nd the elementary particles; and with TBD denoting the three-word phrase to be determined) . . . . . .
use of the word root. Beyond the modeling-based contrast with the term root force, this essay does not necessarily suggest physics meaning for such use of the word simple.) We correlate the three-element term long-range root forces with the G family.
Particle counts in table 23 de-emphasize modeling that would count, for example, a down quark with green color charge as diering from a down quark with red color charge. (See table 22a.) We discuss the elementary particles for which the spin is zero (or, Σ = 0).
The 0H particle is the Higgs boson.
The 0P, or so-called pie, possible particle would correlate with a core ongoing modeling notion of an attractive component of the residual strong force.
The 0I, or so-called aye, particle is a possible zerolike-mass relative of the Higgs boson. Proposed modeling suggests that the aye particle is a candidate for the ongoing modeling notion of an inaton.
We discuss the elementary particles for which the spin is one-half (or, Σ = 1).
The three 1C particles are the three charged leptons -the electron, the muon, and the tauon.
The six 1Q particles are the six quarks.
The three 1N particles are the three neutrinos. Some aspects of ongoing modeling suggest that at least one neutrino mass must be positive. At least one positive mass might explain neutrino oscillations and some astrophysics data. Some aspects of ongoing modeling, such as some aspects of the Standard Model, suggest that all neutrino masses are zero. Proposed modeling suggests that eects of 8G forces might fully explain neutrino oscillations and the relevant astrophysics data. For example, proposed modeling suggests that 8G forces lead to eects that ongoing astrophysics modeling would correlate with a sum of neutrino masses of 3α 2 m . The symbol α denotes the ne-structure constant. The symbol m denotes the mass of an electron. The amount 3α 2 m falls within the range that ongoing astrophysics modeling attributes to observed data. (See equations (142) and (143).) The 8G forces do not interact with the property of mass. Proposed modeling suggests the possibilities that each neutrino has zero mass or that neutrinos have non-zero (zerolike) masses that are signicantly smaller than α 2 m . The six 1R, or so-called arc, possible particles are zero-charge zerolike-mass analogs of the six quarks.
Hadron-like particles made from arcs and gluons contain no charged particles and measure as dark matter.
We discuss the elementary particles, other than G-family elementary particles, for which the spin is one (or, Σ = 2).
The two 2W particles are the two weak interaction bosons -the Z boson and the W boson. The four 2T, or so-called tweak, possible particles are analogs to the weak interaction bosons. The charge of one non-zero-charge 2T particle is two-thirds the charge of the W boson. The charge of one non-zero-charge 2T particle is one-third the charge of the W boson. The non-zero-charge tweak particles may have played roles in the creation of baryon asymmetry. The non-zero charge tweak particles might correlate with unveried ongoing modeling notions of leptoquarks. The 2J particles, or so-called jays, are possible zerolike-mass bosons. The jay particles would correlate with a core ongoing modeling notion of a repulsive component of the residual strong force. (The jay particles would correlate with a core ongoing modeling notion of a Pauli exclusion force.) Proposed modeling suggests that the jay particles played roles that ongoing modeling correlates with times just before the inationary epic and with times during the inationary epoch.
The eight 2U particles are the eight gluons. In each of core ongoing modeling and core proposed modeling, gluons correlate with the strong interaction and bind quarks into hadrons. Proposed modeling suggests that gluons bind arcs into hadron-like particles.
We discuss additional roles for the aye boson and jay bosons.
Some proposed modeling models correlating with the aye particle and the jay particles might correlate with some ongoing modeling models that include notions of interactions with a quantum vacuum.
We discuss G-family forces.
Each G-family force exhibits two modes. Our discussion tends to focus on circularly polarized modes.
One mode correlates with left circular polarization. One mode correlates with right circular polarization.
For 2G, ongoing modeling suggests classical physics models and quantum physics models. The word electromagnetism can pertain. Proposed modeling suggests modeling that provides for 2G aspects that include and complement ongoing modeling electromagnetism. Regarding gravitation, ongoing modeling suggests classical physics models. Proposed modeling suggests modeling for 4G aspects that include and complement ongoing modeling gravitation. Proposed modeling regarding 4G includes classical physics aspects and quantum physics aspects. Proposed modeling regarding 4G includes aspects that ongoing modeling correlates with the four-word term dark energy negative pressure. Proposed modeling suggests that quantum interactions, involving simple fermions, mediated by 4G can correlate with a notion of rebuttable somewhat conservation of fermion generation. Ongoing modeling does not include 6G aspects and does not include 8G aspects. Proposed modeling suggests that 8G interacts with lepton number minus baryon number.
Regarding G-family forces, proposed modeling suggests, in some sense, more than one component for each one of some ΣG. For example, 2G includes one component that correlates with interactions with charge and one component that correlates with interactions with nominal magnetic dipole moment. This notion of components is appropriate because aspects of proposed modeling can address the topics of properties and interactions without necessarily selecting an ongoing modeling model for motion. (See,   for example, discussion regarding table 61 and discussion regarding table 62.) The notion of components is essential for proposed modeling models that suggest explanations for observed ratios of dark matter amounts (or other eects) to ordinary matter amounts (or other eects). (See discussion regarding table   89 and discussion regarding tables 92 and 93.) Proposed modeling suggests that one of equation (48) and equation (49)  Some aspects of table 23 point to possible diculties regarding the scenario that we just described.
The notion of zerolike mass correlates with ongoing modeling KMS modeling. For some models, zerolike means zero. For some models zerolike means -for some elementary particles -non-zero. More generally, ongoing modeling KMS modeling includes models that use the notion of potential energy and, thereby, might bypass some needs to consider elementary bosons. Some of those models correlate with classical physics. Some of those models correlate with quantum physics (and, for example, with the Schrodinger equation).
Similar ambiguities pertained regarding the periodic table for chemical elements. There were two organizing principles -atomic weight and similarity regarding chemical interactions. (Perhaps, note reference [5].) People originally did not understand bases for those principles. Neither principle proved to be strictly rigorous. After people developed nuclear physics modeling and atomic physics modeling, people better understood the principles and the chemical elements.
Our method features an input small data-set that is the set of known elementary particles. The output features a small data-set that might include all elementary particles that nature includes. (See table 23.) We characterize our method as using (non-computerized or mental) techniques that correlate with the two-word term machine learning and with the two-element term big-data techniques.
A pivotal aspect of the method features the following steps. Recognize that some parts of a partial dierential equation, which ongoing modeling uses for KMS PDE modeling, seem to encode information correlating with ongoing modeling KMS modeling for potentials that correlate with electromagnetism and with the strong interaction. Use the equation in a context of proposed modeling PFS PDE modeling.    We continue discussion regarding proposed elementary particle modeling (or, PEPM). (See discussion related to tables 5 and 6.) Mathematics and ongoing modeling include partial dierential equations pertaining to isotropic harmonic oscillators. A partial dierential equation correlating with an isotropic multidimensional quantum harmonic oscillator includes an operator that correlates with r −2 and an operator that correlates with r 2 .
(See equations (3) and (4).) We consider KMS modeling. (See table 17.) The symbol r denotes a radial spatial coordinate. The r −2 operator in equation (4) can model aspects correlating with the square of an electrostatic potential. The potential correlates with r −1 and can be either attractive or repulsive. The force correlates with r −2 and can be either attractive or repulsive. The r −2 operator can model aspects correlating with the square of a gravitational potential. The r −2 operator can model aspects correlating with each G-family force ΣG for which Σ ≤ 8. (See table 25.) The r 2 operator in equation (3) can model aspects correlating with the square of a strong interaction potential. Ongoing modeling includes the concept of asymptotic freedom. The potential correlates with r 1 . The force correlates with r 0 . (Apparently, over time, ongoing modeling discussion might have de-emphasized a possible correlation between asymptotic freedom and the notion that aspects of a potential that might approach -at suciently large |ι 3CH |=n denotes |ι 3CH | = n or 0 We discuss objects and properties. Each of ongoing modeling and proposed modeling includes the notion of an object. (See table 14.) Models for an object may include notions of internal properties upon which all observers would agree.
One such property is charge (or, charge that people would observe in the context of a frame of reference in which the object does not move). Models for objects may include notions of kinematics properties upon which observers might legitimately disagree. One such notion is velocity, relative to the observers, of an object. Models can include notions of interactions between objects. An interaction can changefor an object -at least one of some internal properties and some kinematics properties.    • |ι 3CH |=3 → |ι 3CH |=(2 or 1) denotes extending results for |ι 3CH |=3 to results for |ι 3CH |=2 and to results for |ι 3CH |=1. • The expression n XA0 = 0 ← n XA0 = −1 denotes -for each of XA equals TA and XA equals SA -substituting the number minus one for the number zero.
• The word ongoing denotes aspects of ongoing modeling that model the attractive component of the residual strong force via modeling that includes notions of virtual pions.
• The symbol m π denotes the mass (or masses) of pions. • The notation X denotes the notion that this essay generally de-emphasizes the concept X.   Table 28: Aspects -of modeling -that correlate with some TA-side aspects and some SA-side aspects Aspect • A TA0 n T A0 = 0 or a TA0 n T A0 = n (with nonnegative integer n) correlates -for PFS models for elementary bosons -with a U (1) symmetry. One generator correlates with excitation. One generator correlates with de-excitation.
• A TA-side π @0,@−1 correlates -for UMS models -with a U (1) symmetry and with a quantity that sums across objects (including elementary particles) that a so-called larger object includes.
Here, regarding summing across objects, one might think of the symbol π 0,@−1 and of the notion that the zero correlates with the U (1) symmetry. (Perhaps, compare with tables 20a, 58a, and 111a.) One generator correlates with adding to a value of a property of a larger object. One generator correlates with subtracting from a value of a property of a larger object.
• A TA-side π @0,@−1 correlates -for PFS models and for UMS models -with a rebuttable always conservation law. (See, for example, • A TA-side κ @0,@0 or κ @−1,@−1 correlates -for PFS models for elementary bosons and for UMS models for elementary bosons -with an SU (2) symmetry and with a rebuttable somewhat conservation law.
• A TA-side κ @0,@−1 correlates -for PFS models for elementary bosons and for UMS models for elementary bosons -no symmetry and with a so-called not necessarily conservation law. (See table   18 and table 40.) • A TA-side κ @0,...,@0 (SU (j)) -with j being at least four -correlates -for PFS models for G-family elementary bosons -with a not necessarily conservation law regarding fermion generation. (See, for example, table 48b. Technically the notation correlates with j -not two -TA-side oscillators.) • A TA-side κ @−1,...,@−1 (SU (3)) -correlates -for PFS models for U-family elementary bosonswith a rebuttable always conservation law regarding fermion generation. (See discussion regarding table 54. Technically the notation correlates with three -not two -TA-side oscillators.) • An SA-side π n,@0 or π 0,@0 correlates -for PFS models for G-family elementary bosons -with two modes. One mode correlates with left circular polarization. One mode correlates with right circular polarization.
• An SA-side π @0,@−1 correlates -for PFS models for elementary fermions and for UMS models for elementary fermions -with (for SA1-and-SA2) particle and antiparticle and with (for SA7-and-SA8) positive 3LB number and negative 3LB number.
• An SA-side κ @0,@−1 correlates -for PFS models for elementary bosons -with no dependence • An SA-side κ @0,@0 , κ 0,0 , κ @−1,@−1 , or κ −1,−1 might correlate -for UMS models -with an SU (2) symmetry and with a trio of degrees of freedom for aspects that sum across objects. Proposed modeling PFS ALG modeling has bases in the concept that modeling photons based on four harmonic oscillators has uses. The concept has bases in the ongoing modeling notion of KMS modeling based on four dimensions. One of those four dimensions is temporal. The other three of those four dimensions are spatial. The concept points to equation (38) and to a concept to which we apply the two-element term double-entry bookkeeping. The term refers to ALG modeling that maintains a numeric balance between TA-side aspects and SA-side aspects. The balance reects a notion that a sum pertaining to TA-side aspects equals a sum pertaining to SA-side aspects.
Proposed modeling PDE modeling also exhibits aspects that we correlate with the two-element term double-entry bookkeeping. Here, the balance refers to eects of a TA-side quantum operator and to eects of an SA-side quantum operator. (See, for example, equation (31).)

Patterns regarding properties of known elementary particles
We discuss possibilities regarding an analog -to the periodic table for chemical elements -for elementary particles.
The periodic table reects properties of chemical elements. (Note reference [5].) One relevant property is the types of chemical interactions in which an element participates. One relevant property is the atomic weight. A usual display of the periodic table features an array with columns and rows. Elements listed in a column participate in similar interactions. For a row, the atomic weight of an element is usually greater than the atomic weight for each element to the left of the subject element. Atomic weights in one row exceed atomic weights in rows above the subject row.
We look for patterns regarding the known elementary particles. (See table 23.) Table 29 reects a concept that -for particles for which m>0 pertains -the number of elementary particles in a subfamily correlates with the spin of the elementary particles in the subfamily. Table 29b explains notation that table 29a uses. The spin S correlates with an overall angular momentum for which the expression S(S + 1) 2 pertains. The spin S does not depend on a choice of an axis. Each of the three columns that correlate with the one-element label sub-hadronic correlates with a magnitude of charge that diers from the magnitude of charge pertaining to the other two columns labeled sub-hadronic.        • Solutions for which ν SA = −1/2 can correlate with notions of elds for simple fermions.
• Solutions for which ν SA = −1 can correlate with notions of elds for simple bosons.
• Solutions for which ν SA = −3/2 can correlate with notions of particles for simple fermions.
• TA-side PDE solutions are radial with respect to t, the TA-side analog to the SA-side radial coordinate r.
We anticipate making PFS modeling uses of equations (55) and (56). Here, each of 2S and 2S T A is a nonnegative integer. (We de-emphasize using the symbol S SA instead of the symbol S.) The case that features equation (55), σ SA = +1, and S = ν SA is a restating of equation (8). (Ongoing modeling KMS modeling features expressions of the form that equation (57) shows.) The case that features equation (55) and σ SA = −1 correlates with some aspects of proposed modeling models. (See discussion related to table 76.) Similar concepts pertain regarding equation (56) and σ T A .
2 S(S + 1), for nonnegative integer 2S Along with mathematics correlating with three dimensions and D * SA = 3 and with mathematics correlating with one dimension and D * T A = 1, we anticipate needing mathematics correlating with two dimensions and a case that we denote by D = 2. (For example, discussion above does not adequately cover the topic of notions of particles for simple bosons. The case of D = 2 is relevant to -at leastnotions of particles for simple bosons.) Table 32 shows some relationships between some PDE parameters. The symbol XA can denote either SA or TA. Here, we correlate with D the symbols S , ν , Ω , and σ . Each of S , ν , Ω , and σ does not necessarily correlate with uses of S, ν SA , Ω SA , σ SA , S T A , ν T A , Ω T A , or σ T A in models regarding simple particles. For Ω = 0, the table uses the letters NR to denote that the sign of σ is not relevant. For table 32b, we use equation (25) to develop the relevant expressions for D and to calculate values of D. Similar methodology pertains regarding D in tables 32c, 32d, and 32e. (When considering tables 32b, 32c, 32d, and 32e, perhaps note that calculations of D do not involve values of D * SA , D * T A , and D .)

PDE modeling regarding simple particles
We explore bounds regarding the simple particles that proposed modeling suggests.
We pursue discussion based on relevance of the three TA-side oscillators TA0, TA1, and TA2 and three SA-side oscillators SA0, SA1, and SA2. (Compare with equation (37).) In general, use of equation (37) allows separation of terms into clusters. Equation (37) is a sum of D XA terms. Each one of the D XA terms appears in exactly one cluster. For D XA = 1, there is one term (which correlates with the XA0 oscillator) and one cluster (which contains the one term). For D XA = 3, we use two clusters. One cluster correlates with the XA0 oscillator. One cluster correlates with the XA1-and-XA2 oscillator pair. In these and similar cases, we apply -for each two-oscillator cluster -an analog to equations (3) and (4).
We anticipate aspects regarding modeling -for elds and particles -for simple bosons and simple fermions. D + 2ν SA = 0 We anticipate that, for some purposes, the substitutions that equations (62) and (63) show are useful.
(The notation a←b denotes the notion that b replaces -or substitutes for -a.) We discuss modeling for elds for simple bosons.
Regarding modeling for elds for ι S = 2 simple bosons, one can use the notion of mapping the D = 1 solutions -that tables 32b and 32c show -into the three dimensions that correlate with D = 3.  (See table 34 and discussion related to table 42.) We invoke equation (62). The oscillator pair TA5-and-TA6, correlates with and, in eect, contains the κ @0,@0 (or, SU (2)) symmetry that is relevant to rebuttable somewhat conservation of fermion generation.
Regarding modeling for elds for ι S = 0 simple bosons, one can use results that tables 32b and 32c show. For each of XA equals SA and XA equals TA, D = 3 and D + 2ν XA = 1. For each of XA equals SA and XA equals TA, equation (60) pertains. We invoke each of equations (62) and (63). (See, for example, table 47.) Rebuttable somewhat conservation of fermion generation pertains.
We discuss modeling for particles for simple bosons.
For simple bosons, we expect that modeling regarding particles correlates with the equations D = 2, ν = −1 and D+2ν = 0. (See tables 33 and 32e.) We base this expectation on the notion that, for simple fermions, modeling regarding particles correlates with the expression D T A + 2ν T A = 0 = D SA + 2ν SA .
Regarding modeling for particles for ι S = 2 simple bosons, notions -such as three oscillator pairs and rebuttable somewhat conservation of fermion generation -that pertain for elds for ι S = 2 simple bosons continue to pertain. Paralleling work regarding elds for ι S = 2 simple bosons, we invoke equation (62).
Regarding modeling for particles for ι S = 0 simple bosons, the two perhaps seemingly extra oscillator pairs -TA1-and-TA2 and SA1-and-SA2 -correlate with the notion of rebuttable somewhat conservation of fermion generation. Paralleling work regarding elds for ι S = 0 simple bosons, we invoke equations (62) and (63).
We discuss modeling for elds for simple fermions.
Regarding modeling for elds for ι S = 1 simple fermions, the D * SA + 2ν SA column in table 32b shows a value of two. The 3 + 2ν T A column in table 32c shows a value of two. Seemingly, equation (60) might not pertain. π @0,@−1 This symmetry correlates with matter and antimatter.
We focus on aspects that correlate with elds that correlate with fermion subfamilies 1Φ.
Regarding elds for elementary fermions, modeling can feature an eective D † = 2 instead of D = 3. We focus on aspects that correlate with elds that correlate with individual elementary particles (or, individual generations) within fermion subfamilies 1Φ.
We shift our attention to aspects that are somewhat separate from aspects correlating with D † = 2. From D 1 = D = 3, proposed modeling applies the transformation that correlates with equation (19). (Perhaps note that, in equation (19), j = 2 and that, regarding discussion here, jν SA is an integer.) The result D 2 = (2 · 3) − 2 = 4 pertains. We bring together aspects correlating with D † = 2 and aspects correlating with D 2 = 4. The result D 2 − D † = 4 − 2 = 2 pertains. In eect, the transformation -from D 1 to D 2 adds -compared to models for which D † = 2 pertains -two TA-side oscillators and two SA-side oscillators. Each new oscillator pair can correlate with an SU (2) symmetry. (See table 13 (62) and (63). The SA5-and-SA6 pair correlates with -for each elementary fermion -three generations. Table 34 shows and interprets symmetries that pertain to all elementary fermions. (Note tables 28 and 58.) For each elementary fermion, either @ 0 correlates with three of the four relevant oscillators or @ −1 correlates with three of the four relevant oscillators.
We discuss modeling for particles for ι S = 1 simple fermions. Table 32b shows D = 3 and D + 2ν SA = 0. Table 32c shows D = 3 and D + 2ν T A = 0. Equation (61) pertains. The number D = 3 correlates -regarding table 34 -with one of the number of SA-side @ 0 and the number of SA-side @ −1 . Results that table 34 features pertain. One can reuse results that pertain for elds for ι S = 1 simple fermions.

Concepts regarding representations for photons
We discuss notions that, with respect to ongoing modeling, correlate with KMS modeling.
Ongoing modeling describes photon states via two harmonic oscillators. Ongoing modeling features four space-time-coordinate dimensions.
Why not describe photon states via four harmonic oscillators?
Proposed modeling describes photon states via ALG modeling that features four harmonic oscillators.
The four-oscillator models correlate with PFS modeling.
One might assume that four-oscillator models must correlate with non-zero longitudinal polarization and with a photon rest mass that would be non-zero. However, mathematics allows a way to avoid this perceived possible problem. (See equation (35).) One might assume that using four oscillators would add no insight. However, using four oscillators leads to a framework for expressing aspects of proposed modeling and leads to insight about a family of phenomena that includes photons.

ALG representations for elementary particles
We discuss aspects of ALG modeling.
We consider the left circular polarization mode of a photon. We denote the number of excitations of the mode by n. Here, n is a nonnegative integer. One temporal oscillator pertains. We label that oscillator TA0. The excitation number n T A0 = n pertains. Here, n T A0 = n ≥ 0 pertains. Harmonic oscillator mathematics correlates a value of n + 1/2 with that oscillator. Three spatial oscillators pertain. Here, n SA0 = −1, n SA1 = n, n SA2 = @ 0 . Oscillator SA0 correlates with longitudinal polarization and has zero amplitude for excitation. (See equation (35).) Oscillator SA1 correlates with left circular polarization.
Oscillator SA2 correlates with right circular polarization. The symbol @ _ denotes a value of _ that, within a context, never changes. For left circular polarization, @ 0 pertains for oscillator SA2. The sum n + 1/2 correlates with each of the one TA-side oscillator and the three SA-side oscillators. For the TAside oscillator, the sum -with which we correlate the symbol A ALG T A -equals (n + 1/2). For the SA-side oscillators, the sum -with which we correlate the symbol A ALG SA -equals (−1 +1/2) +(n+ 1/2) +(0 +1/2). For the right circular polarization mode of a photon, one exchanges the values of n SA1 and n SA2 . The result is n SA1 = @ 0 , n SA2 = n. For each mode, for the TA0 oscillator, raising operators and lowering operators that correlate with U (1) symmetry pertain. (Perhaps, note table 28.) One generator correlates with excitation. One generator correlates with de-excitation. This essay does not fully explore the extent to which this U (1) symmetry correlates with the U (1) symmetry that the elementary particle Standard Model associates with photons. (Perhaps, note discussion regarding equation (173).) The representation that table 36 shows is invariant with respect to observer. In interpreting a measurement, each observer would correlate the measurement with the same one of left circular polarization and right circular polarization. For that polarization, each observer, in eect, would measure the same value of n. Observers might disagree with respect to measured values of energy or momentum.
We prepare to explore representations for elementary particles other than photons. Table 37 discusses our uses -regarding elementary particles, regarding objects in general, and regarding environments in which elementary particles and other objects exist -of the word unfree and of the word free. Table 38 discusses aspects regarding modeling for elementary bosons for which n T A0 = −1. Absent such aspects, models might correlate with the notion that such bosons would not excite. (Note equation (35).) Table 39 lists questions that, for this immediate discussion, we de-emphasize fully addressing.  Table 37: The word unfree and the word free -regarding elementary particles, objects in general, and environments Aspect • Regarding elementary particles, we use the word unfree to correlate with the notion that an elementary particle models -in PFS modeling -only as if the particle and its environment entangle • Regarding objects in general, we use the word free to correlate with modeling for which each of conservation of energy, conservation of momentum, and conservation of angular momentum pertains.
We return to discussing photons. We discuss modeling pertaining to the weak interaction (or, Z and W) bosons.
To describe n excitations of the same state of one of the W-family bosons, we use n T A0 = n = n SA_ , with SA_ correlating with the one boson. An isolated interaction that excites or de-excites the boson conserves the generation of the fermion that participates in the interaction. For example, an interaction between an electron (or, generation-one charged lepton) and a W +3 boson produces a generation-one neutrino. (Per notation that this essay uses, the charge that correlates with the symbol W  that table 42 shows to the state characterized by n T A0 = 2, n SA0 = 0, n SA1 = 1, and n SA2 = 1 would violate equation (40). The TA-side raising operations would produce a factor of (1 + 0) 1/2 (1 + 1) 1/2 , which equals 2 1/2 . The SA-side raising operations would produce a factor of (1 + 0) 1/2 (1 + 0) 1/2 , which equals 1. Equations (40) and (41) imply that one of oscillators TA5 and TA6 participates. There are three generations of quarks. Three is the number of generators of SU (2). (See  table 13.) We posit that an approximate SU (2) symmetry pertains. We use the ve-word term rebuttable somewhat conservation of generation (or, the six-word term rebuttable somewhat conservation of fermion generation). Ongoing modeling seems to correlate this proposed modeling notion of non-conservation of generation with the ongoing modeling notion of CP violation. (See, for example, reference [9].) Proposed modeling suggests the possibility that people might be able to detect non-conservation, induced by Wfamily eects, of lepton generation. (Reference [9] suggests that people may be on the verge of observing evidence of lepton CP violation.) Combining the TA5-and-TA6 SU (2) symmetry with the TA0 U (1) symmetry yields an SU (2) × U (1)  Table 43 shows a UMS-centric representation for the weak interaction bosons. The SA1-and-SA2 κ @0,@0 correlates with 3 generators, three spin states, and with three charge states. The TA5-and-TA6 κ @0,@0 correlates with rebuttable somewhat conservation of fermion generation. (See table 18 and table   40.) We discuss representations for charged leptons and for neutrinos.
For elementary fermions, we posit that ALG modeling does not necessarily need to correlate with excitations.   Table 44 shows a representation for the 1C subfamily of charged leptons. The representation comports with the notions of D = 3 and D † = 2. (See discussion related to tables 32b, 32c, and 34.) For each of SA1-and-SA2 and TA1-and-TA2, eectively only one oscillator pertains. For SA1-and-SA2, the symbol π @0,@−1 correlates with the notion of matter particles and antimatter particles. For TA1-and-TA2, the symbol π @0,@−1 correlates with a symmetry that correlates with rebuttable always conservation of charge. For SA0, the symbol @ 0 correlates with non-zero mass and non-zero charge. For TA0, the symbol @ 0 pertains based on double-entry bookkeeping.  (42) and (43). (These applications correlate with interactions that transform a fermion from one of m>0 and m=0 to the other of m>0 and m=0. Regarding notation, see discussion related to table 23. Here, the dierence between 0 and @ 0 is not material. Here, the dierence between −1 and @ −1 is not material.) One application correlates with oscillator SA0. One application correlates with oscillator TA0. For SA0, the symbol @ −1 correlates with zerolike mass and zero charge. For TA0, the symbol @ −1 pertains based on double-entry bookkeeping. Other dierences correlate with two substitutions of the form κ @0,@0 ← κ @−1,@−1 and do not correlate with changes in relevant symmetries. The two κ @0,@0 ← κ @−1,@−1 substitutions correlate with the notion that additional oscillators correlate with n XA_ = n T A0 . The notion of n XA_ = n T A0 is relevant to proposed modeling models regarding refraction. (See discussion related to table 68.) We return to discussing elementary bosons.   @ 0 π @0,@−1 κ @0,@0 SA @ 0 π @0,@−1 κ @0,@0 we use the TA5-and-TA6 item to point to a symmetry that technically correlates with more than just two oscillators. Table 48 points to the possibility that Σ max = 8 pertains (Perhaps, see equation (48).) We consider the notion that n T A0 = 0 correlates with n T A0 = @ 0 . We consider the notion that -regarding 4G, 6G, and 8G respectively -the respective symmetries SU (3), SU (5),and SU (7) pertain. We consider the notion that a limit of SU (7) might pertain. (See, for example, discussion related to equation (46) and discussions related to tables 62a and 64. Perhaps, also consider that 20G does not correlate with SU (17).) We turn our attention to elementary particles that correlate with |ι 3CH |=2 or |ι 3CH |=1. (See table   26d and equation (50).) Table 49 notes concepts regarding values, for objects, of charge, of ι 3LB , of L, and of B. Here, we consider that a proton or other hadron with no more than three quarks can correlate with the notion of free. The following notion also pertains. For a hadron-like particle that includes no more than three quarks and arcs, the restrictions to integer charge and integer baryon number preclude the presence of both quarks and arcs.
Proposed modeling suggests a symmetry regarding ι 3CH . The symmetry suggests that each of the cases ι 3CH = 2 and ι 3CH = 1 is similar to the case ι 3CH = 3. For the 1C subfamily, the cases ι 3CH = 2 and ι 3CH = 1 correlate with the six 1Q (or, quark) elementary fermions. Quarks have fractional charges. Table 50 shows, simple particles that proposed modeling suggests based on the symmetry related to ι 3CH . For the zero-charge 1R and 2T particles that table 50 shows, the number of tick marks in a symbol ΣΦ 0_ equals |ι 3CH |.
A representation for each 1Q particle to which table 50 alludes equals the representation for the corresponding 1C particle. Table 45 provides a PFS-centric representation for quarks.
A representation for each 1R particle to which table 50 alludes equals the representation for the corresponding 1N particle. Table 46 provides a PFS-centric representation for arcs. We discuss the jay bosons. The result n SA0 = −1 correlates with zero charge and zerolike mass. Paralleling results pertaining to the 2W subfamily, the SA7-and-SA8 SU (2) symmetry correlates with three elementary particles and with three spin states. The SA7-and-SA8 and TA5-and-TA6 items comport with notation-centric conventions regarding n XA_ = n T A0 . We use the following notation and posit the following notions regarding the three 2J bosons. 2J 0 can exhibit left circular polarization and right circular polarization. 2J − can exhibit (say) left circular polarization and cannot exhibit right circular polarization. 2J + can exhibit right circular polarization and cannot exhibit left circular polarization. (Elsewhere, we more fully discuss aspects of jay physics.

See table 70.)
We discuss the aye boson. Table 53 shows a PFS-centric representation for the ground state for the aye boson. Table 53 diers   from table 47 -which pertains for the Higgs boson -based on two substitutions -one for TA0 and one for SA0 -of the form n XA0 = 0 ← n XA0 = −1.
• For unfree objects, the minimum magnitudes of some non-zero quantities are |q |/3 for charge and one for |ι 3LB |.
• Each of the quantities charge, ι 3LB , L, and B is additive with respect to components of a multicomponent object.
Attractive SA9-and-SA10, see table 20a.) The representation includes a TA-side SU (3) symmetry that correlates, in PFS-centric models, with oscillators TA0, TA9, and TA10. (Perhaps, regarding the seeming use of three -not two -instances of n T A_ = −1 for aspects that seemingly correlate with just two oscillators, compare with the SU (4) and SU (6)  We discuss the pie boson.
We explore correlations between the 2U solution and the pie (or, 0P) boson.

Results: properties of elementary particles and multicomponent objects
This unit interrelates properties of elementary particles and properties of multicomponent objects.

Summary: a table of properties of elementary particles and multicomponent objects
Other root forces Elsewhere, we speculate that aspects of

Modeling regarding properties of elementary particles and multicomponent objects
We discuss concepts and methods that point to results regarding some properties of elementary particles.

Kinematics conservation laws
We explore modeling regarding conservation of energy, momentum, and angular momentum.
In ongoing modeling, the electromagnetic eld carries information that correlates with events that excited the eld. Via de-excitations, people measure energies, momenta, and polarizations. (Also, people measure or infer that the de-excitation event features de-excitation of a mode of the electromagnetic eld and does not feature de-excitation of a non-electromagnetic eld.) People infer information about excitation events.
We want to discuss the extent to which proposed modeling models for ΣG (or, G-family) elds reect encoded information.
We start by exploring modeling related to energy, momentum, and angular momentum.
Ongoing modeling discusses models for objects, internal properties (such as spin and charge) of objects, motion-centric properties (such as momentum) of objects, and interactions (or, forces) that aect internal properties of objects or motions of objects.
We discuss symmetries that ongoing modeling and proposed modeling correlate with conservation laws related to motion. The following concepts pertain regarding proposed modeling.
Models for the kinematics of objects in free environments need to include the possibility that all three conservation laws pertain. The relevance of all three conservation laws correlates with modeling that correlates with the notion of a distinguishable object and with the notion of a free environment.
Objects can exist as components of, let us call them, larger objects that are free. For one example, an electron can exist as part of an atom. For another example, a hadron can exist as part of an atomic nucleus that includes more than one hadron. The two-word term conned environment can pertain.
Models regarding the kinematics (or, dynamics) of objects in unfree (or, conned) environments do not necessarily need to embrace all three kinematics conservation laws. Unfree objects can model as existing in the contexts of larger free objects.
For a proposed modeling ALG model to embrace conservation of momentum and conservation of angular momentum, one, in eect, adds (to a model for an object) four SA-side oscillators and expresses two instances of SU (2) symmetry. Double-entry bookkeeping suggests adding four TAside oscillators. Proposed modeling suggests that, for each of the eight added oscillators, n _ = n T A0 .
Rest energy minus freeable energy - Color charge 3 (r, b, g) - • The column labeled properties lists properties.
• Numbers in the column labeled SA-side count equal the number of generators for the groups in the column labeled SA-side symmetry.
• For a row for which the column labeled TA-side symmetry shows the group U (1), the property is a conserved quantity and the property sums across components of a multicomponent object.
(c) Notes about rows and items that pertain for the catalog Note • The notion of zerolike rest energy pertains for some elementary particles and not for other objects.
• Each object has a charge. The charge is an integer multiple of one-third the magnitude of the charge of an electron. The symbol (−,0,+) correlates with the following three possibilities. The integer is negative. The integer is zero. The integer is positive.
• For an object that remains intact during an interaction with other objects, the quantity rest energy minus freeable energy remains unchanged by the interaction. The pairs XA3-and-XA4 correlate with rest energy. The pairs XA5-and-XA6 correlate with freeable energy.
• The row for which the XA column shows just the integers three and four is a sub-case of the row immediately above that row.
• The row for which the XA column shows just the integers ve and six is a sub-case of the row two rows above that row.
• The one-element item gens abbreviates the word generations. The notion of generations pertains for elementary fermions only.
• Each object has a 3LB number. The 3LB number is an integer multiple of the magnitude of the baryon number for a quark. The symbol (−,0,+) correlates with the following three possibilities.
The integer is negative. The integer is zero. The integer is positive.
• As far as we know, other permuting, among rows, of the items that table 58a shows as correlating with XA9-and-XA10 through XA15-and-XA16 would not make a dierence regarding modeling that this essay discusses.
• The three-element item (r, b, g) correlates with three color charges -red, blue, and green.
• The one-element item DoF abbreviates the three-word phrase degrees of freedom.
Conservation of angular momentum  For some modeling, it might be appropriate to use SU (4) plus S1G. For some modeling, it might be appropriate to use SU (4) plus U (1). In proposed modeling, each of S1G and U (1) can correlate with one harmonic oscillator. (See   table 13.) In ongoing modeling, S1G correlates with one dimension with respect to spacetime coordinates. This essay de-emphasizes discussing details of mathematical relationships between S1G and U (1).  60 correlates with interactions and with conservation laws that pertain regarding kinematics.
The following proposed modeling aspects can pertain regarding combining two free objects to form one free object.
Each of the two original objects contributes two SA-side SU (2) symmetries.

G-family phenomena, including electromagnetism and gravity
We explore aspects regarding G-family forces and regarding components of G-family forces.
In ongoing modeling KMS modeling, an excitation of a G-family force carries information through which people infer aspects of an event that includes the excitation. For example, people measure the energy of a photon and might use that information to infer information about an atomic transition that excited the photon.
We We consider an excitation that models conceptually as combining an excitation of the left circular mode of 4G and the right circular mode of 2G. (This essay de-emphasizes the possible relevance of an actual object that combines a graviton and a photon.) The combination yields a left circular polarization spin-1 excitation. The combination correlates with 2G.
Equation (65) provides notation that we use for such combinations. The symbol ΣG denotes a subfamily of the G-family of solutions to equation (38). The symbol Γ denotes a set of even integers selected from the set {2, 4, 6, 8}. We use the symbol λ to denote an element of Γ. Each value of λ correlates with the oscillator pair SA(λ − 1)-and-SAλ. (Elsewhere, we discuss aspects correlating with the limit λ ≤ 8. See discussion related to table 62.) For the above example of subtracting spin-1 from spin-2, the notation Γ = 24 pertains and equation (66) In table 62, the rightmost seven columns comport with double-entry bookkeeping. For example, a TA-side SU (3) symmetry alludes to two additional TA-side oscillators for each of which n T A_ = 0. Those two oscillators plus the TA0 oscillator correlate with κ 0,0,0 (or, with SU (3) symmetry). The symbol A0+ correlates with an oscillator pair for which, for each of the two oscillators, the symbol @ 0 pertains. (Perhaps, see table 13.) In table 62a, the column regarding span pertains regarding aspects of dark matter specically and, generally, aspects of astrophysics and cosmology. (See table 93 and table 62b.) Regarding each Σ > 0 solution that the table shows, the KMS radial behavior of the potential is r n SA0 . The RSDF is r n SA0 −1 . Table 63 generalizes from table 62b. Table 64 lists notions that might correlate with a limit of λ ≤ 8. Possibly, each one of the notions is relevant. Table 65 lists G-family solutions ΣGΓ for which both Σ does not exceed eight and Σ appears in the list Γ. The expressions | − 2 + 4 − 6 + 8| and | − 2 − 4 − 6 + 8| show that two solutions comport with the notion of 4G2468. The expressions | + 2 + 4 − 6 + 8| and | − 2 − 4 + 6 + 8| show that two solutions comport with the notion of 8G2468. We use the symbol Σγ to refer to the set of G-family solutions ΣGΓ for which Σ appears in the list Γ. (See equation (67).) We use the symbol γλ to refer to the set of G-family solutions ΣGΓ for which λ appears in the list Γ and Σ does not appear in the list Γ. (See equation (68).) Notes regarding excitations and regarding information that correlates with specic ΣGΓ Note • An excitation of a ΣG eld does not (directly) encode information about a relevant ΣGΓ.
• Proposed modeling includes so-called PRι I ISP modeling, with ι I being one of the integers one, six, and 36. The models address aspects of astrophysics and aspects of cosmology. The integer ι I denotes a number of so-called isomers of simple particles.
• In this respect, PR1ISP modeling correlates with core ongoing modeling. The notion of span is not relevant. (Or, one can say that each simple particle and each component of root forces has a span of one.) • For PRι I ISP modeling for which ι I ≥6, an excitation (for example, of a ΣG eld) encodes information that species relevant isomers of simple particles. Here, the word relevant denotes relevant to the excitation. The word span denotes the number of relevant isomers.
• For PRι I ISP modeling for which ι I ≥6, a de-excitation must correlate with an isomer in the list of isomers that correlates with the relevant excitation. • An excitation of a root force does not encode information correlating directly with a specic component of the root force.
• A de-excitation must correlate with an isomer in the list of isomers that correlates with the relevant excitation.
• In this essay, PFS modeling uses of terms such as the two-element term _pole gravity refer to notions that correlate with isomers. Examples of such terms include the two-word phrase monopole gravity, the two-element term non-monopole gravity, and the four-word term quadrupole component of gravity.
• In this essay, KMS modeling uses of terms such as the two-element term _pole gravity refer to notions that an object can have a mass distribution that is not spherically symmetric and can have a mass distribution that rotates. • The limit might correlate with a scaling law. For the Γ of 2468 10 , the one-element phrase hexadecimal-pole would pertain. Here, the symbol 10 denotes the number ten. Assuming KMS Newtonian modeling, the RSDF (or, radial spatial dependence of force) would be r −6 . We consider interactions between two similar, neighboring, non-overlapping, somewhat spherically symmetric objects. A ΣG2468 10 force would scale like (υ 3 ρ) 2 /(υr) 6 , in which υ is a non-dimensional scaling factor that correlates with linear size (or, a length), ρ is the relevant object property for the case for which υ = 1, and r is the distance between the centers of the objects. The factor υ 3 provides for scaling for an object that has three spatial dimensions. The force would be independent of υ.
That independence might suggest, from a standpoint of physics, that = 0 pertains. • The limit might correlate with the notion of three eras in the rate of expansion of the universe.
(See discussion related to table 102.) Proposed modeling correlates those eras with (respectively, working backwards in time from the present era) dipole repulsion, quadrupole attraction, and octupole repulsion. We know of no evidence for an era that would correlate with hexadecimal phenomena.
• The limit might correlate with a TA-side SU (9) symmetry. Based on thinking that leads to table 62, 10G 10 correlates with a TA-side SU (9) symmetry. We posit that remarks regarding equation (46) pertain. Here, we de-emphasize the notion that 16G 16 has relevance to physics. (See   discussion related to table 123.) The solution 16G 16 would correlate with TA-side SU (17) symmetry.
• The limit might correlate with the notion of channels. Discussion related to equation (135) suggests that a λ that exceeds eight is not relevant regarding G-family physics.
• The limit might correlate with modeling that correlates with aspects of table 20. This essay de-emphasizes this possibility.   Statements above regarding 2G and 4G correlate with concepts that equations (69) and (70)  ΣG ↔ quantum excitations (69) ΣGΓ ↔ a bridge between quantum excitations and kinematics forces (70) We explore the extent to which components of G-family forces interact with simple particles. (This exploration correlates with PFS modeling.) We combine aspects of equation (46), The tables share their respective n T A0 = 0 values. Seven plus ve minus one is 11.) For example, for 4G4, a TA-side SU (7) symmetry would pertain. For example, for 2G2 or 2G24, a TA-side SU (5) symmetry would pertain. We posit a limit that correlates with aspects of equation (46). We posit that each component that appears in  side symmetry that table 62 shows with the conservation of energy symmetry produces, respectively, SU (9) or SU (11).) We posit that a combined symmetry of either SU (9) or SU (11) correlates with possible interactions with multicomponent objects.
For example, 2G68 can interact with an atom but not with an isolated electron. (Table 62   We contrast aspects of proposed modeling G-family modeling with a possible proposed modeling interpretation of aspects of ongoing modeling.

Conservation of lepton number minus baryon number
We explore the notion of conservation of lepton number minus baryon number.
Equation (71) We correlate, with ι 3LB , the two-element term 3LB number. Sometimes, we use the one-element term 3LB to denote 3LB number. The four-element term conservation of 3LB number pertains.  (72), (73), (74), and (75) shows an interaction that would involve the 2T +1 simple particle; transform a matter quark into another simple fermion; and conserve ι 3LB , L, and B. Here, for fermions, the notation 1Φ ι 3CH ι 3LB;3L,3B pertains. Here, for bosons, equations show notation of the form 2Φ ι 3CH ι 3LB;3L,3B and might suggest that each of L, conservation of L, B, and conservation of B is appropriate. However, discussion related to equation (76) indicates that none of L, conservation of L, B, and conservation of B is relevant to the relevant boson physics. Each of the rst three equations (that is, equations (72), (73), and (74) More generally, equation (76) shows possible charged 2T simple bosons that convert simple fermions between matter and antimatter. Equation (77) This essay de-emphasizes the possibilities that equation (77) shows.
Regarding equation (76), each of the four possibilities, of which one possibility is 2T +1 −2; , correlates with two possible L-and-B pairs. We assume that charged 2T bosons are ambiguous with respect to each of L and B. Generally, interactions conserve ι 3LB , do not necessarily conserve L, and do not necessarily conserve B. Non-conservation of L and B correlates with involvement -in the interactions -of 2T ± bosons. One might deploy the six-word phrase rebuttable somewhat conservation of lepton number and the six-word phrase rebuttable somewhat conservation of baryon number. One might deploy, regarding elementary fermions, the seven-word phrase rebuttable always conservation of fermion 3LB number.

Refraction and similar phenomena
We explore modeling regarding contexts in which a zerolike rest mass elementary particle interacts with We posit that PFS ALG modeling extends to include notions of non-isotropic harmonic oscillators.
Each of equations (78) and (79) oers, based on using the range −1 < n SA0 < 0, a possible basis for modeling regarding a zerolike rest mass elementary particle. (We contrast −1 < n SA0 < 0 with n SA0 < −1. Uses of the expression n SA0 < −1 pertain for applications related to components of Gfamily forces and not necessarily for other purposes. Regarding applications related to components of G-family forces, see table 62.) In the sense of KMS modeling, E denotes energy, Here, double-entry bookkeeping pertains to models for which at least one of the PFS ALG TA-side set of harmonic oscillators and the PFS ALG SA-side set of harmonic oscillators is not necessarily isotropic.
For each of the three physics-relevant cases, each of equations (78) and (79)  For the case of fermion and n T A0 = −1, for each relevant SA-side oscillator, n SA_ = −1. One cannot satisfy double-entry bookkeeping by adding to A ALG SA . Satisfying double-entry bookkeeping correlates with adding something positive to at least one of the two TA-side oscillators that correlate with SU (2) rebuttable somewhat conservation of generation symmetry or to at least one of the TA-side oscillators that correlate with conservation of energy symmetry. Assuming that conservation of energy pertains, (rebuttable always) conservation of generation does not pertain. This modeling comports with the notion Table 69: PFS representation for SA-side aspects regarding 2U erase or paint ground states (with some aspects -for example, TA-side aspects related to conservation of charge -omitted) of neutrino oscillations. This case correlates with neutrino oscillations. Observations suggest that rates at which neutrinos oscillate vary with the energies of the neutrinos. (See reference [10].) This essay does not pursue the notion that double-entry bookkeeping techniques and an equation such as equation (78) might correlate with a model -for symmetry breaking -that correlates with rates of neutrino oscillations.
For the case of boson and n T A0 = −1, equations (80), (81) and (82) can pertain. Here, the symbol n SA_ correlates with an oscillator for which n SA_ = −1 originally pertained. (Perhaps, compare with discussion, pertaining to refraction, regarding equations (78) and (79).) Here, the notation a ← b correlates with the three-element phrase a becomes b (or, with the notion that b replaces a). Here, the notion of n SA_ = (−1) + correlates with concepts such as refraction and with modeling that correlates with non-isotropic harmonic oscillators. Here, discussion is not necessarily as straightforward as is discussion for the other two physics-relevant cases. Discussion related to table 69 pertains regarding gluons.

Gluon interactions
We explore modeling regarding gluons and modeling regarding U-family interactions.
The 2U solutions correlate with gluons. Here, we provide details correlating with PFS ALG modeling.
We denote three relevant PFS oscillators by the symbols SA0, SA9, and SA10. (Perhaps, compare with table 54.) Regarding quark or arc simple fermions, each of oscillators SA0, SA9, and SA10 correlates with a color charge. Relative to an ongoing modeling standard representation for gluons, one of SA9 and SA10 correlates with the color red, the other of SA9 and SA10 correlates with the color blue, and SA0 correlates with the color green. Table 69 shows aspects regarding three erase or paint ground states.
A gluon correlates with a weighted sum of two or three erase-and-paint pairs. For each pair, the erase part correlates with, in eect, an ability to erase, from the quark or arc simple fermion that absorbs the gluon, a color. The paint part correlates with, in eect, an ability to paint, on to the quark or arc simple fermion that absorbs the gluon, a color. The value n SA_ = (−1) + denotes an ability for a gluon to erase or paint the color charge correlating with the SA_ oscillator. Equation (83)    The notion of three color charges comports with the notion that D = 3 pertains regarding TA-side aspects of modeling for fermion elementary particles. (See table 32c.) This discussion might correlate with a notion that three (and no more than three) color charges pertain for each quark and each arc.

Interactions involving jay bosons
We note -as perspective -one observational result that might correlate with eects correlating with jay bosons.
Reference [11] reports a discrepancy between the observed energy correlating with one type of nestructure transition in positronium and a prediction based on core ongoing modeling. (Perhaps, see also reference [12].) Equation (84) states a transition frequency. The observed value of transition frequency correlates with the energy that correlates with the transition. Equation (85) correlates with ongoing modeling. The observed energy exceeds the predicted energy. Reference [11] characterizes the transition via the expression 2 3 S 1 → 2 3 P 0 .

A series of formulas for lengths, including the Planck length
We discuss three related formulas that produce lengths. The formulas correlate with aspects pertaining to elementary particles and to other objects.
We suggest a series of formulas for lengths. Equation (86)      • We posit that 2J ± bosons correlate with some interaction vertices that involve an incoming spin-one fermion, an incoming or outgoing ΣG for which Σ ≥ 4, and an outgoing spin-one fermion.  • The pie has a range that correlates with the distance, within an atomic nucleus, between neighboring hadrons.   We discuss the Higgs boson and the weak interaction bosons. We discuss the aye boson.

Ranges for interactions that correlate with elementary bosons
We correlate the mass of the aye (or, 0I) boson with the result D + 2ν = 0 that pertains for the row   (91) and equation (92), the rst item (and, hence, the rst two solutions) correlates with the expression 0 ± 0.
Proposed modeling suggests that 2T 0 and 2T 0 correlate with two solutions that equation (91) shows.
The other two solutions that the equation shows would correlate with 2T 2 and 2T 1 . We use these results to estimate masses for 2T simple bosons. (See discussion related to equations (98) and (99).) We discuss the jay bosons. We discuss the pie boson. Table 55 suggests correlating the 0P boson with the U-family and not necessarily with the G-family.
This essay does not explore mathematics that might correlate modeling for the 0P boson with a notion of a 0U solution.
We discuss the possibility of correlations between 0G solutions and simple fermions.  Table 75c reects aspects of table 75b, based on notions that the next three sentences mention. The TA0 result correlates with transforming 0 to @ 0 (which is appropriate for fermions). The SA1-and-SA2 result π @0,@−1 correlates with transforming 0 to @ 0 (which is appropriate for fermions) and transforming one @ 0 to @ −1 (which is also appropriate for fermions). The TA5-and-TA6 result correlates with applying double-entry bookkeeping and with transforming κ 0,0 to κ 0,−1 (for which the notation of

Predictions and correlations regarding properties of elementary particles
We explore masses and other properties of elementary particles.
(c) A PFS-centric representation for the 1C subfamily (with π @ 0 ,@ −1 omitted regarding TA1and-TA2)  We explore relationships between masses of the 2W (or, W and Z) and 0H (or, Higgs) bosons. Table 76 shows, in the column for which the label includes the word experimental, rest energies for the known non-zero-mass simple bosons. (See reference [13].) Notation such as 2W1 and 0H0 extends the notion of Γ -as pertaining to oscillators relevant in ALG models for G-family solutions -to notions of Γ for ALG models relevant to elementary particle families other than the G family. The most accurately known of the three masses is the mass of the Z boson.
We discuss approximate ratios for the squares of masses of the Higgs, Z, and W bosons. To the extent that m W does not exactly comport with equation (93), proposed modeling suggests the possibility that an anomalous moment pertains. The W boson has non-zero charge, non-zero nominal magnetic dipole moment, and non-zero mass. We suggest that the anomalous moment might correlate mostly with the 6G24 solution. (Compare with discussion related to equation (196).) The contribution of minus two (compared to the Z boson) -that equation (93) We explore modeling for the mass of the aye (or, 0I) boson.
We suggest that the aye boson correlates with the solution for which σ = +1 and S = 1. (See table  32e.) The result D + 2ν = 0 pertains and correlates with a zero square of mass.

Possible masses of the tweak bosons
We explore possibilities regarding masses of T-family bosons.
We explore using patterns that have bases in G-family solutions and in aspects of table 32e. Table 77 points to a possible mass for zero-charge 2T bosons. Table 77a  (m T 0 ) 2 /(m H 0 ) 2 = 49/17 (96) 47/17 ≤ (m T ± ) 2 /(m H 0 ) 2 ≤ 49/17 (97) (m T 0 )c 2 ≈ 212.5GeV (98) Proposed modeling suggests that equations (98) and (99) (104) shows, with a standard deviation of less than one eighth of the standard deviation correlating with the experimental result. (For relevant data, see reference [14].) Equation (105) shows an approximate value of β that we calculate, using data that reference [14] shows, via equation (102).) Elsewhere, we correlate the numbers four and three in the left-hand side of equation (102)        The following concepts pertain regarding developing and using equation (108). We use equation (102) to calculate β. Equation (108) calculates the same value of m τ that equation (104) calculates.
Equation (108) in table 79 show. Regarding the tauon, our calculation correlates with a mass that may be more accurate, and more accurately specied, than the mass that references [13] and [14] show. (See equations (104) and (100).) To the extent that people measure quark masses more accurately, people might nd relationships between d (0), d (1), and d (2), and thereby reduce the number of parameters to less than seven.
The charge q correlates with β via equation (102). The charge q appears in α, via equation (109).
Based on equations (93) and (108) and based on modeling for the G-family, proposed modeling entangles concepts related to mass and concepts related to charge more deeply than does ongoing modeling.
Equations (119) and (120) explore the possibility for a relationship -perhaps similar to equation (102) -regarding the ratio m µ /m or the ratio m τ /m µ . Equation (121) shows the result that we compute based on data from reference [13]. Equation (122) shows the result that we compute based on data from reference [14]. The main dierence between the two sets of data lies in values of the gravitational constant, G N . (The two references present the same value for the tauon mass. However, for each result, we use a tauon mass that is based on equation (102).) We do not explore possible signicance for the notion that 1 + x ≈ 10/9.
x ≈ 0.110033 (121) x ≈ 0.110031 4.3.6. The relative strengths of electromagnetism and gravity We explore concepts that might correlate with the ongoing modeling notion that the strength of gravity is much less than the strength of electromagnetism.
We explore modeling for interactions that involve a charged simple fermion, such as an electron.
We assume that we can work within aspects of proposed modeling that de-emphasize translational motion and multicomponent objects. We assume that conservation of angular momentum pertains.
The notion that 1F + 4G → 1F + 0I does not pertain might correlate with ongoing modeling notions that the strength of gravity is much less than the strength of electromagnetism.
We explore the strengths -for the monopole components of interactions between pairs of charged leptons -of electromagnetism and gravity. We use KMS Newtonian modeling.

Channels and interactions that involve G-family bosons
The notion of channels pertains to, at least, the relative strengths of the 2G2 component of 2G ( We elaborate regarding the selection of equation (135) to compute numbers of channels.
Regarding 2G, some objects measure as having charge (which correlates with 2G2) and not having intrinsic magnetic elds (which would correlate with 2G24). Other objects measure as having intrinsic magnetic elds and not having net non-zero charge. We think that such notions point to the notion that channels correlate directly with 2GΓ and not directly with 2G.  includes the term (q / ) 2 . The Josephson constant K J equals 2q /h (or, q /(2π )). Ongoing modeling considers that magnetic ux is always an integer multiple of h/(2q ). (We note the existence of an analog -to equation (136) -for which α = (· · ·) · K J . Elsewhere, this essay links spin to aspects pertaining to the squares of masses of elementary bosons. See, for example, discussion related to equation (93) and discussion related to equation (95). Elsewhere, this essay mentions the notion that aspects pertaining to squares of masses of elementary bosons might link with nominal magnetic dipole moment. See, discussion related to equation (93). Possibly, the α = (· · ·) · K J analog to equation (136) has relevance to aspects pertaining to squares of masses of elementary bosons. This essay does not further discuss possible relevance of the α = (· · ·) · K J analog to equation (136).) We explore a concept regarding ongoing modeling notions that correlate with relationships between the strengths of the electromagnetic, weak, and strong interactions.
We use the symbol ΣB to denote an elementary boson having a spin of Σ/2. The expression 1F+2B→1F+0B can pertain for each of the following cases -2B correlates with 2G, 2B correlates with 2W, and 2B correlates with 2U. This notion might correlate with ongoing modeling notions that correlate with relationships between the strengths of the electromagnetic, weak, and strong interactions.   We explore aspects that would be relevant for the case of Σ max = 20 but not for the case of Σ max = 8. For each G-family physics-relevant ΣGΓ solution for which Σ ≥ 10, there is a G-family physics-relevant Σ GΓ solution for which Σ is less than Σ. (Compare table 92c with the combination of table 92a and  table 92b  Eects correlating with each G-family physics-relevant ΣGΓ solution for which Σ ≥ 10 might be dicult to observe. For each one of those solutions, the word monopole does not pertain and there is a relevant G-family Σ GΓ solution (for which the same word out of the list dipole, quadrupole, and octupole pertains) that contributes an eect that is at least a factor of 10 4 larger than eects of the ΣGΓ solution.  83: Possible relevance -regarding some interaction strengths -of the ne-structure constant (with the symbol O denoting the two-word term ongoing modeling; with the symbol P denoting the two-word term proposed modeling; with KMS denoting KMS modeling; with PFS denoting PFS modeling; with QED denoting the two-word term quantum electrodynamics; and with the symbol * denoting the expression (

Numbers of fermion generations
Unveried ongoing modeling includes notions of a fourth generation of neutrino. People use the two-word term sterile neutrino. We know of no data that supports the existence of a fourth neutrino.  [13]. Reference [15] provides the lowest of the upper limits that reference [13] lists.) The integer j correlates with generation. Equation (142)     Here, x can be either one of a and b.
• A notion that the factor α pertains twice is relevant. (See equation (136).) Each factor of α correlates with the unit of spin.
• For electrons, the ratio of the strength of 8G2468x to the strength of 4G2468x is α 2 .
• For each of the three neutrinos -the strength of 8G2468x equals the strength of 8G2468x for electrons.

Models that might estimate an ongoing modeling sum of neutrino masses
We explore possibilities for developing models that would estimate a non-zero ongoing modeling sum of neutrino masses.
One possibility has bases in the notion that one can extrapolate, based on equation (108), to results that pertain to neutrino masses. We do not nd a seemingly useful method. We de-emphasize this possibility.
One possibility assumes the ongoing modeling notion that neutrino oscillations correlate with interactions that we correlate with the 4G subfamily.  (Perhaps, the notion of rest energy minus freeable energy pertains. Perhaps, that notion correlates with the notion that, for ΣG2468x, each of 4 ∈ Γ and 6 ∈ Γ pertains.) We discuss possible implications regarding ongoing modeling.
Ongoing modeling astrophysics modeling does not include modeling that proposed modeling correlates with 6G and 8G. We posit one or two conceptual mapping steps. First, in the context of proposed modeling, modeling for 8G octupole components of force maps to modeling for octupole components of 4G forces. Perhaps that step suces. In this context, ongoing modeling paralleling aspects of proposed modeling 4G2468a and 4G2468b interprets 8G eects on neutrinos as correlating with non-zero neutrino  [13] provides the data that we use for these calculations.) The lepton number for an electron equals the lepton number for a matter neutrino. Equation (146) correlates with results based just on the component that correlates with proposed modeling 8G eects.
(One exponent of two correlates with the exponent of two pertaining, in essence, to equation (143).
One exponent of two correlates with the notion that the interaction involves two simple fermions.) The result that equation (146) shows is less than the result that equation (145) shows. In this context of ongoing modeling, the proposed modeling interaction, between two electrons, based on lepton number is not incompatible with measurements of electron masses.

Neutrino masses
Discussion related to table 84 suggests that proposed modeling can be compatible with modeling that is compatible with either one of the following two statements. All neutrinos have zero mass. Some neutrinos have non-zero mass.
We explore the notion that all neutrinos have zero mass, even though people interpret data as suggesting that at least one avor of neutrino correlates with non-zero mass. We know of no data about neutrino speeds that would settle the question as to the extent to which neutrinos have non-zero masses.
As far as we know, observations of impacts of possible neutrino lensing have yet to produce relevant results.
As far as we know, other possibly relevant experiments and observations do not provide additional insight about the extent to which neutrinos have non-zero masses. (See, for example, references [16] and [17].) Proposed modeling suggests that each neutrino might correlate with zero rest mass.

A possible lack of neutrino asymmetry
Reference [18] suggests that people might be on the verge of nding an asymmetry, which would correlate with CP violation, between matter neutrinos and antimatter neutrinos. The article suggests that ongoing modeling interpretation of data seems to point toward such an asymmetry and that it might be reasonable to anticipate that, with more data, people will conclude that the asymmetry exists.
Proposed modeling oers an alternative explanation for such data.
People produce the relevant neutrinos 295 kilometers from where the measurements take place. Between production and detection, the neutrinos pass through earth. Along the path, if one just considers protons in atomic nuclei and electrons in materials, ι 3LB is essentially zero. If one considers also the neutrons in atomic nuclei, ι 3LB is negative. Core proposed modeling suggests that, via ongoing modeling virtual interactions, relevant neutrinos interact via 8G interactions with an ι 3LB that is negative essen- This explanation suggests that the would-be asymmetry might correlate with the material through which the neutrinos pass. This explanation suggests that the would-be asymmetry would not necessarily correlate with a CP violation asymmetry pertaining to neutrinos themselves.

Results: astrophysics and cosmology
This unit describes dark matter particles. This unit predicts and explains data about dark matter, galaxy formation, other aspects of astrophysics, and the cosmos.

Summary: a table of predictions and explanations re astrophysics and cosmology
We discuss aspects of nature -correlating with the terms dark matter, dark energy, astrophysics, and cosmology -for which proposed modeling might provide, relative to ongoing modeling, new details or better-dened explanations. Table 87 lists some topics for which proposed modeling seems to provide insight that augments insight that ongoing modeling suggests.
We discuss immediately below some, but not all, of the items that table 87 lists.
Ongoing modeling explores various hypotheses regarding the fundamental components of dark matter.
Proposed modeling suggests specic components for dark matter. Proposed modeling uses its description of dark matter fundamental components to explain data that ongoing modeling seems not to explain. • Eras during which the rate of expansion of the universe increases or decreases.
• Ratios of dark matter amounts or eects to ordinary matter amounts or eects.
• Details regarding phenomena just before the inationary epoch.
• Details regarding the inationary epoch.
• Details regarding mechanisms leading to baryon asymmetry.
• An additional source of acoustic oscillations that inuenced the formation of laments.
• Details regarding some aspects of galaxy formation.
• Details regarding dark matter objects that would be smaller than galaxies.
Ongoing modeling suggests notions regarding three known eras in the rate of expansion of the universe.
One era features an accelerating (or, increasing) rate and correlates with the so-called inationary epoch.
A later multi-billion-year era features a decelerating (or, decreasing but still positive) rate. The current multi-billion-year era features an accelerating rate. Proposed modeling suggests an explanation that has bases in components of 4G forces. The explanation does not necessarily depend on ongoing modeling notions of dark energy negative pressure or on ongoing modeling models that have bases in general relativity. The proposed modeling explanation might be generally compatible with ongoing modeling models. The proposed modeling explanation points to some subtleties that ongoing modeling might miss.
Ongoing modeling seems not to explain patterns regarding ratios of dark matter to ordinary matter.
Observations point to ratios of ve-plus to one regarding densities of the universe and regarding amounts in galaxy clusters. Observations regarding ratios of amounts in early galaxies seem to cluster around zero-plus to one and four to one. Observations regarding ratios of amounts in later galaxies seem to cluster around zero-plus to one, four to one, and one to zero-plus. Ongoing modeling suggests that the early universe includes an inationary epoch. Ongoing modeling proposes a role, during that epoch, for a so-called inaton particle. Proposed modeling suggests that jay (or, 2J) bosons played key roles just before the inationary epoch. One such role correlates with producing aye (or, 0I) bosons. Proposed modeling suggests that the aye simple particle correlates with the notion of an inaton. Proposed modeling suggests that octupole components of 4G forces provided for rapid expansion.
Ongoing modeling suggests that the achievement of baryon asymmetry occurred after the formation of the universe. Ongoing modeling proposes mechanisms that might have catalyzed baryon asymmetry.
Ongoing modeling does not necessarily point to the tweak simple bosons that proposed modeling suggests exist. Proposed modeling suggests that tweak bosons might have catalyzed the achievement of baryon asymmetry.
Ongoing modeling provides hypotheses regarding possibilities for substantial objects that might be signicantly smaller than galaxies and contain mostly dark matter. Proposed modeling suggests some specics regarding some objects that would be signicantly smaller than galaxies and would contain mostly dark matter.

Modeling pertaining to astrophysics and cosmology
We discuss concepts and methods that lead to proposed modeling results regarding astrophysics and cosmology.

Modeling that describes dark matter particles
We discuss one type of dark matter.
We introduce the symbols that equations (147) and (148) show. The symbol 1Q⊗2U denotes a particle that includes just quarks and gluons. The word hadron pertains for the particle. The one-element term hadron-like pertains for the particle. Examples of such particles include protons, neutrons, and pions. The symbol 1R⊗2U denotes a particle that includes just arcs and gluons. The one-element term hadron-like pertains for the particle. The particle does not include quarks.
1Q ⊗ 2U A 1R⊗2U hadron-like particle contains no charged simple particles. The 1R⊗2U hadron-like particles do not interact with 2γ. The 1R⊗2U hadron-like particles measure as being dark matter.
We correlate work above with the two-element term PR1ISP modeling.
The existence of 1R⊗2U hadron-like particles seems insucient to explain ratios of dark matter eects to ordinary matter eects of (for example) ve-plus to one, four to one, and maybe one to one.
We explore the notion that some ve-plus to one ratios reect something fundamental in nature. We ) We label those isomers as isomer one, isomer two, . . ., and isomer ve. We posit that each of the six isomers correlates with its own 2U particles (or, gluons). We posit that one isomer of 4G4 interacts with each one of the one ordinary matter isomer and ve dark matter isomers.
We posit that the next two sentences pertain. The six-isomer notion explains the ve that pertains regarding ve-plus to one ratios of amounts of dark matter to ordinary matter. The existence of isomerzero 1R⊗2U hadron-like particles explains the plus that pertains regarding ve-plus to one ratios of amounts of dark matter to ordinary matter. Such ve-plus to one ratios pertain regarding densities of the universe and regarding the compositions of (perhaps most) galaxy clusters. and [21].) People suggest that nature might include dark matter photons. (See, for example, reference [22].) Regarding each one of the six PR6ISP isomers, we suggest that each combination - that table 79 shows -of magnitude of charge and magnitude of mass pertains to a simple fermion that correlates with the isomer. For example, each isomer includes a charged lepton for which the magnitude of charge equals the magnitude of the charge of the ordinary matter electron and for which the rest energy equals the rest energy of the electron. However, regarding charged leptons, the combination of mass and generation number does not necessarily match across isomers. (See table 98.) For example, for so-called isomer one, the generation three charged lepton may have the same mass as the ordinary matter electron. (See table   79.) The ordinary matter electron has a generation number of one.
Tables 21b and 27d discuss the symbol ι I . Discussion just above pertains regarding PRι I ISP, with ι I being one or six. Within any one PRι I ISP, equation (149) pertains for each simple particle, for each component of G-family force, for each U-family particle, and for each hadron-like particle. For example, for PR6ISP modeling, for the electron, the number of isomers is six and the span of each isomer is one. • Explains observed dark matter to ordinary matter ratios of ve-plus to one, four to one, one to one, zero-plus to one, and one to zero-plus. (PR36ISP modeling oers a dierent explanation for the one known ratio of one to one. See discussion regarding equation (149)       • Absent the notion that some components of G-family forces have spans of more than one, PR36ISP would correlate with 36 non-interacting sub-sub-universes.
• In PR36ISP models, each sub-sub-universe would consist of an isomer of PR1ISP.
• In PR36ISP models, six sub-universes pertain.  • The spans for charged elementary particles are one. There may be no relevant symmetries that would suggest that spans for other elementary particles should be anything but one.
• The G-family of elementary particles is the only family for which n T A0 = 0 and n T A0 = −1.
• There are no apparently relevant dierences in symmetries between 1C and 1N. Each isomer correlates with its own 1N. Similar notions -of spans of one for some particles implying that other particles have spans of one pertain. Regarding such notions, the following ordered pairings pertain -1Q and 1R, W and Z, 2W and 2T, 2W and 2J, and 0H and 0I.
• We posit a span of one for 2U. (Possibly, 2W and 2U is another ordered pairing. Possibly, in some sense, a span of one for 1Q implies a span of one for 2U.) • We posit that a span of one pertains for 0P. (2U and 0P would be another ordered pairing.) of SU (3), SU (5), and SU (7) divides evenly the integer 48, which is the number of generators of SU (7). Regarding 4G4, we posit that the expression 6 = g 7 /g 3 is relevant. (Regarding notation, see equation (46).) We generalize. We assert that, for each G-family solution for which a TA-side symmetry of SU (j) pertains, equation (150) provides the span. We assume that we can generalize from the assumption that the span of 2G2 is one. For each G-family solution with no TA-side symmetry, the span is one. Table 91 discusses aspects correlating with our positing that the span for each elementary particleother than the G-family elementary particles -is one.
The span for 1Q⊗2U is one, based on the non-zero charges of 1Q particles. We assume that the span for 1R⊗2U is one.
Equation (151) shows notation for denoting the span, s, for a simple particle or for a component of a root force.
Excitation of a boson encodes information specifying, in eect, the isomer or isomers that correlate with the excitation. We discuss concepts regarding the 2(2)G68 solution.  interactions with atoms and other objects. We posit that those interactions include so-called hyperne interactions.
Unlike for the cases of electromagnetic interactions that correlate with 2(1)G2 and 2(1)G24, 2G produced by ordinary matter objects interacts with dark matter objects (for the case in which PR6ISP pertains to nature) or doubly dark matter objects (for the case in which PR36ISP pertains to nature) via 2(2)G68. Unlike for the cases of electromagnetic interactions that correlate with 2(1)G2 and 2(1)G24, 2G produced by some dark matter objects (for the case in which PR6ISP pertains to nature) or by some doubly dark matter objects (for the case in which PR36ISP pertains to nature) interacts with ordinary matter via 2(2)G68.

Dark matter to ordinary matter ratios that modeling might predict or explain
We discuss ratios that PR6ISP modeling or PR36ISP modeling might predict or explain.

Some properties of isomers of quarks and charged leptons
We consider PR6ISP modeling and PR36ISP modeling. We explore modeling that correlates each of the six relevant isomers with a range of M . In equation (152), the integer n numbers the isomers. Here, the ordinary matter isomer correlates with n = 0.  • For each of PR1ISP modeling, PR6ISP modeling, and PR36ISP modeling, de-excitation of an excitation of a eld must correlate with a set of isomers that includes an isomer that the excitation-centric list includes. Amount of stu in some early galaxies

≈4:1
Amount of stu in some early galaxies 1:0 + Amount of stu in some early galaxies 0 + :1 Amount of stu in some later galaxies

≈4:1
Amount of stu in some later galaxies 1:0 + Amount of stu in some later galaxies ≈3:2 to ≈4:1 Amount of stu in dark matter halo to amount of stu near galaxy center (for some later galaxies) • The number, six, of isomers correlates with the number, six, of generators of the SM6a SU (2) × U (1) symmetry.
• The SM6a symmetry breaks -across the six isomers -based on aspects that correlate with relationships between -for charged leptons -mass and generation.    Here, for n ≥ 1, the M = 3n generation relevant to isomer n equals the M = 3(n − 1) + 3 generation relevant to isomer n − 1. Within an isomer, an overall result correlates with the same cyclic ordering, for generations, that table 79 shows.
We de-emphasize the following notions. Dark matter lepton masses might correlate with m(M , 3) and M > 3. Mathematics -such as for M < 0 -related to equation (108) might help estimate ongoing modeling values for neutrino masses. Results that correlate with M < 0 might be useful for estimating magnitudes of ordinary matter 2G interactions with dark matter analogs to ordinary matter charged leptons. Table 98 shows, for each value of n, relationships between quark generation and lepton aspects. Table  98 extends table 97 and includes quarks. For each n, the order for quarks is generation one, generation two, and then generation three. Table 98 has roots in models that correlate with the relative strengths of 2G2 and 4G4. We posit that aspects regarding mass correlate with the column with label M . We posit that, for the lepton for which n = 1 and M =3, the generation is three and the mass equals the mass of the ordinary matter electron.   Case D Each of the six isomers evolves dierently from the other ve isomers.
We correlate the two-word term case S with work above.
We do not know of data that correlates with the actual fractions of dark matter that pass through the collision with just gravitational interactions having signicance. (See table 104.) Case S can comport with fractions that are less than or that somewhat exceed four-fths (or, percentages that are less than or that somewhat exceed 80 percent).
Observations of more than 80-plus percent might correlate with geometric aspects such as the sizes and trajectories of the two galaxy clusters.
We explore the possibility that observations correlate with percentages that are too big for the combination of geometric aspects and case S to explain.
For percentages that are signicantly above 80-plus percent, modeling might need to correlate with a signicant dierence in evolution between isomer three and isomer zero.
Proposed modeling allows for aspects that might comport with a signicant dierence in evolution between isomer three and isomer zero.
We correlate the two-word term case D with work below. (See table 99 table 98.) Aspects of this possibility might correlate with relationships between the 3CH-centric π @0,@−1 that correlates with oscillators SA1-and-SA2 and the 3LB-centric π @0,@−1 that correlates with oscillators SA7-and-SA8. (See table 45.) For example, the following sentences might pertain.

Possible dierences regarding the evolution of dark matter isomers
We explore possible dierences regarding the evolution of various dark matter isomers.
We explore case S. (See discussion related to table 98 and see table 99.) We compare isomer one and isomer zero. (See discussion related to table 98.) For isomer one, the generation one charged lepton has a mass that is equal to the mass of an ordinary matter tauon. The isomer one generation one charged lepton has more mass than does the isomer zero generation one lepton (which is the electron). The isomer one generation two charged lepton has a mass that is equal to the mass of the isomer zero electron. The isomer one generation three charged lepton has a mass that is equal to the mass of the isomer zero muon. Regarding isomer one, each one of the generation two and generation three charged leptons has a mass that is less than the mass of the respective isomer zero charged lepton.
We discuss times for which the density and temperature suce to catalyze tweak-based interactions that do not conserve fermion generation. Regarding generation one quarks, more transitions to higher generations of leptons occur for isomer one than for isomer zero. (For isomer one, the higher generations of leptons are less massive than the generation one lepton. Also, the isomer one generation one charged lepton is more massive than the isomer zero generation one charged lepton.) Regarding generation two and generation three quarks, fewer transitions -per unit time -to lower generations of leptons occur for isomer one than for isomer zero.
The formation of hadron-like particles based on generation one quarks occurs later for isomer one than for isomer zero.
Isomer one phenomena such as star formation and nuclear fusion start later and at lower densities of

Predictions and explanations regarding astrophysics and cosmology
We explore aspects of astrophysics and cosmology.

A specication for dark matter and ordinary matter
We summarize a combined description of dark matter and ordinary matter. Regarding each ordinary matter simple particle, each one of the ve dark matter isomers includes a simple particle that has the same spin, the same magnitude of charge, and the same mass. If the ordinary matter simple particle is a charged lepton, for each of four of the ve dark matter isomers the respective same-spin, same-magnitude-of-charge, and same-mass charged lepton correlates with a generation number that diers from the generation number that pertains for the ordinary matter charged lepton.
For each one of those four dark matter isomers, evolution regarding objects diers from the evolution regarding ordinary matter objects. Those four isomers evolve into cool dark matter. (See table 100.)

Densities of the universe
Ongoing modeling discusses ve partial densities of the universe. The symbol Ω ν denotes neutrino density of the universe. The symbol Ω c denotes dark matter (or, cold dark matter) density of the universe. The symbol Ω b denotes ordinary matter (or, baryonic matter) density of the universe. The symbol Ω γ denotes photon density of the universe. The symbol Ω Λ denotes dark energy density of the universe.
Each of the ve densities correlates with data. Equation (153) pertains regarding the total density of the universe, Ω.
In ongoing modeling, the symbol Ω c correlates with all dark matter. To the extent that proposed modeling PR6ISP modeling or PR36ISP modeling comports with nature, the symbol Ω c correlates with all of the three aspects -1R⊗2U hadron-like particles, the four dark matter isomers that we correlate above with the word cool, and the one dark matter isomer that we do not necessarily correlate above with the word cool -that proposed modeling correlates with the term dark matter.
Proposed modeling suggests equation (154). The symbol Ω 1R2U,0 denotes the density of the universe that correlates with 1R⊗2U that correlates with the ordinary matter isomer (or, isomer zero). The symbol Ω b,>0 denotes the baryonic density of the universe that correlates with the ve dark matter isomers (or, isomers one through ve). The symbol Ω γ,>0 denotes the photon density of the universe that correlates with the ve dark matter isomers (or, isomers one through ve). The symbol Ω ν,>0 denotes the neutrino density of the universe that correlates with the ve dark matter isomers (or, isomers one through ve).
We interpret data regarding recent states of (ordinary matter) CMB (or, cosmic microwave background radiation) as correlating with equation (155). The symbol Ω 1R2U,0 correlates with the plus in the ratio ve-plus to one. The relationships Ω b Ω γ and Ω b Ω ν pertain regarding data. (Reference [13] provides data regarding Ω b Ω γ and Ω b Ω ν .) Each of isomers one, two, . . ., and six has its own 1R⊗2U, Equation (156) pertains.

Constancy of actual density of the universe ratios re DM and OM
We discuss modeling regarding the ratio of actual dark matter density of the universe to actual ordinary matter density of the universe.
Elsewhere, we discuss possible threshold energies pertaining to reactions that might produce 1R⊗2U hadron-like particles. (See, for example, discussion regarding equations (206) and (207).) For each of the six isomers, the relative densities of the universe of 1R⊗2U hadron-like particles and ordinary matter 1Q⊗2U hadron particles might be essentially constant after the universe cools to a temperature correlating with an energy of 81 GeV. (See discussion regarding equations (206) and (207).) Regarding PR6ISP modeling and PR36ISP modeling, proposed modeling does not necessarily include interactions that would convert ordinary matter 1Q⊗2U to dark matter 1Q⊗2U or interactions that would convert dark matter 1Q⊗2U to ordinary matter 1Q⊗2U.
The actual ratio of dark matter density of the universe to ordinary matter density of the universe might not much change after the cooling to the temperature correlating with the energy 81 GeV. That energy correlates with a temperature of about 10 15 degrees Kelvin. That temperature correlates with a time that is less than 10 −4 seconds after the Big Bang. (Reference [23] notes that a temperature of 10 13 degrees Kelvin correlates with a time of 10 −4 seconds after the Big Bang.) Measured ratios of dark matter density of the universe to ordinary matter density of the universe would not much change regarding times for which equation (161) pertains. (Perhaps, see equations (157) and (159).) That time range starts somewhat after 380,000 years after the Big Bang and continues through now.

A possibly DM eects to OM eects ratio inferred from data regarding CMB
People measure specic depletion of CMB and attribute some of that depletion to hyperne interactions with (ordinary matter) hydrogen atoms. (See reference [24].) The amount of depletion is twice or somewhat more than twice the amount that people expected. At least one person speculates that the amount above expectations correlates with eects of dark matter. (See reference [25].) Proposed modeling suggests the following explanation. Solution 2(2)G68 has a span of two. 2G68 To the extent that the absorption by ordinary matter is less than half of the total absorption, the following explanations might pertain. One explanation correlates with the notion that the evolution of the relevant non-ordinary-matter isomer might dier from the evolution of the ordinary matter isomer.
The non-ordinary-matter isomer might have more hydrogen-atom-like objects than does the ordinary matter isomer. One explanation correlates with 2GΓ solutions with spans of at least two. Each one of solutions 2(6)G46 and 2(6)G468 might pertain. The number six appears in both the Γ for 2(2)G46 and the Γ for 2(6)G468. Solution 2(2)G46 correlates with a dipole eect. Solution 2(6)G468 correlates with a quadrupole eect.
Proposed modeling might contribute to credibility for assumptions and calculations that led to the prediction for the amount of depletion that correlates with ordinary matter hydrogen atoms. (Regarding the assumptions and calculations, see reference [26].) 5.3.6. The rate of expansion of the universe Two thought experiments set the stage for discussing aspects regarding the rate of expansion of the universe.
We consider one thought experiment. We consider two similar neighboring clumps of stu. We assume that the clumps are moving away from each other. We assume that the clumps will continue to move away from each other. We assume that, initially, interactions correlating with RSDF r −(n+1) dominate regarding interactions between the two clumps. We assume that the two clumps interact via interactions correlating with RSDF r −n . We assume that no other forces have adequate relevance. We assume that the distance between the objects increases adequately. Eventually, the RSDF r −n force dominates the RSDF r −(n+1) force.
We consider a similar thought experiment. We consider two similar neighboring clumps. We assume that these clumps are less interactive (for example, less massive) than the two clumps in the rst thought experiment. Generally, dominance of the RSDF r −n force over the RSDF r −(n+1) force occurs sooner for the two clumps in the second thought experiment than it does for the two clumps in the rst thought experiment. Table 102 summarizes, regarding the rate of expansion of the universe, eras and 4G force components.
In this context, the eras pertain to the largest objects that people can directly infer. Early acceleration pertains for some time after the Big Bang. Then, deceleration pertains for some billions of years.
Acceleration pertains for the most recent some billions of years. (Regarding observations that correlate with the eras that correlate with deceleration and recent acceleration, see references [27], [28], [29], and [30].) Regarding smaller objects, dominant forces within objects and between neighboring objects have, at least conceptually, generally transited parallels to the above-mentioned eras and now generally exhibit  4γ that table 102 lists, the two-word term net attractive correlates with a notion of essentially always attractive (though perhaps sometimes not signicantly attractive).
Proposed modeling suggests that the ongoing modeling notion of dark energy negative pressure correlates with the 4(2)G48 component (and possibly with the 4(1)G2468a and 4(1)G2468b components) of 4γ.
A better characterization than the six-word term rate of expansion of the universe might feature a notion of the rates of moving apart of observed very large astrophysical objects.

Phenomena -including the creation of isomers -before through just after ination
Ongoing modeling suggests that an inationary epoch might have occurred. Ongoing modeling suggests that the epoch started around 10 −36 seconds after the Big Bang. (This essay de-emphasizes discussing aspects that might correlate with a time that people correlate with the two-word term Big Bang.) Ongoing modeling suggests that the epoch ended around 10 −33 seconds to 10 −32 seconds after the Big Bang. We are not certain as to the extent to which data conrms the occurrence of an inationary epoch.
Ongoing modeling includes models that people claim would support notions of ination. The models point to states of the universe, at and somewhat after the inationary epoch, that would provide bases for evolution that would be consistent with observations about later phenomena and would be consistent with aspects of ongoing modeling. (Reference [31] summarizes aspects related to ination, points to references regarding ongoing modeling, and discusses some ongoing modeling work.) Reference [32] suggests the possibility that a repulsive aspect of gravity drove phenomena correlating with the inationary epoch. The reference suggests that the composition of the universe was nearly uniform spatially. The reference suggests the importance of a so-called inaton eld.
We anticipate discussing phenomena that might correlate with times during and just after the inationary epoch.
We speculate about phenomena that might have occurred before the inationary epoch.  We assume that the particle density is suciently large that modeling can correlate the production of 4G with the 4G2468x components of 4G. (Regarding the symbol 4G2468x, see table 82.) Equation (163) describes a possible interaction. The span for each of 2J − , 4G2468x and 0I is one. For PR6ISP models, the one six-fold (or, SU (2) × U (1)) relevant symmetry could correlate with equal creation of six isomers for each of 2J − , 4G2468x, and 0I. (See tables 21 and 58.) For PR36ISP models, the two six-fold (or, SU (2) × U (1)) relevant symmetries might correlate with equal creation of 36 isomers for each of 2J − , 4G2468x, and 0I.

2(1)J
We turn our attention to the inationary epoch. We turn our attention to just after the inationary epoch.
References [32] and [31] suggest that inaton particles dominated (what proposed modeling might characterize as) the non-root-force composition of the universe for some time after the inationary epoch. We discuss isomers and spans.
Our work considers three PRι I ISP cases -ι I is one, ι I is six, and ι I is 36. Table 93 suggests that the span for each of the 2J bosons, 0I boson, quadrupole component of 4γ, and the two octupole components of 4γ is one.
We explore the case for which ι I is six.
As soon as 4G excites -for example, via the interaction that equation (163) symbolizes -isomers can couple to each other. We consider an excitement of 4G that -for discussion purposes -we correlate with equation (163). The excitement can interact with any one of the six isomers of 2J. The excitement can interact with any one of the six isomers of 0I. Such (in eect, monopole and also -via 4(2)G48 -dipole) coupling has impact, even though -from a standpoint of kinematics or dynamics -octupole components play dominant roles. Similar notions pertain regarding 2G. Most notably, some components -such as 2(2)68 and 2(6)248correlate with interactions between isomers.
We explore the case for which ι I is 36. Concepts similar to concepts pertaining for the case for which ι I is six pertain. However, for any one isomer of a span-one elementary particle (such as a 2J boson), the span of six correlating with 4(6)G4 is, in eect, orthogonal to the span of six correlating with 2(6)248.

Baryon asymmetry
We explore the notion that the universe transited from an early state that did not exhibit baryon asymmetry to a later state that exhibits baryon asymmetry.
To the extent that the early universe featured essentially the same number of antimatter quarks as matter quarks, something happened to create baryon asymmetry. The two-word term baryon asymmetry correlates with the present lack, compared to matter quarks, of antimatter quarks.
Aspects of ongoing modeling consider that early in the universe baryon symmetry pertained. Unveried ongoing modeling posits mechanisms that might have led to asymmetry. Some conjectured mechanisms would suggest asymmetries between matter simple fermions and antimatter simple fermions.
One set of such simple fermions might feature the neutrinos. (See reference [18].) Proposed modeling suggests scenarios that might have led to baryon asymmetry.
In one scenario, the interactions that equations (167) A threshold energy might be in or above the range of 208 GeV to 213 GeV. (See equation (99).) A corresponding temperature is about 2 × 10 15 degrees Kelvin. As far as we know, this result -regarding temperature or (equivalently) regarding time after the Big Bang -is not inconsistent with core ongoing modeling.
We note two possible causes for an occurrence of more 2T −1 +2; lasing than 2T +1 We explore a concept that involves isomers. Table 98 suggests possibilities for taking a multiple-isomer view of baryon asymmetry. We consider PR6ISP modeling. In this view, the lepton range 9 ≤ M ≤ 12 and quark range 9 ≤ M ≤ 11 might provide for an antimatter-centric complement to the matter-centric lepton range 0 ≤ M ≤ 3 and quark range 0 ≤ M ≤ 2. Similar results pertain for each of the two pairs n = 1-and-n = 4 and n = 2-andn = 5. With this view, there may be no need to posit interactions that led to baryon asymmetry. A similar conclusion can pertain regarding PR36ISP modeling. This essay does not further explore details regarding or implications of this concept.

Filaments and baryon acoustic oscillations
Proposed modeling is compatible with the ongoing modeling notion that ordinary matter baryon acoustic oscillations contributed to the formation of laments.
Regarding models for which ι I (as in PRι I ISP) exceeds one, each of the ve dark matter isomers has its own baryon-like particles and its own 2(1)G physics. Proposed modeling suggests, for models for which ι I exceeds one, that dark matter baryon-like acoustic oscillations occurred in the early universe.
Proposed modeling suggests that dark matter baryon-like acoustic oscillations contributed (along with ordinary matter baryon acoustic oscillations) to the formation of laments.

Amounts of clumping for large clumps of ordinary matter gas and of dark matter
Reference [33] discusses observations that point to the notion that clumping of matter -ordinary matter gas and dark matter -might be less than ongoing modeling models suggest. The article alludes to a dozen observational studies and points to three papers -reference [34], reference [35], and communication 124a. For example, the last one of the three references studies distortions regarding images of galaxies.
The work studies amounts of clumping of -for example -dark matter along the path that the observed light took. Clumps would be -to use wording from reference [33] -too thin. (Reference [33] suggests a result of too thin by about ten percent. This essay does not explore the topic of quantifying such thinness.) A distribution of galaxies would be -to use wording from reference [36] -too smooth. The reference suggests a notion of ten percent more evenly spread than ongoing modeling predicts.
Proposed modeling suggests that such eects might correlate with the notion that 4(2)G48 repels more stu than would 4(1)G48. (See table 102.) Early formation of clumps correlates with 4(1)G246 attraction. Early clumps correlate with single isomers. Eects of 4(2)G48 repulsion would dilute matter around early clumps more than would eects that ongoing modeling might correlate with, in eect, 4(1)G48 repulsion. Eects of dilution might carry into the times for which 4(6)G4 attraction dominates and leads to the clumps to which observations pertain.

Galaxy clusters -ratios of dark matter to ordinary matter
Regarding some galaxy clusters, people report inferred ratios of dark matter amounts to ordinary matter amounts.
References [37] and [38] report ratios of ve-plus to one. The observations have bases in gravitational lensing. Reference [39] reports, for so-called massive galaxy clusters, a ratio of roughly 5.7 to one.
(Perhaps, note reference [40].) The observations have bases in X-ray emissions.
Proposed modeling is not incompatible with these galaxy cluster centric ratios. Either one of PR6ISP modeling and PR36ISP modeling can pertain.
Reference [41] suggests a formula that correlates -across 64 galaxy clusters -dark matter mass, hot gas baryonic mass (or, essentially, ordinary matter mass), and two radii from the centers of each galaxy cluster. The reference suggests that the formula supports the notion of a correlation between dark matter and baryons. This essay de-emphasizes discussing the extent to which proposed modeling comports with this formula. Proposed modeling might suggest a correlation, based on proposed similarities between most dark matter and ordinary matter.

Galaxy clusters -an explanation for aspects of the Bullet Cluster
We consider either PR6ISP modeling or PR36ISP modeling. For each case, there are ve dark matter isomers and one ordinary matter isomer.
Possibly, the evolution of each one of the six isomers paralleled the evolution of each of the other ve isomers.
Such parallel evolution might lead to diculties regarding explaining observations regarding the socalled Bullet Cluster.
People use the two-word term Bullet Cluster to refer, specically, to one of two galaxy clusters that collided and, generally, to the pair of galaxy clusters. The clusters are now moving away from each other. Ongoing modeling makes the following interpretations based on observations. For each of the two clusters, dark matter continues to move along trajectories generally consistent with just gravitational interactions. For each of the two clusters, stars move along trajectories generally consistent with just gravitational interactions. For each of the two clusters, (ordinary matter) gas somewhat generally moves along with the cluster, but generally lags behind the other two components (dark matter and stars).
Regarding such gas, people use the acronym IGM and the two-word term intergalactic medium. Ongoing If each of the six dark matter or ordinary matter isomers evolved similarly, there might be problems regarding explaining aspects of the Bullet Cluster. One might expect that, in each galaxy cluster, more (than the observed amount of ) dark matter would lag. The lag would occur because of one-isomer 2Gmediated interactions within each of the ve dark matter isomers. Possibly, for each dark matter isomer, there would not be enough star-related stu to explain the amount of dark matter that is not lagging.
Possibly, there would not be enough 1R⊗2U dark matter to signicantly help regarding explaining the amount of dark matter that is not lagging.
We assume that four dark matter isomers correlate with proposed modeling notions of cool dark matter and that one dark matter isomer exhibits behavior similar to behavior that ordinary matter exhibits. (See discussion related to table 98 and see table 100.) Proposed modeling suggests that, for each of the two galaxy clusters, essentially all the stu correlating with isomers one, two, four, and ve would pass through the collision with just gravitational interactions having signicance. For isomer three, incoming 1R⊗2U would pass through. For isomer zero, incoming • Much of the stu correlating with ordinary matter stars passes through with just gravitational interactions having signicance.
• No more than somewhat less than 20 percent of dark matter interacts with dark matter and slows down. (For each galaxy cluster, this dark matter correlates with the IGM correlating with isomer three.) • At least 80 percent of dark matter passes through with just gravitational interactions having signicance.
• Essentially all of the incoming 1R⊗2U passes through the collision with just gravitational interactions having signicance.
1R⊗2U (which measures as dark matter) would pass through. Thus, at least 80 percent of the incoming dark matter would pass through the collision with just gravitational interactions having signicance. Table 104 lists aspects regarding a collision between two galaxy clusters. Here, we assume that each of the two galaxy clusters has not undergone earlier collisions. Here, we assume that case S pertains.
(See table 100.) We suggest that these proposed modeling notions might comport with various possible ndings about IGM after a collision such as the Bullet Cluster collision. The ndings might point to variations regarding the fractions of IGM that, in eect, stay with outgoing galaxy clusters and the fractions of IGM that, in eect, detach from outgoing galaxy clusters.
We discuss possible aspects regarding an outgoing galaxy cluster.
Suppose that, before a collision, ordinary matter IGM comprised much of the ordinary matter in the galaxy cluster. Suppose that, because of the collision, the galaxy cluster has a signicant net loss of ordinary matter IGM. After the collision, the galaxy cluster could have a (perhaps somewhat arbitrarily) large ratio of amount of dark matter to amount of ordinary matter.
To the extent that IGM detaches from galaxy clusters after the galaxy clusters collide, the detached IGM might form one or more objects. Some such objects might have roughly equal amounts of dark matter and ordinary matter. The dark matter would correlate with isomer three.

Galaxies -formation
We discuss galaxy formation scenarios.
We assume that nature comports with at least one of PR6ISP modeling and PR36ISP modeling.
(Neither ongoing modeling nor PR1ISP modeling includes the notion of more than one dark matter isomer. Regarding each of ongoing modeling and PR1ISP modeling, we think that it would be, at best, dicult to explain -based on for example 1R⊗2U dark matter -ratios, that observations suggest, of dark matter amounts to ordinary matter amounts.) For now, we de-emphasize some phenomena such as collisions between galaxies.
We anticipate that such galaxy formation and evolution scenarios will explain galaxy centric data that table 95 shows.
Models for galaxy formation and evolution might take into account the following factors -one-isomer repulsion (which correlates with the 4G2468a and 4G2468b solutions), one-isomer attraction (which correlates with 4G246), two-isomer repulsion (which correlates with 4G48), six-isomer attraction (which correlates with 4G4), dissimilarities between isomers, the compositions of laments and galaxy clusters, statistical variations in densities of stu, and collisions between galaxies. Modeling might feature a notion of a multicomponent uid with varying concentrations of gas-like or dust-like components and of objects (such as stars, black holes, galaxies, and galaxy clusters) for which formation correlates signicantly with six-isomer (or 4G4) attraction.
We focus on early-stage galaxy formation and evolution. For purposes of this discussion, we assume that we can de-emphasize collisions between galaxies. We suggest the two-word term untouched galaxy for a galaxy that does not collide, before and during the time relevant to observations, with other galaxies.
We emphasize formation scenarios and evolution scenarios for untouched galaxies. (Communication 124b and communication 124c discuss data that pertains regarding a time range from about one billion years • Early on, stu correlating with each one of the six isomers expands, essentially independently from the stu correlating with other isomers, based on repulsion correlating with 4(1)G2468a and 4(1)G2468b.
• Then, each isomer starts to clump, essentially independently from the other isomers, based on attraction correlating with 4(1)G246.
• With respect to clumps correlating with any one isomer, 4(2)G48 repels one other isomer and repels some stu correlating with the rst-mentioned isomer.
• A galaxy forms based on a clump that contains mostly the featured isomer.
• The galaxy attracts and accrues, via 4(6)G4 attraction, stu correlating with the four isomers that the featured isomer does not repel. The galaxy can contain small amounts of stu correlating with the isomer that the featured isomer repels.
after the Big Bang to about 1.5 billion years after the Big Bang. Observations suggest that, out of a sample of more than 100 galaxies or galaxy-like rotating disks of material, about 15 percent of the objects might have been untouched.) We assume that dierences -in early evolution -regarding the various isomers do not lead, for the present discussion, to adequately signicant dierences -regarding 4G interactions and galaxy formation -between isomers. (We think that this assumption can be adequately useful, even given results that We organize this discussion based on the isomer or isomers that originally clump based, respectively, on 4G246 attraction or on 4G246 attraction and 4G4 attraction. Each one of some galaxies correlates with an original clump that correlates with just one isomer. Multi-isomer original clumps are possible.
Because of 4G48 repulsion, an upper limit on the number of isomers that an original clump features might be three. Table 105 discusses a scenario for the formation and evolution of a galaxy for which the original clump contains essentially just one isomer. Regarding this isomer, we use the word featured. We assume that PR6ISP modeling pertains. We assume that stu that will become the galaxy is always in somewhat proximity with itself. We assume that no collisions between would-be galaxies or between galaxies occur. 5.3.14. Galaxies -ratios of dark matter stu to ordinary matter stu We continue to explore the realm of one-isomer clumps.
One of two cases pertains. For so-called case A, one isomer of 4G48 spans (or connects) isomers zero and three. (Regarding numbering for isomers, see n in table 100.) For so-called case B, one isomer of 4G48 spans isomer zero and one isomer out of isomers one, two, four, and ve. The existence of many spiral galaxies might point to the notion that case A pertains. (Compare the rightmost column in table   106a and the rightmost column in table 106b.) However, we consider the possibility that people might not know of data or current modeling that would adequately point to the one of case A and case B that pertains. We discuss both cases. occurs early on. The notation DMA:OMA=1:0 + denotes the notion that the ratio of OMA to DMA might be arbitrarily small. The notion of three or four DM isomers in a halo refers to the notion that one or zero (respectively) of the DM isomers in the halo is the featured isomer. We de-emphasize some aspects regarding 1R⊗2U hadron-like particles. Table 106 reects at least two assumptions. Each core clump features one isomer. Each galaxy does not collide with other galaxies. Yet, data of which we know and discussion below seem to indicate that ratios that table 106 features pertain somewhat broadly. We think that galaxies that have core clumps that feature more than one isomer are more likely to appear as elliptical galaxies (and not as spiral galaxies) than are galaxies that have core clumps that feature only one isomer. Such likelihood can correlate with starting as being elliptical. Such likelihood can correlate with earlier transitions from spiral to elliptical. We explore the extent to which the galaxy formation scenario comports with observations.
Observations regarding stars and galaxies tend to have bases in ordinary matter isomer 2G phenomena (or, readily observable electromagnetism). (The previous sentence de-emphasizes some observationsregarding collisions between black holes or neutron stars -that have bases in 4G phenomena.) People report ratios of amounts of dark matter to amounts of ordinary matter.
We discuss observations correlating with early in the era of galaxy formation. Table 95 comports with these results. We suggest that visible early galaxies correlate with generalization of label-A0 or with generalization of label-B0. (See table 106.) Label-A3 or label-B3 evolves similarly to label-A0 or label-B0, but is not adequately visible early on.
Reference [42] provides data about early stage galaxies. (See, for example, gure 7 in reference [42]. The gure provides two graphs. Key concepts include redshift, stellar mass, peak halo mass, and a stellar -peak halo mass ratio.) Data correlating with redshifts of at least seven suggests that some galaxies accrue, over time, dark matter, with the original fractions of dark matter being small. Use of reference [43] suggests that redshifts of at least seven pertain to times ending about 770 million years after the Big Bang.
Reference [44] reports zero-plus to one ratios. The observations have bases in the velocities of stars within galaxies and correlate with the three-word term galaxy rotation curves. Proposed modeling suggests that the above galaxy evolution scenario comports with this data.
We discuss observations correlating with later times. This example features spiral galaxies. Label-A0 suggests a correlation with spiral galaxies. Each other label -pertaining to case A or to case B -either correlates with dark matter galaxies or might suggest a correlation with -at least statistically -evolution into elliptical galaxies. See table 106.) To the extent that such an MED09 galaxy models as being nearly untouched, proposed modeling oers the following possibility. The galaxy began based on a one isomer clump. The clump might have featured the ordinary matter isomer. The clump might have featured a dark matter isomer that does not repel ordinary matter. Over time, the galaxy accrued stu correlating with the isomers that the original clump did not repel. Accrual led to a ratio of approximately four to one.
To the extent that such an MED09 galaxy models as not being untouched, proposed modeling oers the following possibility. One type of collision merges colliding galaxies. One type of collision features galaxies that separate after exchanging material. For either type of collision, incoming galaxies having approximately four times as much dark matter as ordinary matter might produce outgoing galaxies having approximately four times as much dark matter as ordinary matter.
Reference [47] [48].) The observations have bases in light emitted by visible stars. This case correlates with the three-word term dark matter galaxy.
We suggest that label-A3 or label-BP might pertain. (See table 106.) The following notions pertain regarding other data of which we know. Here, the ratios are ratios of dark matter amounts to ordinary matter amounts. Table 95 seems to comport with these results. (See table   106.) Reference [49] discusses six baryon-dominated ultra-diuse galaxies that seem to lack dark matter, at least to the radius studied by gas kinematics via observations of light with a wavelength of 21 centimeters. These observations seem not to be incompatible with the early stages of label-A0 or label-B0.
Reference [50] discusses 19 dwarf galaxies that lack having much dark matter, from their centers to beyond radii for which ongoing modeling suggests that dark matter should dominate. These observations measure r-band light that the galaxies emitted. These observations seem not to be incompatible with the early stages of label-A0 or label-B0.
People report two disparate results regarding the galaxy NGC1052-DF2. Proposed modeling seems to be able to explain either ratio. Proposed modeling might not necessarily explain ratios that would lie between the two reported ratios.
Reference [51] suggests a ratio of much less than one to one. The observation has bases in the velocities of stars -or, galaxy rotation curves. This observation seems not to be incompatible with the early stages of label-A0 or label-B0.
Reference [52] suggests that at least 75 percent of the stu within the half mass radius is dark matter. This ratio seems similar to ratios that reference [45] discusses regarding some MED09 galaxies. (See discussion above regarding MED09 galaxies.) We suggest that each label -other than label-A3 or label-BP -that table 106 shows can pertain.
The galaxy NGC1052-DF4 might correlate with a ratio of much less than one to one. (See reference [53].) The observation has bases in the velocities of stars -or, galaxy rotation curves. This observation seems not to be incompatible with the early stages of label-A0 or label-B0. People report other data. Table 95 and table 106 seem not to be incompatible with these results. We are uncertain as to the extents to which proposed modeling provides insight that ongoing modeling does not provide.
One example features a rotating disk galaxy, for which observations pertain to the state of the galaxy about 1.5 billion years after the Big Bang. (See reference [56].) People deduce that the galaxy originally featured dark matter and that the galaxy attracted ordinary matter.
One example features so-called massive early-type strong gravitation lens galaxies. (See reference [57].) Results suggest, for matter within one so-called eective radius, a minimum ratio of dark matter to dark matter plus ordinary matter of about 0.38. Assuming, for example, that measurements correlating with material within larger radii would yield larger ratios, these observational results might support the notion that the galaxies accumulated dark matter over time.
One example pertains to early stages of galaxies that are not visible at visible light wavelengths.
(See reference [58].) Observations feature sub-millimeter wavelength light. We might assume that proposed modeling galaxy formation scenarios comport with such galaxies. We are not certain about the extent to which proposed modeling might provide insight regarding subtleties, such as regarding star formation rates, correlating with this example.
We are uncertain as to the extent to which proposed modeling might provide insight regarding possible inconsistencies -regarding numbers of observed early stage galaxies and numbers of later stage galaxies -that correlate with various observations and models. (For a discussion of some possible inconsistencies, see reference [59].) We are uncertain as to the extent to which proposed modeling might provide insight regarding the existence of two types -born and tidal -of ultra-diuse galaxies. (See reference [60].) Observations that we discuss above indicate that some galaxies do not exhibit dark matter halos. Proposed modeling that we discuss above comports with the notion that some galaxies do not exhibit dark matter halos.

Aspects regarding some components of galaxies
We discuss eects, within galaxies, that might correlate with dark matter.
Reference [61] reports, based on a study of 11 galaxy clusters, more instances of more gravitational lensing -likely correlating with clumps of dark matter that correlate with individual galaxies -than ongoing modeling simulations predict. (Perhaps, see reference [62].) Reference [62] suggests that the number of instances -13 -compares with an expected number of about one. We suggest the possibility that the clumps might be dark matter galaxies. (See, for example, table 106.) Perhaps some of the dark matter galaxies are dwarf dark matter galaxies. We suggest the possibility that galaxies with signicant amounts of ordinary matter gravitationally captured (or at least attracted) such dark matter clumps.
People study globular cluster systems within ultra-diuse galaxies. Regarding 85 globular cluster systems in ultra-diuse galaxies in the Coma cluster of galaxies, reference [63] suggests that 65 percent of the ultra-diuse galaxies are more massive than people might expect based on ongoing modeling relationships, for so-called normal galaxies, between stellar mass and halo mass. We are uncertain as to the extent to which proposed modeling might explain this result. For example, proposed modeling might suggest that phenomena related to isomers might play a role. (See, for example, table 106.) Higher-mass galaxies might tend to feature more dark matter isomers (or tend to feature more material that correlates with such isomers) than do lower-mass galaxies.
Discussion related to For one example, data regarding the stellar stream GD-1 suggests eects of an object of 10 6 to 10 8 solar masses. (See reference [67].) Researchers tried to identify and did not identify an ordinary matter object that might have caused the eects. The object might be a clump of dark matter. (See reference [68].) Proposed modeling oers the possibility that the object is an originally dark matter centric clump of stu.
For other examples, people report inhomogeneities regarding Milky Way dark matter. (See references [68] and [69].) Researchers note that simulations suggest that such dark matter may have velocities similar to velocities of nearby ordinary matter stars. We suggest that these notions are not incompatible with proposed modeling notions of the existence of dark matter stars that would be similar to ordinary matter stars.

High-mass neutron stars
We discuss proposed modeling that might explain some aspects regarding high-mass neutron stars.
The following results have bases in observations. An approximate minimal mass for a neutron star might be 1.1M . (See reference [70].) The symbol M denotes the mass of the sun. An approximate maximum mass for a neutron star might be 2.2M . (See references [71] and [72].) Some ongoing modeling models suggest a maximum neutron star mass of about 1.5M . (See reference [72].) Observations correlate with most known neutron star pairs having masses in the range that equation We discuss possible bases for high-mass neutron stars.
The PR6ISP span of 4G4 is six.
Some high-mass neutron stars might, in eect, result from mergers of neutron stars, with each merging neutron star correlating with an isomer that diers from the isomer pertaining to each other neutron star that forms part of the merger.

Dark energy density
We explore possible explanations for non-zero dark energy density.
Equation (172) shows an inferred ratio of present density of the universe of dark energy to present density of the universe of dark matter plus ordinary matter plus (ordinary matter) photons. (Reference [13] provides the four items of data.) We know of no inferences that would not comport with a somewhat steady increase, regarding the inferred ratio correlating with equation (172)  6. Discussion: core ongoing modeling and core proposed modeling This unit discusses possibilities for adding aspects of core proposed modeling to core ongoing modeling.

The elementary particle Standard Model
We explore synergies between proposed modeling and the elementary particle Standard Model.

Concordance cosmology
We discuss aspects that people might want to add to concordance cosmology.
We note aspects that discussion elsewhere in this essay de-emphasizes.
Early in the evolution of the universe, quarks, arcs, and gluons might have formed hadron-like seas. The seas might have undergone phase changes, with the last changes featuring at least one transition from seas to hadron-like particles.
Scenarios regarding clumping suggest that a signicant fraction of early black holes contained stu correlating with essentially just one isomer. Regarding PR6ISP modeling, approximately one-sixth of such one-isomer black holes features ordinary matter and approximately ve-sixths of such oneisomer black holes features dark matter.
Proposed modeling is not necessarily incompatible with an ongoing modeling notion of possible large-scale atness for the universe.

Large-scale physics
Ongoing modeling concepts that people use to try to model observed changes in the rate of expansion of the universe include the Hubble parameter (or, Hubble constant), equations of state (or, relationships between -at least -density and pressure), and general relativity.
While general relativity comports with various phenomena, people discuss possible problems regarding the applicability of general relativity to large-scale physics. (See, for example, reference [77].) People suggest possible incompatibilities between observations and ongoing modeling models. (See, for example, reference [78], reference [79], reference [80], reference [36], and communication 124e. However, some people note possible objections to some notions of incompatibility. See, for example, references [81] and [82].) People suggest phenomenological remedies regarding the modeling. (See, for example, reference [83].) Proposed modeling oers possible insight and resolution regarding such concerns.
We consider modeling that might pertain to large-scale phenomena for other than the very early universe. We assume that general relativity pertains regarding PR1ISP modeling, including 4G aspects of PR1ISP modeling.
We consider the case of PR6ISP modeling. We assume that galaxy clusters tend to have equal amounts of stu correlating with each of the six isomers.
We consider modeling that includes both the multi-billion-year era of decreasing rate of expansion of the universe and the current multi-billion-year era of increasing rate of expansion of the universe. The 4G246 attractive component of 4G has a span of one isomer. The 4G48 repulsive component of 4G has a span of two isomers. Tuning a model to the era of decreasing rate might produce a model that underestimates repulsive eects that lead to the increasing rate that correlates with the current era.
We generalize. Regarding the large-scale universe and motions of objects, one might need to limit applications of equations of state and general relativity to motions of objects that modeling can treat as having a span of six and as having roughly equal amounts of stu correlating with each isomer.
We explore a possible concern regarding smaller objects.
We consider modeling regarding black holes and neutron stars. To the extent that a black hole or neutron star includes signicant amounts of material correlating with each of at least two isomers, modeling -based on general relativity -for gravitational eects regarding high-outow phenomena might be less than adequately accurate. Inaccuracy might occur, for example, to the extent that the outow material does not interact via 4G48 with an isomer for which the black hole or neutron star has a signicant amount. People observe high-outow phenomena related to -for example -quasars, blazars, and pulsars.
We consider the case of PR36ISP modeling.
Six isomers of 4(6)G4 pertain. General relativity might pertain somewhat for each of the six PR6ISPlike isomers. The concept of geodesic motion would not pertain across PR6ISP-like isomers.

Quantum electrodynamics regarding positronium
Reference [11] reports a discrepancy between the observed energy correlating with one type of nestructure transition in positronium and a prediction based on core ongoing modeling. (See discussion regarding equation (84).) Proposed modeling suggests the discrepancy correlates with a limit to the applicability of current core ongoing modeling. Table 70 [13] provides data regarding hadron masses.) The rest energies of 1R⊗2U hadron-like particles that contain exactly two arcs might approximate the rest energy of the zero-charge pion, which is about 135 MeV.
We explore another concept for estimating masses for 1R⊗2U hadron-like particles. The concept has bases in the relative densities of the universe of 1Q⊗2U hadrons and 1R⊗2U hadron-like particles.
Nature might have created concurrently, essentially, the current populations of 1Q⊗2U hadrons and 1R⊗2U hadron-like particles. We assume that each of 1Q⊗2U hadrons and 1R⊗2U hadron-like particles consists mainly of three-fermion particles.
Equation (174) might estimate the current relevant ratio of density of 1R⊗2U hadron-like particles to density of ordinary matter. (Regarding the symbol Ω 1R2U,0 and the ratio Ω 1R2U,0 /Ω b ∼ 0.055, see discussion related to equation (154).) The symbol m _ denotes the rest mass of a typical hadron-like particle. The leftmost use of the ratio m 1R⊗2U /m 1Q⊗2U correlates with rest energy (or rest mass) per particle. The rightmost use of the ratio m 1R⊗2U /m 1Q⊗2U occurs as the input to a calculation of an exponential and correlates with a hypothesis regarding the relative numbers of particles that nature created.
Two mathematical solutions exist. The respective solutions, expressed in terms of m_c 2 and in units of GeV are ∼ 0.06 and ∼ 4. 6.6. Relationships between core proposed modeling and core ongoing modeling We develop -elsewhere -some aspects of core proposed modeling in a manner that does not necessarily correlate with core ongoing modeling. However, the core proposed modeling list of suggested elementary particles might not necessarily be independent of core ongoing modeling, which tends to feature laws of motion. Table 109 notes instances in which core proposed modeling PFS models might seem to depend onor at least might seem to reect -aspects of core ongoing modeling KMS models. 7. Discussion: unveried ongoing modeling and core proposed modeling This unit discusses possibilities that core proposed modeling provides insight regarding unveried aspects of ongoing modeling. Table 23

String theory
We discuss the notion that aspects of proposed modeling might help people explore the relevance of string theory to elementary particle physics.
We suggest perspective about string theory and about proposed modeling.

Theory of everything
We speculate that proposed modeling points toward possibilities for a superset of a so-called theory of everything.
People discuss the notion of modeling that would describe much of fundamental physics. Within this context, people use the three-word term theory of everything to allude to modeling that would unify quantum mechanics and general relativity. People use the one-element term ToE to abbreviate the three-word phrase theory of everything.
We suggest that such a use of the term ToE might correlate with overlooking key aspects of nature.
In the context of proposed modeling and ongoing modeling, that use of the term ToE might correlate with a notion of a unied modeling of motion and might overlook the topic of objects that move.  • Modeling that unies the aspects above.
People characterize some ongoing modeling candidates for a ToE by (mathematical) groups with which the candidates correlate.
We discuss the possibility that people can nd a group theoretic statement that correlates with the superset. We structure this discussion based on the rows in table 110.
We suggest that the properties portion of our work might correlate with the group SU (17). Table 111 illustrates the notion that table 58 correlates with the group SU (17) and with six applications of equation (47). This essay does not speculate regarding possibilities for detecting phenomena that would correlate with PR216ISP but not with PR36ISP. Notions above may suce to embrace much modeling of motion -including classical physics models and quantum physics models -that comports with six isomers of all elementary particles except Gfamily elementary particles, conservation of energy, conservation of momentum, and conservation of angular momentum. (Regarding six isomers of simple particles, see table 111a. The notion of six isomers of simple particles correlates with the notion that one might need to limit the range of applicability of modeling based on general relativity.) Notions above include quantum gravity -as an aspect of core proposed modeling PFS modeling and with independence from classical models (including general relativity) regarding motion. Classical modeling regarding motion correlates with ongoing modeling KMS modeling.
Beyond notions above, we are uncertain as to the extent to which people might want to add group theoretic concepts related to specic modeling regarding motion. (For example, people might treat Newtonian physics as comporting with special relativity in the limit of small velocities. If so, people might not want to add group theoretic concepts related to Newtonian physics.) Notions above might suce for people to state a group theoretic expression that correlates with the superset.

The strong CP problem
We discuss insight, that proposed modeling might provide, regarding the strong CP problem.
Ongoing modeling explores the possibility that the strong interaction contributes to violation of CP symmetry (or, charge conjugation parity symmetry). People might have yet to detect strong interaction contributions to the violation of CP symmetry. People use the three-element term strong CP problem.
Unveried ongoing modeling suggests that such violation might correlate with the existence of axions.  • PRι I ISP modeling might -for each of ι I = 1, ι I = 6, and ι I = 36 -correlate with use of log 6 (ι I ) uses of the SU (2) × U (1) symmetries.
• To the extent that PR36ISP is not relevant to physics, an overall SU (15) symmetry might suce.    • As successful or more successful regarding describing allowed states.
• As successful or less successful regarding estimating -based on limited use of observed dataenergies for allowed states.
• Easier or simpler -when applicable -to use.
• Based on more rigorous use of mathematics. Discussion above in this essay features proposed modeling suggestions regarding elementary particles and dark matter particles, plus ongoing modeling models regarding motion. We generally assume that the PEPM particle set and ongoing modeling models for motion are adequately compatible with each other. We generally assume that the PEPM particle set and ongoing modeling models for motion are adequate for modeling relevant aspects of nature.
Discussion herein speculates about proposed modeling that would have bases in core proposed modeling models and would pertain directly to motion. This work generalizes from work above that, nominally, pertains for simple particles. Equations (53) and (54) pertain regarding all simple particles and all root forces. We posit that results -regarding some  (180) shows.

Supplementary proposed modeling dynamics models re multicomponent objects
We discuss the possibility that CQFM extends to include interactions involving objects that are not elementary particles.
For proposed modeling models of interactions that involve simple particles and root forces in free environments, the KMS PDE notion of the mathematical limit expression (η SA ) 2 → 0 pertains. (See discussion related to equation (13).) Here, (η T A ) 2 → 0 pertains. We say that the vertex models as being Angular momentum times length Energy times square of time point-like with respect to KMS coordinates. Here, point-like refers to the temporal coordinate and refers to either a radial spatial coordinate or three spatial coordinates.
An example of modeling of interactions that involve simple particles in so-called conned environments might feature modeling regarding interactions with a quark that exists within a proton.
For proposed modeling models of interactions that involve simple particles and root forces in conned environments, the PDE notion of (η SA ) 2 > 0 can pertain. The expression that equation (181) shows might correlate with the size of the multicomponent object that correlates with the term conned environment.
We say that the vertex models as being volume-like with respect to coordinates. Here, volume-like refers to, at least, either a radial spatial coordinate or three spatial coordinates. Volume-like correlates also with a non-point-like domain for the temporal coordinate.  Table 116 notes aspects of PDE mathematics that can pertain for dynamics modeling and ν SA ≥ 0.
In table 116, the associations that the rst row shows provide a basis for the remaining rows. The row that notes ξ SA (η SA ) +2 might point to a series -momentum, angular momentum, and angular momentum times length.
PDE-based modeling might correlate with some aspects of unication of the strong, electromagnetic, and weak interactions. We consider modeling for which 2ν SA is a non-negative integer. Based on the r −2 spatial factor, the V −2 term might correlate with the square of an electrostatic potential. (See table 8.) Based on the r 2 spatial factor, the V +2 term might correlate (at least, within hadrons) with the square of a potential correlating with the strong interaction. The sum K 0a + K 0b might correlate with the strength of the weak interaction. (The eective range of the weak interaction is much smaller than the size of a hadron. Perhaps, the spatial characterization r 0 correlates with an approximately even distribution, throughout a hadron, for the possibility of a weak interaction occurring.) Based on the V −2 term, we expect that ξ SA includes a factor 2 .
Electrostatics includes each of interactions that attract objects to each other and interactions that repel objects from each other. One might consider the possibility that, in some modeling, the term proportional to Ω SA /r 2 might seem to allow for repulsion, but not for attraction. (See equations (3) and (4). The term correlates with a contribution that is proportional to +r −2 . The potential decreases as r increases.) However, when equations (31), (182), and (183) pertain, one can swap the Ω SA /r 2 term and the Ω T A /t 2 term in equation (31). The swap leads, in eect, to a new Ω SA /r 2 that has a sign that is opposite to the sign correlating with the old Ω SA /r 2 . The new Ω SA /r 2 would correlate with attraction.
We anticipate exploring notions correlating with the third and fourth rows in table 30.

Dynamics models for hadron-like particles
We discuss various topics regarding hadron-like particles.
We discuss the notion that each hadron-like particle that includes no more than three quarks (or, 1Q particles) and arcs (or, 1R particles) does not include both quarks and arcs.
Discussion related to table 49 suggests that a hadron-like particle has a charge for which the magnitude is either zero or a non-zero integer multiple of |q | and has a baryon number that is either zero or a nonzero integer multiple of one. For a hadron-like particle that includes no more than three quarks and arcs, the restrictions to integer charge and integer baryon number preclude the simultaneous presence of more than zero quarks and more than zero arcs.
We discuss modeling for dynamics in hadrons that contain no more than three quarks.
Ongoing modeling QCD (or, quantum chromodynamics) modeling correlates with symmetries, for each of quarks and gluons, that correlate with special relativity.
We explore the notion that proposed modeling suggests possibilities for modeling that correlates, with each of quarks and gluons, a less than full set of symmetries correlating with special relativity.
Modeling for a free hadron requires two TA-side SU (5) symmetries and four SA-side SU (2) symmetries. (See discussion -regarding combining two objects to form one free object -related to table 60. There, we assume that the original two objects are objects that can model as being free objects. Here, we do not assume that the original objects necessarily can model as being free. Here, we retain the notions of a set of kinematics symmetries for the motion of a combined object and a set of dynamics symmetries for internal aspects of the same combined object.) Proposed modeling suggests that each one of bosons (within the hadron) and simple fermions (within the hadron) can contribute one TA-side SU (5) symmetry and two SA-side SU (2) symmetries. One TA-side SU (5) symmetry and two SA-side SU (2) symmetries correlate with modeling for the free hadron. The other TA-side SU (5) symmetry correlates with modeling for dynamics regarding internal aspects of the hadron. For each one of bosons and simple fermions, modeling might correlate with just one SA-side SU (2) symmetry.
This proposed modeling dynamics modeling correlates with the notion that neither one of quarks and gluons behaves like free simple particles. Proposed modeling suggests that a hadron-like particle must include at least two (non-virtual) unfree fermions. (The notion of virtual correlates with ongoing modeling. Core proposed modeling can work in conjunction with modeling that includes the notion of virtual fermions and in conjunction with modeling that does not include the notion of virtual fermions.) We discuss notions that might correlate with modeling that might output masses for hadrons.
References [86] and [87] suggest opportunities to improve understanding regarding modeling that might explain the masses of hadrons such as protons. Proposed modeling suggests concepts that might help regarding such opportunities. One concept correlates with avoiding relying on modeling that correlates with special relativity. (See discussion nearby above.) One concept correlates with equations (3) and (4) and with D = 3. Here, the term that is proportional to r 2 might correlate with the square of a potential. For a two-quark hadron, the potential associated with one quark aects the other quark. For a three-quark hadron, the potential associated with two quarks aects the third quark.
We discuss modeling for dynamics in hadrons and hadron-like particles that contain more than three quarks.
Reference [88] discusses an observation of tetraquarks that feature four charm quarks, of which two are matter quarks and two are antimatter quarks. The article suggests that people might benet by considering that such tetraquarks might feature two components. Each component would feature a matter charm quark and an antimatter charm quark. Proposed modeling suggests that the pie boson might correlate with the binding to each other of the two components.
Reference [89] suggests that some of the dynamics within at least some pentaquarks correlates with the dynamics for a system composed of a meson-like particle and a baryon-like particle. The meson-like particle features a matter quark and an antimatter quark. The baryon-like particle features three matter quarks. Aspects that proposed modeling correlates with the pie boson might play roles in such dynamics.

Dynamics models for nuclear physics
We discuss possibilities for developing proposed modeling models for atomic nuclei.
Ongoing modeling bases some aspects of modeling on notions of a Pauli exclusion force and on notions of a Yukawa potential. Ongoing modeling correlates these eects with notions of a residual strong force.
The Pauli exclusion force keeps hadrons apart from each other. The Yukawa potential attracts hadrons to each other. Modeling suggests virtual pions as a source for the Yukawa potential.
Reference [90] expresses concerns regarding modeling some aspects of nuclear physics based on the notion of virtual pions. We are uncertain as to the extent to which such models for atomic nuclei would improve on ongoing modeling techniques.

Dynamics models for atomic physics
We discuss possibilities for developing proposed modeling models for atomic physics.
Regarding some atomic physics, people might want to explore using modeling that correlates with equations (187) [13].) The subscripts , µ, and τ denote, respectively, electron, muon, and tauon. The symbol a correlates with anomalous magnetic dipole moment. The symbol α denotes the ne-structure constant. (See equation (109).) a − (α/(2π)) ≈ −1.76 × 10 −6 (190) a µ − (α/(2π)) ≈ +4.51 × 10 −6 (191) −0.052 < a τ < +0.013 (192) Ongoing modeling provides means, correlating with Feynman diagrams, to calculate an anomalous magnetic dipole moment for each of, at least, the electron and the muon. The ongoing modeling Standard Model suggests computations whereby the anomalous magnetic dipole moment for a charged lepton is a sum of terms. The rst term is α/(2π). The second term is proportional to α 2 . The third term is proportional to α 3 . The exponent associated with α correlates with a number of virtual photons.
Regarding the tauon, equation (193)  We explore the possibility that proposed modeling suggests that contributions to a scale as α (Σ−2)/2 .
We try to estimate a τ . We assume that the 4G26 solution correlates with the ongoing modeling result of α/(2π). We assume that the 6G24 solution correlates with contributions of the order α 2 .
We assume that, for a charged lepton cl, equation (194) pertains. Here, t cl is the construct that the rst column of table 117 identies.
a cl − (α/(2π)) ≈ a 6G24,1 + a 6G24,t t cl (194) Table 117 shows approximate possible values for a 6G24,1 and a 6G24,t , based on tting data that equations (190) and (191) show and based on using various candidates for t cl . We de-emphasize the notion that 8G26 might also contribute to an actual value.   Based on the notion that contributions to a scale as α (Σ−2)/2 and on results that table 117 shows, it might seem unlikely that a 6G24,1 correlates with 8G26. However, it is possible that the strength of interactions correlating with 4G26 diers from the ongoing modeling result that correlates with α/(2π) and that a 6G24,1 correlates with such a dierence.
Given remarks just above, we explore another approach to estimating a τ .
We assume that the strength of each of 4G26 and 8G26 does not change with generation. We assume that, in eect, equation (195)   For this example, the notion of freeable energy correlates with generation.) The exponent of two in the expression (generation) 2 parallels the exponent of two that pertains regarding the factor (q ) 2 in α in the sense that contributions seem to scale as the squares of particle properties.
We think that the second approach illustrates comparisons that table 114 suggests.
We also note that, regarding choices -that table 118 shows -regarding t cl and ignoring the choices of m and m 2 , each of the three quadratic choices -(M ) 2 , (generation) 2 , and (log(m/m )) 2 -might be more appropriate than any of the three linear choices -M , generation, and log(m/m ). This essay de-emphasizes looking for deeper meaning regarding the role of aspects -such as this one regarding table 118 or similar ones regarding equation (133) -that pertain to squares of properties.

Possibilities to complement ongoing modeling classical physics
We explore possibilities that supplementary proposed modeling might oer useful complements to core ongoing modeling classical physics modeling. 8.3.1. Possibilities for using Newtonian modeling in place of general relativity Table 119 lists aspects related to 4GΓ solutions. In the context of PR1ISP modeling, each row (possibly except for the last row) in the table points to a possible correlation with general relativity. For each row, the extent to which the possible correlation pertains might be an open question. People associate the twoelement term Lense-Thirring eect with the two-element term rotational frame-dragging. The Einstein eld equations allow solutions that correlate with repulsion. This essay does not explore the extent to which modeling based on the notion of an RSDF (or, radial spatial dependence of force) of r −6 and on the notion of ρ = 0 might correlate with general relativity modeling for which a non-zero cosmological  • Hone some measurements regarding some known particles.
• Verify or rule out the notion that gravity does not produce the main contributions to neutrino oscillations.
• Verify or rule out the relationship that we suggest regarding the tauon mass and the gravitational constant.
• Verify, hone, or refute relationships, that we suggest, between particle properties and other constants.
• Verify or rule out the description of dark matter that we propose. • Determine properties of dark matter. • Hone, extend, or rule out aspects that we suggest regarding galaxies.
• Determine the extent to which our work regarding dark matter isomers and the Bullet Cluster comports with observations regarding collisions between galaxy clusters.
• Add details -or rule out aspects that we suggest -regarding the cosmological timeline. • Explore, for times after recombination, evolution of density of the universe ratios for inferred (or inferable) dark matter to inferred (or inferable) ordinary matter.
• Explore evolution of density of the universe ratios for inferred (or inferable) dark energy to inferred (or inferable) dark matter plus ordinary matter.
• Explore each of the following topics and relationships between the following topics -the domain of applicability of general relativity; equations relating pressures to densities; the notion and applicability of the concept of a Hubble parameter; notions regarding geodesic motion; and the spans and the strengths of forces correlating with the 4G48, 4G246, 4G2468a, and 4G2468b solutions.
• Determine ranges of usefulness regarding -and test synergies between -various models.
• Predict and try to verify other phenomena that might correlate with proposed modeling. correlate with aspects of translational motion. The three properties correlate respectively with the words monopole, dipole, and quadrupole. The three properties correlate respectively with the terms scalar (or, rank-zero tensor), vector (or, rank-one tensor), and rank-two tensor. The other up to three properties would correlate with motion of the rst three properties. For example, one property would be charge current, which correlates with the notion of moving charge.
Our work might suggest possibilities for yet another example. The previous example features three properties that do not necessarily correlate with translational motion. People might extend the previous example by considering the three-element series -which is related to translational motion -static, moving with an unchanging velocity, and moving with a changing velocity. Here, the notion of moving with a changing velocity might correlate with linear motion and acceleration and might correlate with angular velocity.  Table 120 suggest themes for experiments and observations that people might want to conduct. This essay de-emphasizes the topic of when techniques and technology will suce to enable specic experiments or observations. We de-emphasize the topic of when -for each of various predictions we or other people make based on proposed modeling -falsiability becomes feasible.  • The 0I and 2J particles help explain phenomena that ongoing modeling correlates with terms such as vacuum energy, vacuum uctuations, or quintessence.
• The 0I and 2J particles explain phenomena that ongoing modeling correlates with density of dark energy. (See discussion related to equation (172).) • The 0I and 2J solutions simplify some aspects of modeling (and, regarding such, do not necessarily correlate with nature). 9.1.2. Possibilities for detecting or inferring aye and jay bosons Table 121 lists possible roles for the aye particle and for the 0I solution and for the jay particles and 2J solutions. Each item in table 121a might point to possibilities for detecting or inferring at least one of aye bosons and jay bosons. For example, the item regarding positronium might correlate -regarding jay bosons -with such a detection or inference.
We discuss some items -that table 121a shows -for which we can oer information to which table 121a does not point. Some aspects of ongoing modeling propose interactions that would produce unspecied particles that people might not have detected. For example, people propose an interaction K 0 L → π 0 +X for which there is an intermediate state of two simple fermions that interact via a W boson and produce the so-designated X particle. (See reference [94].) Here, the symbol K 0 L correlates with the K-long meson. The symbol π 0 denotes a zero-charge pion. To the extent that this interaction actually occurs, proposed modeling suggests the possibility that the X particle is an aye boson or a jay boson.
Ongoing modeling proposes concepts such as interactions with a so-called quantum vacuum.
We discuss aspects that table 121b shows. We discuss possibilities for observing dark matter eects without creating dark matter.
We discuss possibilities for inferring the presence of dark matter in seemingly ordinary matter neutron stars.
People might want to consider possibilities for inferring the presence of dark matter content in neutron stars. (See discussion related to equations (170) and (171).) We discuss other possibilities for observing dark matter eects without creating dark matter.
Possibly, people can develop techniques for detecting gravitationally the presence of nearby dark matter.
People attempt to directly detect dark matter. (See, for example, reference [95].) Some eorts look for WIMPs. We are uncertain as to the extent to which these eorts might be able to detect 1R⊗2U hadron-like particles. Some eorts look for axions. We are uncertain as to the extent to which these eorts might attribute axion sightings to eects that correlate with the dierence that equation (199) shows.
Reference [96] discusses two attempts to detect dark matter bosons that would correlate with interactions between neutrons in ordinary matter atomic nuclei and electrons in ordinary matter atoms that include the atomic nuclei. (Reference [96] cites reference [97] as exemplifying experiments regarding isotopes of ytterbium and reference [98] as exemplifying experiments regarding isotopes of calcium.) Proposed modeling suggests that at least one of equation (199) and 2(2)G68 = 2(1)G68 might explain the types of eects that both attempts report.
To the extent that PR6ISP pertains to nature and PR36ISP does not pertain to nature, the following discussion pertains to detecting dark matter. To the extent that PR36ISP pertains to nature, the following discussion pertains to detecting doubly dark matter. The basis for one possibility is the dierence between 2(6)G248 and 2(1)G248. Here, a detector might feature a rotating magnetic dipole moment, with the axis of rotation not matching (and perhaps being orthogonal to) the axis correlating with the magnetic dipole.
(We are uncertain as to the extent that people might want to try to use, in the context of 2(6)G248, detectors based on magnons. See reference [99]. The reference discusses possibilities for detecting light dark matter and not necessarily the types of dark matter that proposed modeling suggests. However, the proposed detection would be via magnetic elds.) Independent of that possible means for detection, people might try to infer 2(6)G248 phenomena correlating with dark matter magnetic elds (or -for the PR36ISP case -2(6)G248 phenomena correlating with doubly dark matter magnetic elds). A basis for another possibility is the dierence between 2(2)G68 and 2(1)G68. Proposed modeling suggests that 2G68 correlates with, at least, some atomic transitions.
We discuss three possibilities for making and detecting dark matter.
Equations (200) For an experiment, the number of conversions might be small. The following notions might correlate with such smallness. The range of the 2T ± boson might be small compared to the size of a neutron. (See discussion related to equation (88).) Eects that ongoing modeling correlates with the two-word term Pauli exclusion might imply that the probability for the original three quarks to be adequately close to each other is low.
We speculate about means for detecting such a conversion of a neutron into a three-arc hadron-like particle. We assume that the neutron resides in an atomic nucleus in a target material. Given the relevant energies, we assume that the three-arc particle exits the target. We speculate that people would not detect the three-arc particle. With one target and enough conversions that do not produce escapes of atomic nuclei, people might detect a change in the isotopic composition of the target. Possibly, an easiest detection would correlate with eects other than those we just mentioned. Such eects might correlate with byproducts of the interactions.
Equations (203), (204), and (205) show interactions that would convert a proton into a dark matter 1R⊗2U hadron-like particle that features three arc (or, 1R) simple fermions. (A proton includes two Q +2 quarks and one Q −1 quark.) The minimum energy to trigger this set of interactions correlates with the sum of the rest energies of one proton and three charged tweaks. A minimum range for that minimum energy is 625 GeV to 640 GeV. (Here, we assume results that equations (98) and (99) show.) Compared with trying to detect the conversion of a neutron into dark matter, the possibility for converting a proton oers advantages and disadvantages. One advantage might be the possibility for detecting the weak interaction that the W +3 boson would catalyze. Another advantage might correlate with an ability to use colliding beams instead of an approach that might feature one beam and a xed target. One disadvantage might be the need to use higher energy for the incoming particles.
Equations (206) and (207) show interactions that would convert a positron and an electron into the fermion components for a 1R⊗2U hadron-like particle that would have some similarity to a neutral pion.
A threshold energy could be about 81 GeV. Detecting the 1R⊗2U particle might prove dicult. To the extent that the preferred decay of the particle features a matter neutrino and an antimatter neutrino, detecting decay products might be possible and prove dicult.
C +3 → R 0 + W +3 People might want to explore possible opportunities -regarding mathematics or modeling -related to the transformation -regarding numbers of dimensions -that correlates with equation (15). We note bases for some possible opportunities. Possibly, people can nd additional signicance regarding the array of numbers for which Some proposed modeling uses of notions of D * SA = 3 and D * T A = 1 include modeling that correlates with ν SA < 0 and that outputs a list of known and possible elementary particles. (See table 30.) As far as we know, ongoing modeling does not include parallels to such aspects of proposed modeling.
Ongoing modeling aspects that correlate with three spatial dimensions and one temporal dimension tend to correlate with proposed modeling aspects for which ν SA ≥ 0 pertains. (See table 30.) Equations (53) and (54) might provide a characterization that can be useful, for much physics modeling, regarding the notions of three spatial dimensions and one temporal dimension. 9.3.2. Arrow of time Equation (184) and discussion related to equation (37) suggest a notion of a Ψ(t, r) that correlates with the TA0-and-SA0 oscillator pair. (See equation (6).) We suggest that equation (208) might pertain.
(Perhaps, see also discussion related to equation (184) and discussion related to equation (186).) The domains t > 0 and r > 0 pertain for Ψ(t, r). Without loss of generality, we posit that η T A > 0 pertains regarding after an interaction, η T A > 0 does not pertain regarding before an interaction, η T A < 0 pertains regarding before an interaction, and η T A < 0 does not pertain regarding after an interaction. We posit that η SA > 0 pertains regarding elementary particles that exit an interaction, η SA > 0 does not pertain regarding elementary particles that enter an interaction, η SA < 0 pertains regarding elementary particles that enter an interaction, and η SA < 0 does not pertain regarding elementary particles that exit an interaction. Of the four possibilities η T A > 0 and η SA > 0, η T A < 0 and η SA < 0, η T A > 0 and η SA < 0, and η T A < 0 and η SA > 0, mathematically, Ψ normalizes for only the rst two possibilities. Ψ(t, r) ∝ exp(−tr/(η T A η SA )) (208) To the extent that this modeling correlates with the topic of arrow of time, the lack of dual normalization regarding each of the case of incoming and the case of outgoing might provide insight.
The proposed modeling notion that aspects of modeling of conservation of energy correlate with an SU (5) symmetry (and not necessarily with an ongoing modeling notion of S1G symmetry) might provide insight regarding the topic of arrow of time. Proposed modeling tends to correlate SU (_) symmetries with origins (with respect to coordinates) and with radial coordinates. We discuss the possibility that proposed modeling provides insight regarding the possible equivalence of inertial mass and passive gravitational mass.
We assume that ongoing modeling Newtonian mechanics pertains. Equation (209) describes the acceleration − → a of an object of inertial mass m in because of a force − → F . Equation (210) describes the force that an object of passive gravitational mass m pg experiences because of an object -of active gravitational mass m ag -that is located a distance − → r from the object correlating with m pg . (To some extent, regarding − → r , we assume that we can model all objects as being point-like.) The three-word term passive gravitational mass refers to a mass that correlates with reactions of an object to externally generated gravitational elds. The three-word term active gravitational mass refers to a mass that correlates with the gravitational eld that correlates with an object (or, that the object generates). Also, r = | − → r |. The notion that modeling based on equation (211) seems to pertain for objects has been a topic of discussion for centuries.
For purposes of this discussion, we posit that one can assume that freeable energy equals zero. (See, for example, tables 58 and 111.) Table 122 shows possible correlations between some types of models and three notions of mass. For some rows in table 122, oscillator pairs of the form XA3-and-XA4 pertain.
Aspects related to table 122 might suggest insight regarding possible equivalences -at least for purposes of modeling -among the three notions of mass. 9.3.4. Notions that might link physics constants and modeling Table 123 shows speculation about possible conations regarding two notions. One notion is the Σ in G-family mathematical solutions ΣGΓ. One notion is quantities (or, properties) with which some Σγ components of G-family forces interact. Each quantity (or, property) might pertain for each of some aspects of classical physics modeling and some aspects of quantum physics modeling. (Compare with   table 66 and table 84.) In table 123, an item in parentheses shows a non-zero magnitude that pertains for modeling that correlates with the notion of free environment. Except for regarding speed, the number is a minimal non-zero magnitude. (For charge, for unfree environments, |q |/3 pertains. For 3LB, for unfree environments, the number one pertains. Except for regarding speed, the numbers are minimal nonzero magnitudes.) Some modeling regarding refraction and eective mass might correlate (via, aspects correlating with longitudinal polarization) with a lack of a minimal non-zero quantity. (See discussion related to equations (78) and (79).) Regarding the case of Σ = 16, there might be a correlation with the notion that modeling might correlate boost symmetry with the oscillator pair SA15-and-SA16. (See discussion that includes discussion of table 60.) Such a correlation might be useful with solutions that allow λ = 16 ∈ Γ.
Some items in table 123 might correlate, in essence, with other physics constants. Charge might correlate with 1/(4πε 0 ) and the vacuum electric permittivity ε 0 . Magnetic ux correlates with |q | and and might correlate with µ 0 , the vacuum magnetic permeability. Mass might correlate with G N , the gravitational constant.
Proposed modeling might suggest opportunities to further explore relationships between charge and mass and relationships between strengths of components of G-family forces. For example, table 83 points to possible relationships between charge and mass. Proposed modeling might suggest another opportunity to explore modeling related to masses. We discuss a possibly useful notion regarding masses of non-zero-mass simple particles. Equations (212) and (213) pertain. The symbol m denotes mass. Boson simple particle masses tend to feature relationships regarding squares of masses. Equation (212) We are uncertain regarding the usefulness of further pursuing notions that we discuss immediately above.

Entropy
We consider cases of multicomponent objects that involve k + 1 peer component objects. Here, k is a nonnegative integer.
We consider the case of k = 1. The multicomponent object includes two peer component objects.
Compared with dynamics symmetries for the multicomponent object, the two peer components collectively contribute one too many instance of each of conservation of energy symmetry, conservation of angular momentum symmetry, and conservation of momentum symmetry. Modeling might re-assign the extra three symmetries to a combination of the two peer components and a eld -such as a gravitational eld -that correlates with interactions between the peer components.
We consider the case of k > 1. Here, we de-emphasize the possibility of stepwise subdivision. An example of stepwise subdivision involves the sun, earth, and moon. For this example of stepwise subdivision, one might use two steps, each correlating with k = 1. The rst step considers each of the sun and the earth plus moon to be objects. The second step considers the earth plus moon to be a multicomponent object consisting of the earth and the moon. Without adequately signicant additions to modeling, this example might correlate with modeling for which -regarding ocean tides -eects of lunar gravity pertain and eects of solar gravity do not pertain.
For k > 1 and no stepwise subdivision, ongoing modeling models become more complex than ongoing modeling models for two-body (or, k = 1) systems. Many applications might pertain -for example, to astrophysical systems, to ideal gasses, and so forth. For some applications, keeping the number of elds at one might correlate with a notion of entropy and, at least within that notion, with the ongoing modeling expression for entropy that equation (215) shows. Here, people might want to consider at least one of the two cases j = k + 1 and j = k. Here, people might want to consider each of a notion of entropy for physical systems and a notion that might correlate, regarding mathematics-based modeling, with a term correlating with the word entropy.
j log(j) (215) 10. Concluding remarks This unit discusses possible opportunities based on proposed modeling.
Proposed modeling might provide impetus for people to tackle broad agendas that our work suggests.
Proposed modeling might provide means to fulll aspects of such agendas. Proposed modeling might fulll aspects of such agendas.
Opportunities might exist to develop more sophisticated modeling than the modeling that we present.
Such a new level of work might provide more insight than we provide.
Proposed modeling might suggest applied mathematics techniques that have uses other than uses that we make.
Proposed modeling might suggest -directly or indirectly -opportunities for observational research, experimental research, development of precision measuring techniques and data analysis techniques, numerical simulations, and theoretical research regarding elementary particle physics, nuclear physics, atomic physics, astrophysics, and cosmology.

Acknowledgments
William Lama provided useful comments regarding the eectiveness of drafts that led to parts of this essay.
The following people pointed, via presentations or writings, to topics or aspects that we considered for inclusion in the scope of the work: Alex Filippenko, Brian Greene, Robert McGehee, Risa Wechsler, and various science journalists.
The following people pointed, via personal contact, to topics or aspects that we considered for inclusion  Table 124 lists communications for which the following two sentences pertain. This essay cites the communications. We did not necessarily nd information sucient to qualify the communications for inclusion in the bibliography.