Dimensional Change And Singularities

Let us initially consider that general Ward-Cauchy-related set of conditions, that are appertaining to spatial dimensionality, that is to be considered for one given arbitrary superstring of discrete energy permittivity -- that is Not in consideration of what is to otherwise be in a directly correlative relationship with the Ward-Cauchy-based conditions of Beti numbers, (to where this is not here to be directly considering what happens, right before and right after each of such iterations of BRST) -- but, instead, to where this is to be taken in a directly correlative relationship with the Ward-Cauchy-based conditions that are here to be during each sequential iteration of BRST -- over an evenly-gauged Hamiltonian eigenmetric.  Let us then say, that for the just mentioned superstring of discrete energy permittiivty, over the course of each iteration of BRST that is here to be correlative to the said evenly-gauged Hamiltonian eigenmetric -- that the here mentioned superstring is to oscillate back-and-forth, from being a two-dimensional spatial entity into being a three-dimensional spatial entity.  Let us next say that the general holomorphic direction of the said string, is here to be maintained -- over the set framework of time.  Since the just so-eluded-to back-and-forth alteration in spatial dimensionality, is here to alter the directoral-related flow of the said string's directly corresponding angular momentum eigenindices -- such a back-and-forth alteration in the directly corresponding dimensions of the spatial parameters of the said string, will then tend to alter the dimensional-related direction of the holonomic substrate of the correlative string in and of itself, at the Poincare level to the topological surface of the directly corresponding superstring of discrete energy permittivity, during each succeeding iteration of BRST for such a said string.  Such an alteration of dimensional-related direction for the holonomic substrate of a discrete quantum of energy, will then tend to work to form the presence of metrical-related Chern-Simons singularities over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Polyakov Action And Chern-Simons Singularities

If an orbifold eigenset is to change in its correlative Lorentz-Four-Contraction, then, it is to change in its Polyakov Action eigenstate in what is here to be of an inverse-based manner.  If an orbifold eigenset is then to alter in its Polyakov Action eigenstate, to any viable scalar amplitude -- such a said orbifold eigenset will then tend to work to bear a set of one or more metrical-based Chern-Simons singularities.  Such a genus in the perturbation of the metrics of an orbifold eigenset, will also as well work to tend to help at causing the directly corresponding superstrings of discrete energy permittivity that work to comprise the said orbifold eigenset, to work to bear metrical-based Chern-Simons singularities -- since all of the superstrings of discrete energy permittivity that work to comprise any one said orbifold eigenset, will tend to work to bear both the same Lorentz-Four-Contraction and the same scalar amplitude of the Polyakov Action -- as the said eigenset that these work to come together in so as to make-up.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

A Little More As To Lagrangian Versus Metrical

Let's initially consider the fundamental condition, that a superstring is a discrete quantum of energy permittivity.  Its motion through a path is its Lagrangian.  The relationship of the direction of the wave-tug/wave-pull of the dimensional-related directorals, that are of the said superstring, when this is taken in a correspondence with its heading, over a relatively considered holomorphic direction over a set duration -- is the metric of a superstring.  In a very real way -- both a Lagrangian-based tense of a Chern-Simons singularity and a metrical-based tense of a Chern-Simons singularity, are related to the pulse of a Ward-Cauchy-based phenomenology.  The main difference is -- that a Lagrangian-related Chern-Simons singularity tends to happen when a quantum of discrete energy is to alter relatively abruptly in the conveyance of the motion of its energy over time, -- whereas, a metrical-related Chern-Simons singularity tends to happen, when a quantum of discrete energy is to alter in its dimensional-related direction -- as a velocity-based tensor relative to light, over a sequential series of correlative group-related instantons.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Chern-Simons Singularities And Relative To Light

Whenever a superstring of discrete energy permittivity is to change in the angular momentum-based eigenindices -- that are of the velocity of its motion relative to light, whenever such a superstring that has altered in such a so-eluded-to manner, relative to light, is here to be taken as a Noether-related phenomenon -- it will then to have tended to alter in its directorial-based pulse.  Such a Noether-related superstring -- that has then to have altered in the velocity of its motion relative to light -- will then to have tended to have altered in either its relative directoral-related speed and/or in its relative holomorphic direction.  Such a said superstring will then become of such a nature -- to where it will then to have tended to have worked to have formed a set of one or more metrical-based Chern-Simons singularities, over the course of that evenly-gauged Hamiltonian eigenmetric, in which its has to have altered in the velocity of its motion -- when this is taken relative to light.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Some Stuff About The Manner Of Chern-Simons Invariants

Let us here initially consider a given arbitrary orbifold eigenset -- that is here to be traveling in a hermitian manner, over time.  Often -- not even if such a said respective orbifold eigenset is to be working to form a De Rham cohomology, in so as to be exclusively forming both hermitian Lagrangian-based singularities and hermitian metrical-based singularities over such a so-eluded-to respective evenly-gauged Hamiltonian eigenmetric -- the individual superstrings that work to comprise such a so-stated orbifold eigenset, may often work to constantly bear metrical-based Chern-Simons invariants, in the process in which the so-eluded-to overall Hamiltonian operator of energy, is to go through its directly corresponding Lagrangian-based path, over time.  This is due to the general condition -- that often, in order for certain respective orbifold eigensets to be able to undergo the process of working to form a De Rham cohomology, during which time the said eigenset is here to work to maintain the process of not changing in its relative holomorphic direction -- the composite superstrings, of which are to bear a tendency of bearing a holomorphic wave-tuge that depends in part on the genus of field that it is here to be exhibiting, are often in and of themselves not able to maintain the process of maintaining their relative holomorphic direction in the meanwhile.  Pulse involves the process of velocity.  Velocity is speed in a direction.  So, if a superstring is here to be constantly changing in its relative holomorphic direction, in spite of such a discrete quantum of energy permittivity to possibly be maintaining its speed -- then, such a said superstring is here to not be in the process of keeping the same pulse.  This will then work to mean, -- that the Ward-Cauchy-related condition of such a discrete quantum of energy permittivity, that is here to be constantly changing in its pulse -- in spite of condition that the overall orbifold eigenset that such a superstring works to comprise it is to here be maintaining its pulse in the meanwhile, -- will then work to cause the composite said strings to be constantly undergoing the process of working to bear metrical-based Chern-Simons singularities, over the course of the Hamiltonian-related orbifold eigenset to here be traveling through its directly corresponding Lagrangian-based path, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Higher Dimensionality Of Chern-Simons Singularities

The higher that the dimensionality that is of a phenomenon, that is here to be undergoing a Lagrangian-related Chern-Simons singularity over the course of its traveling through time and space -- the tighter that the directly corresponding region will be -- at which that phenomenology that is here to be going through such a said Lagrangian-based Chern-Simons singularity, is to then to be fidgeting through space-time-fabric -- in so as to be changing in more derivatives than the number of spatial dimensions that it is here to be traveling through -- over the course of its traversal across its directly corresponding Hamiltonian operand over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Superstring And Chern-Simons Singularities

Let us initially consider a superstring of discrete energy permittivity, that is traveling through a Lagrangian-based path.  Let us next say that, as such a superstring is to undergo a sequential series of group-related instantons -- that its angular momentum is to become spurious at the Poincare level to the topoloigical stratum that is at its proximal local reference-frame.  This will then tend to mean -- that such a said superstring of discrete energy permittivity -- will then work to undergo the general Ward-Cauchy-related condition of then to bear a Lagrangian-based Chern-Simons singularity, due to a resultant change in more derivatives than the number of spatial dimensions that it is traveling through.  If such a said superstring is to then to undergo the mappable-tracing of a Lagrangian-based Chern-Simons singularity over time -- then, the directly corresponding orbifold eigenset that such a string is here to work to comprise, will likewise often tend to bear the Ward-Cauchy mappable-tracing of a Lagrangian-based Chern-Simons singularity, over time.  If such a said spur in the angular momentum of the said superstring, is to change the Ward-Cauchy-related conditions of either the holomorphic direction and/or the directoral-related pulse of such a string -- during such a so-eluded-to evenly-gauged Hamiltonian eigenmetric -- such a string will then, as well, undergo a metrical-based Chern-Simons singularity.  Likewise, such a metrical-based Chern-Simons singularity in the said string -- will only tend to result in a metrical-based Chern-Simons singularity in the correlative orbifold eigenset that such a string is here to work to comprise, If there is a resultant change in either the holomorphic direction and/or the directoral-related pulse of the said overall orbifold eigenset of such a said given case.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Open Strings And "Swivel-Shaped" Phenomenology

The higher that the Absolute Value is of the Bette Number, that is here to be directly corresponding to either an open-looped or an open-strand related superstring of discrete energy permittivity, during any one given arbitrary respective iteration of instanton -- the more "swivel- shaped" that such an either respective open-looped or open-strand related superstringular phenomenology will tend to be -- during the directly corresponding iteration of BRST that is correlative to the said iteration of instanton.  The more "swivel-shaped" that such a so-eluded-to open string or fermionic superstring of discrete energy permittivity is to be -- during any one given arbitrary respective iteration of BRST, (which is during a majority of the directly corresponding iteration of instanton), the more likely that such a said superstring is to ensue in so as to become of a tachyonic nature -- as opposed to, instead, of being of a Noether-related nature.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

As To Mass, The Rarita Structure, And Gravity

The strong force is eminently predominant, at the multiplicit local region at which there is here to be an eigenstate of the centralized knotting of the Rarita Structure.  The strong force as explained here,  is basically that force that works to inter-bind subatomic particles into masses.  So, the strong force is predominantly associated with the mass-bearing superstrings of discrete energy permittivity.  The Rarita Structure, is that set of mini-stringular segmentation -- by which those Schwinger-Indices that are formed by the action of gauge-bosons upon the light-cone-gauge -- of which are to oscillate in so as to commute their vibrations into that "encodement" by which the Hamiltonian operations of the various forces are to then be able to interdependantly interact, happens, in so that the holonomic substrate of space-time-fabric may then be able to different in a kinematic manner, with other space-time-fabric -- over the multivarious Fourier-related transforms, in which there is here to be any viable physical relationships over time.  When such Schwinger-Indices are propagated in both a perpendicular an in a transversal manner -- as an integrative tense of Hamiltonian-related operators over time, -- such sets of integrative Schwinger-Indices act, in so as to work to form gravity waves.  This would then logically mean, that those nodes that are most directly associated with the presence of gravity -- are predominantly associated with the presence of mass-bearing discrete quanta of energy.  This works to help at explaining, as to why gravity is so highly associated with the multivarious mass-bearing relationships that exist throughout space and time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

An Ellaboration Of Quotients Of A Certain Genus Of Expressions

Let's say that there is here to be the progression of three dividends or quotients, that may be determined by working to divide the euclidean expression of four different resultant dilatino-related functions, (the second to the first, the third to the second, and the fourth to the third), which is here to result in a Bianchi-related scalar curvature, that may be extrapolated into a four-spatial-dimensional Bianchi-curvature , that works to help at determining the scalar Lagrangian-related path of an ulterior particle, -- to where such a resultant scalar flow, that is to be extrapolated by the so-eluded-to respective quotients, is to work to bear the flow of an overall continuous function.  Once the four-spatial dimensional curvature is extrapolated, one may then attach directorals in an arbitrary yet consistent manner to the variable-related attributes, that are of the determined Bianchi-related scalar curvature.  The chirality is not altered over the said progression, and the pulse is here to remain unchanged per quotient -- to where the resultant integrative cohomology that such a so-eluded-to ulterior particle is here to traverse, would then here be able to be of a De Rham nature, over time, when this is taken as one whole.  The progression of the three consecutive quotients is to dampen, from the first quotient-determined path to the second quotient-determined path to the third quotient-determined path.  This means that the integrative cohomological expansion of the trajectory of the second quotient is of a lower amplitude of proximal divergence than the first one, and that the cohomological expansion of the trajectory of the third quotient is of a lower amplitude of proximal divergence than the second one.  Each of such quotients takes place, over a span of one million consecutive iterations of group-related instantons -- as an evenly-gauged Hamiltonian eigenmetric.  This will then mean that the overall Fourier Transformation that is here to be directly associated with the three consecutive quotients -- is to occur over an evenly-gauged Hamiltonian eigenmetric that is to span a duration of 3 millions consecutive group-related instantons. This dampening is an exponential decay in the rate of the expansion of the directly associated Lagrangian-related path, -- of which may be described of here as a natural logarithmic action -- that is taken in so as to work to decrease the rate of the expansion of the directly associated Lagrangian-based path.  One may then say that an inverse Clifford Expansion had happened to the general flow of the Ward-Cauchy-related eigenstate or Hamiltonian operator, that is here to had undergone the traversal of the three said consecutive quotients -- in so as to decrease the divergence of the said eigenstate or Hamiltonian operator, from propagating out of the adjacent general locus spontaneously.  Hint:  Each of the three directoral-related dependant variables are to be equidistant from the origin, at each endpoint of the three different quotient-based functions!  Such an eigenstate or Hamiltonian operator would here happen to be a Ward-Cauchy-related holonomic substrate, other than a superstring.  (It could, though however, be an orbifold eigenset -- that may act as one perturbating Hamiltonian operator.)
I will continue with the suspense later!  To Be Continued!  To Be Continued!  Sincerely, Samuel David Roach.

Gauge-Bosons Working To Help Form The Various Forces

Here are some details -- as to the general idea as to how the various different activities of gauge-bosons, help to work at forming the crucible of the four different general forces of the overall unified field homotopy of space-time-fabric.  Gauge-Bosons work to strike the correlative second-order light-cone-gauge eigenstates, in so as to form Schwinger-Indices that are thence to be propagated along the multiplicit Rarita Structure over time.  When such said Schwinger-Indices are here to work to form eigenstates that are of a centralized knotting, along the here mentioned Rarita Structure, -- this works to help at forming discrete increments of the strong force.  When, instead, certain various Schwinger-Indices work to form the condition of a cohomological generation per successive iteration of instanton -- that is orthogonal to the condition of the number of discrete quanta of energy that are here to be produced per cohomological generation -- as is according to the right-hand-rule (due to the dual general condition that the general holomorphic direction is to the relative left, and, as well, the other so-eluded-to condition of touch being associated with tangency, of which is likewise associated with an orthogonal nature), which works to help at forming the electromotive force.  The oscillations of mini-stringular segmentation are caused by the propagation of Schwinger-Indices.  The integration of Schwinger-Indices that propagate in both a perpendicular and in a transversal manner work to help at forming the gravitational force.  And, the spontaneous degeneration of the cohomology that is proximal local to the multiplicit eigenstates of the relatively centralized knotting of the Rarita Structure, works to help at forming the weak force.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

An Example Of A Group-Attractor

Let us say, that one is to have a substringular situation -- to where there is to be one Majorana-Weyl-Invariant-Spinor -- that is working to "try" to diverge from a second Majorana-Weyl-Invariant-Spinor, while the second mentioned spinor is to work to "try" to converge upon the first just mentioned spinor.  Now -- let us say that there ensues to be a situation -- to where there is to be a third substringular entity, -- that acts upon the earlier mentioned scenario, to where the Fourier-related activities of the two different mentioned Majorana-Weyl-Invariant-Spinors are to coalesce into one group-acting Hamiltonian operator, after the particle that is here to act upon the two initially mentioned spinors, is to engage upon such an embarking in a Yukawa-related manner, over time.  This would be one general genus of a group-attractor, which here may more specifically be named of as a gauge-attractor, as it is here to be a Ward-Cauchy-related substringular phenomenology -- that works at least in part, via the Fourier-related activity of potentially integrative Schwinger-Indices -- that are here to be propagated along the general Rarita Structure, over time.  Again -- as an aside, such Schwinger-Indices (before these are here to coalesce into groups of such indices), are here to initially to be formed by the kinematic activity of gauge-bosons upon the topological stratum of the multiplicit light-cone-gauge.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Superstrings Acting On Their Own

Let's say that the discrete spatial dimensionality, that is of one given arbitrary superstring of discrete energy permittivity -- during each successive iteration of BRST -- is invariant, over an evenly-gauged Hamiltonian eigenmetric.  The superstring of such a case, may either be a closed-loop, an open-loop, or an open strand.  Mini-Stringular segmentation, as always, works to bind it (the so-implied substringular loop-related phenomenology of such a general case) into a tense of homotopy -- in so long as the so-eluded-to substringular topology that is here to be correlative, is not to be frayed by a black-hole.  The respective spatial dimensions are here to compactify, right before BRST, And, the respective spatial dimensions are here to decompactify, during the multiplicit ensuing Regge Action.  The dimensional compactification and the dimensional decompactification of such a general case, is here to bear a Real Reimmanian scalar amplitude, -- to where the Bette number is, in this general genus of a case, to never to be equal to zero.  Let's say that the given arbitrary respective superstring is here to not to work to bear an E(8)XE(8) genus of an oscillation-related tendency.  If the given arbitrary superstring of discrete energy permittivity of this general given case, is to act alone, in so as to be of its own orbifold eigenset, and if such a general genus of a superstring so mentioned here -- is to be of a Noether-related nature over time, -- the, the absolute value of the correlative Bette number, is here to be of a value of at least six.  This is in so as to work to allow for the correlative gauge-bosons, to have a plausible gain and/or loss here, of a discrete quantum of the directly pertinent homotopic residue -- per each individually taken increment of instanton.  You see, the E(6)XE(6) string is both a Hamitonian operator that acts as a genus of a bosonic string, as well as this also being an oscillation-related tendency.  The oscillation-related tendency of such a so-eluded-to heterotic string, is here to work to allow -- for what is here to be the added need for gauge-bosons -- to exchange discrete quanta of homotopic residue, as well.  The higher the correlative Bette number is, the greater the chance of a superstring to be put into a position -- of either gaining or losing discrete increments of homotopic residue per instanton.  This includes the need for gauge-bosons, as well, to either gain or lose homotopic residue -- per each individually taken instanton.
((e^12)/(e^6))/600 is less than one, -- where as ((e^12)/(e^5))/600 is greater than one.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Spinors And Dilatinos

Take the expression for the euclidean expansion, that is of any one given arbitrary Majorana-Weyl-Invariant-Spinor eigenstate -- that is of cotangent bundle R4.  This just mentioned expression -- of which is here to be in terms of its scalar amplitude, is here to be considered when this is coupled while from within the framework of its directoral-related conditions.  The respective externalized reference-frame, via which this said eigenstate that is spinning in a back-and-forth manner at an internal reference-frame -- is here to be, as well, propagating through a Lagrangian-based path in a kinematic manner, via a Fourier Transform as a Hamiltonian operator, in a transversal manner, over time.  Now -- couple the said expression for the euclidean expression of the said spinor, with both the brief time that it is propagating through as it is traveling (as is it is spinning) along the course of its said Lagrangian-based path, AND a pointal-related mass, AND the average angle that the here mentioned spinor is to be spinning in a back-and-forth manner through, as it is spinning via a central coniaxial.  At this point in derivation -- the just eluded-to metric-gauge-related pulsation per cubic directoral-based meter -- that is here to be resulted in, may be thought of as a dilatino.  The consideration of meter that I have mentioned here, is generally to be conveyed, via the usage of the correlative Hodge-based indices that are of any one respective given arbitrary case. Such so-eluded-to Hodge-Indices, are to directly correspond to the correlative litigee of directorals, that are here to be most applicable to the coherent Ward-Cauchy-related situation of such a general genus of a case.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Symmetries Of Cohomologies

Let us consider a given arbitrary quantum of discrete energy permittivity, during BRST.  This is when both the Polyakov Action and the Beti Action are happening to the correlative discrete quantum of energy, simultaneously -- through the vantage-point of a central conipoint.  The so-eluded-to superstring and its counterstring, during such a tense of a gauge-metric, are not to then to be in the process of going through a Lagrangian-related genus of motion -- since this is here to be happening, over the course of one discrete instant of time.  As this is happening, -- the said superstring is to be vibrating at the correlative proximal locus of its Sterling Approximation.  During BRST, the said string -- whether the correlative superstring of discrete energy permittivity is here to be either of a bosonic nature or whether it is here to be of a fermionic nature -- is here to form a vibrational oscillation, that is to be either of a respective harmonic nature or of a respective anharmonic nature.  (Such a said vibration is here to be of a harmonic oscillation if it is of a bosonic nature, or such a said vibration is here to be of an anharmonic oscillation if it is of an fermionic nature.)  As an aside:  The topology itself of a superstring at the Poincare level, that is inherent to a discrete quantum of energy permittivity, is extraordinarily smaller in thickness than the respective circumference or its respective length than such a so-eluded-to superstring.  (As a general idea so that you get the jist -- a superstring is on the order of 10^(-43)* as thin, as it is respectively round (bosonic) or long (fermionic.)   So, as such a said given arbitrary superstring of discrete energy permittivity and its directly corresponding counterstring, are vibrating during BRST -- the directly corresponding topology of the holonomic substrate of the said discrete quantum of energy -- is to be interacting in a Gliosis manner with the norm-state-projections that surround it, in so as to work to form what may here to termed of here as a Gliosis-Sherk-Olive cohomology.  Such a GSO cohomology, tends to be of a toroidal-related shape for such a so-eluded-to bosonic string, and such a GSO cohomology tends to be either disc-shaped, washer-shaped ( if the correlative superstring is swivel-shaped), or conical-shaped, for such a so-eluded-to fermionic string.  Consequently, the GSO cohomology of a superstring of discrete energy permittivity, that is bosonic in nature -- tends to be symmetric in differential geometry to its directly corresponding counterstring, during BRST, -- whereas, the GSO cohomology of a superstring of discrete energy permittivity, that is fermionic in nature -- tends to be assymetric in differential geometry to its directly corresponding counterstring, during BRST.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Some Stuff As To Clifford Expansion

Take the Lagrangian-based path of the cohomological generation, that is of a discrete quantum of energy.  The resultant tangential motion or the divergence, that such a said Lagrangian-based path is to tend to make over time -- may be described of here as a euclidean expansion.  The euler of such a euclidean expansion, may often be thought of as a Clifford Expansion.
 I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Cohomology And A Unitary Lagrangian

Any cotangent bundle of R3, that acts as a single cohomological-forming closed-loop superstring --that is of a single Hamiltonian operation, that neither acts as a Majorana-Weyl-Invariant spinor, nor would it here act as working to bear a tree-amplitude of a directoral-related topological sway, -- is going to tend to act thru  a unitary Lagrangian over time.  The discrete bundle of energy permittivity here is a superstring.  The motion of a superstring over time is its Lagrangian.  What this string-related motion travels spatially through, is its Hamiltonian operand.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Considering Certain Proportions As To The Polyakov Action

The higher the Lorentz-Four-Contraction, the lower the Polyakov Action.  The lower the Polyakov Action, the less partition-related discrepancies, that are here to exist among the directly corresponding mass-bearing superstrings of discrete energy permittivity.  The less partition-related discrepancies, that are here to exist among the directly corresponding mass-bearing superstrings of discrete energy permittivity -- the more superstrings of mass that are here to exist from within the Ward-Cauchy-bounds of that orbifold eigenset of such a case -- in which the said orbifold eigenset is here to be approaching the speed of light.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

"Quota" Of Strings In A Closed-Loop Orbifold Eigenset

Whenever one is to have an orbifold eigenset -- that is here to consist exclusively of discrete quanta of energy permittivity that are here to be closed-looped Noether-based superstrings of discrete energy permittivity, that are here to exhibit an E(8)XE(8) heterotic string oscillation-based tendency, -- such a general genus of an orbifold eigenset, is here to tend to consist of a minimum of at least 2,981 superstrings of discrete energy permittivity -- per each individually taken duration-related span of group-related instanton.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Net Exchange Of Partition-Related Discrepancies

If the Lorentz-Four-Contraction of a phenomenology of mass-bearing superstrings is to be maintained over time -- to where the correlative Polyakov Action eigenstate, that is of the self-same phenomenology of mass-bearing superstrings, is here as well to be maintained over that same period of time, -- the number of partition-related discrepancies that the said phenomenology of mass-bearing superstrings is to gain per each individually taken instanton, will tend to equal the number of partition-related discrepancies that the so-stated phenomenology of mass-bearing superstrings will lose per each individually taken instanton -- over the said duration of time.  This will then mean, that the directly corresponding absolute value of the Beti number per instanton -- that is here to be correlative to the directly corresponding scalar amplitude of spatial dimensional compactification, will here tend to be equal to that directly corresponding absolute value of the Beti number per instanton -- that is here to be correlative to the directly corresponding scalar amplitude of spatial dimensional decompactification, -- over the so-eluded-to evenly-gauged Hamiltonian eigenmetric, that is here to correspond to the said time period of such a said case.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

First Discussion As to Flow Of Partition-Related Discrepancies

The higher that the Beti number is, during a dimensional compactification, of which is to here to happen right before any one given arbitrary iteration of BRST -- the more partition-related discrepancies will tend to flow out of or diverge from a correlative superstring just before the said iteration of BRST.  Furthermore, -- the higher that the absolute value of the Beti number is, during a dimensional decompactification, which is here to happen during any one iteration of the Regge Action -- the more partition-related discrepancies will tend to flow into or converge upon a correlative superstring, during the so-stated iteration of the Regge Action.  Compactification of dimensions tends to work to involve a tangential flow of exchanged homotopic residue, whereas, decompactification of dimensions tends to work to involve a cotangent-related flow of exchanged homotopic residue. 
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach. 

The Beti Number And Dimensional Compactification

When a superstring compactifies in the number of spatial dimensions that it expresses -- its correlative Beti number is positive.  When a superstring decompactifies in the number of spatial dimensions that it expresses -- its correlative Beti number is negative.  A positive Beti number works to express the number of spatial dimensions that a superstring has just compactified in.  The absolute value of a negative Beti number works to expresses the number of spatial dimensions that a superstring has just decompactified in.  If the Beti number is +2 -- the correlative superstring of discrete energy permittivity has just decreased in its spatial dimensionality by two dimensions, -- it has just compactified by two dimensions.  However, if the Beti number is -2 -- the correlative superstring of discrete energy permittivity has just increased in its spatial dimensionality by two dimensions, -- it has just decompactified by two dimensions.
 I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Time And Energy

...The sequential series of group-related instantons through a Lagrangian, -- the duration of this is time, and the action of this is energy.
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

Homotopic Residue Being Made Tangent, Cotangent

Just as a superstring is about to enter BRST -- the tendency is that a residual sub-quantum of partition-based discrepancies are released or taken away from a superstring of discrete energy permittivity.  This is to where the holonomic substrate of that homotopic residue that acts as partitional-based discrepancies, that are here to be detracted from such a said superstring, are here to be made tangential to such a so-stated superstring.  During the Regge Action (of which is ensuing the duration of BRST) -- the tendency is that a residual sub-quantum of partition-based discrepancies, that are here to be added to such a said superstring, are gained or brought into a superstring of discrete energy permittivity.  This is to where the holonomic substrate of that homotopic residue that acts as partitional-based discrepancies, that are here to be added to the said superstring, are here to be made cotangent to such a so-stated superstring.  Parition-related discrepancies diverge from a superstring just before BRST, whereas partition-related discrepancies converge into a superstring during the ensuing Regge Action.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Next Part Of Partition-Based Discrepancies

The expression i*PI(del) -- refers to the holonomic substrate of the homotopic residue that is gained and/or lost, as the partitional-based discrepancies (as a topological stratum) -- that are indirectly utilized, are here to help at the generation and/or the degeneration of homotopic cohomological phenomenology -- for one orbifold eigenset per instanton, as may be averaged over an evenly-gauged Hamiltonian eigenmetric over time.  With any unscattered electromagnetic energy, there is to be no net gain nor loss of such so-eluded-to increments -- to where there is here to be no net gain nor loss of partition-related discrepancies per each individually taken orbifold eigensets of such electromagnetic energy, over the course of any one set instanton in which such an electromagnetic tense of phenomenology is here to be unscattered.  (This is to where the said electromagnetic energy is here to neither strike the externalized core-field-density of any light-cone-gauge eigenstate, nor, even more potentially rarer, no electromagnetic energy that is here of the earlier mentioned nature is to strike head-on.)
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

An Introduction To The "i*PI(del)Action"

Any superstring of discrete energy permittivity, has what I term of as partition-based discrepancies -- which are equal in the scalar magnitude of Hodge-based index -- to the scalar amplitude of their directly corresponding Polyakov Action eigenstate.  I call such partition-based discrepancies "i*PI(del)" increments.  The general oscillation-based tendency that is to happen, on account of the loss and/or the gain of such i*PI(del) increments -- is what I term of as the "i*PI(del) Action.  Such a so-stated genus of oscillation-based tendency, works to help at forming both the structural integrity of any directly corresponding orbifold eigenset, as well as helping to work to assist at the attraction of one orbifold to any other given arbitrary orbifold. Enough for now!  To Be Continued!  Sincerely, Samuel Roach.

Some Stuff As To The Beti Number And Orientable Supertrings

When the Beti number is even, during either BRST and/or during the directly ensuing Regge Action, for any one given superstring of discrete energy permittivity -- the said string is orientable, -- and thence, the so-stated superstring of discrete energy permittivity is then to ensue as being of a Noether-related flow.  The reason to this -- is that, when a superstring is to bear an even chirality-related parity, -- it is then to tend to bear a resulting Reimman-based scattering.  A Reimman-based scattering is of a harmonic delineation.  When the Beti number is of an even integer, -- the consequent partition-based discrepencies of the correlative superstring, is then to work to bear a harmonic flow of a distribution among the consequent partition-based discrepencies of the directly corresponding counter string of that self-same discrete quantum of energy permittivity.  Such a delineation of an even ordering, is here to work to form a homeomorphic field between the said superstring and its correlative counter string, during BRST.  Such an even ordering will then help at working to allow for the directly corresponding discrete energy to not be perturbated-out of Noether Flow.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Solution 8 Of Test 2 Of Course 20

From the time that any one given arbitrary photon is to be scattered, until it is re-quantized back into a beam of light -- such a so-eluded-to entropic photon, is here to toggle from being delineated at a Laplacian-based extrapolation, in an orthogonal manner from its initial directoral-related tense of holomorphicity, -- as one may trace such a delineation from the point of scattering up to the covariant positioning at which it is to ensue in so as to re-quantize back into a beam of light, to then toggle back into being delineated at a Laplacian-based extrapolation, that is here to then be able to be extrapolated as working to bear a tense of holomorphicity, --  that is in a general linear distribution from where the photon was to have been scattered, up to the covariant positioning at which it is to re-quantize as I have mentioned earlier, back to toggling back into the earlier mentioned general genus of orthogonation ( a tense of Ward-Polarization, that may be traced in an extrapolation from its space-related point of scattering up to where its is to be re-quantized), and so-on, -- until the here initially stated entropic photon, is to be brought back into the beam of light as a Yang-Mills-related topological phenomenon that is here to bear partially Yau-Exact singularities. (To where the said photon is to go back into being as a standard discrete quantum of electromagnetic energy over time.)
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

Solution 7 Of Test 2 Of Course 20

7)  When a photon -- which is a discrete quantum of electromagnetic energy -- scatters upon another discrete quantum of energy, the holomorphic end of the photon that is here to be in the process of just being scattered, -- is made to be Gliosis to the externalized core-field-density of that light-cone-gauge eigenstate that is here of that specific quantum of energy, that the said photon is here to be scattering upon.  This would then work to make the relatively forward-holomorphic end of the incoming photon to be tangent upon the Njenhuis side of that phenomenology that the so-stated photon is here to be coming into a direct contact with, in so as to scatter.  Tangency is a tense of orphoganation.  In this general genus of a case, the just mentioned tangency also bears the general tense of orphoganation -- to where the forward-holomorphic end of the photon of this case, that is here to strike, in so as to be scattered, -- is to be at a generic right angle to the general flow that may here be subtended by making a Laplacian-related tracing -- that is to be extrapolated from the relative reverse-holomorphic end of the just struck discrete bundle of energy towards the relative forward-holomorphic end of the same mentioned just struck discrete bundle of energy.  This shows a tense of normalcy or orphoganation.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Gauge-Bosons And Forces

Often, when gauge-bosons work to form a different general genus -- as to the manner in which these act in so as to "pluck" their directly corresponding second-order light-cone-gauge eigenstates -- this may often work to perturbate or alter the general genus of the force that may be exhibited out in the Ward-Cauchy-related bounds of the substringlar.  For instance -- one general genus of such a "plucking" may work to help at forming the strong force.  Another general genus of such a "plucking" may work to help at forming the electromotive force.  Another general genus of such a "plucking" may work to help at forming the gravitational force.  And another general genus of such a "plucking" may work to help at forming the weak force.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

More As To The Activity of Group-Attractors

Let us initially consider an orbifold eigenset, that is here to be comprised of by a set Hodge-Index -- as to the number of discrete quanta of energy, that work to comprise the said eigenset.  Let us next consider another orbifold eigenset -- that is of another universal setting -- that is here as well to be comprised of by a set Hodge-Index, as to the number of discrete quanta of energy that work to comprise the said eigenset.  Let us next say, that the layer of adjacency, that is here to exist between and among the superstrings that are here to work to comprise the two covariant orbifold eigensets that are here to be moving over a set evenly-gauged Hamiltonian eigenmetric -- is here to be consistent in both a codifferentiable and in a codeterminable manner over time.  Let us then say that a group-attractor is to happen to the two said orbifold eigensets, in so as to work to make the angular positioning of those discrete quanta of energy -- that work to help in comprising the two individually taken orbifold eigensets, to be of such a manner, to where the two said orbifold eigensets are to then to be of the same universal setting.  This will then not only work to make the manifolds of the two different mentioned orbifold eigensets to be of a Real Reimman-related Gaussian spacing -- the one to the other --, yet, it will also make the two individually taken orbifold eigensets to now act in such a way that is made, the one to the other, in such a manner, that is viable in a Yukawa manner that is of a potentially spontaneous Gliosis-related tense, that is of both a codetermiable and of a codifferentiable relationship over time.  I will continue with the suspense later!  To Be Continued!  Sincerely,
Samuel David Roach.

Solution 6 Of Test 2 Of Course 20

6)  Individual quanta of electromagnetic energy exist as photons.  As with basically all discrete increments of energy quanta besides gauge-bosons that are of a closed-loop nature -- photons are comprised of by both a bosonic superstring of discrete energy permittivity as well as its correlative counter string, and also by both the said string's directly corresponding Fadeev-Popov-Trace eigenstate as well as its correlative light-cone-gauge eigenstate.  The said superstring and its correlative counter string, work to act as the respective primarily thought of pointal-based and the primarily thought of wave-based holonomic substrate of the said photon.  Whereas -- the said Fadeev-Popov-Trace eigenstate and its correlative light-cone-gauge eigenstate, work to act as the respective primarily thought of pointal-based and the primarily thought of wave-based holonomic substrate of the said photon.The just mentioned light-cone-gauge eigenstate, works to inter-relate the said Fadeev-Popov-Trace eigenstate with both its directly corresponding superstring of discrete energy permittiivty and its correlative counter string.  Individually taken photons work to coalesce via quantization -- by working to tend to conjoin at their relative Njenhuis periphery of core-field-density.  One may here use a metaphor to view a photon as being the overall beam of electromagnetic energy, as well as that the just mentioned overall beam of electromagnetic energy as being the photon, -- just as a drop of water from the ocean may be viewed of as being the ocean, as well as the ocean may be thought of as being at one with the said drop of water.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.