More As To The Nature Of Light-Cone-Gauge Topology

Generally -- during any given arbitrary iteration of BRST -- when one is to have a discrete quantum of energy, that is to bear a Yang-Mills light-cone-gauge topology (non abelian) -- those second-order light-cone-gauge eigenstates, that are positioned at the immediately reverse-holomorphic side of the directly corresponding superstring of discrete energy permittivity, that is of such a respective case, -- when this is here to be taken at a level that is Poincare to the topology of the here mentioned individually taken second-order light-cone-gauge eigenstates, -- are here to tend to work to bear a relatively sinusoidal Laplacian-related delineation (like a relatively sinusoidal standing wave, that is being increased in its relative length -- by the activity of an increased scalar amplitude of mini-stringular segmentation -- that is being fed-into the relatively adjacent proximal locus), that are then to be plucked like a harp, at their correlative "troughs," by the directly corresponding gauge-bosons, -- in so as to work to produce those Schwinger-Indices, that operate via their propagated vibrations, in so as to help at working to do Their Part, at influencing the formation of the existence of the four general forces of nature.
Furthermore:  generally -- during any given arbitrary iteration of BRST -- when one is to have a discrete quantum of energy, that is to bear a Kaluza-Klein light-cone-gauge topology (abelian) -- those second-order light-cone-gauge eigenstates, that are positioned at the immediately reverse-holomorphic side of the directly corresponding superstring of discrete energy permittivity, that is of such a respective case, -- when this is here to be taken at a level that is Poincare to the topology of the here mentioned individually taken second-order light-cone-gauge eigenstates, -- are here to tend to work to bear a relatively supplemental Laplacian-related delineation (like a relatively supplemental standing wave, that is being increased in its relative length -- by the activity of an increased scalar amplitude of mini-stringular segmentation -- that is being fed-into the relatively adjacent proximal locus), that are then to be plucked like a harp, at the correlative alterations that are of a proximal local change in the first-derivative (where there is ulterior mini-stringular segmentation touching it), of such a so-eluded-to wave, by the directly corresponding gauge-bosons, -- in so as to work to produce those Schwinger-Indices, that operate via their propagated vibrations, in so as to help at working to do Their Part, at influencing the formation of the existence of the four general forces of nature.  To Be Continued!  To Be Continued!  Sincerely, Samuel David Roach.

As To The General Tendency Of The Relative Positioning Of The Angular Momentum

Basically, whenever a given arbitrary Hamiltonian operator is here to be traveling, over the course of a respective Fourier Transformation, in a given direction -- its directly corresponding angular momentum eigenindices, will tend to be delineated at a positioning, that is generically centered upon a spot, that is here to be existent at the relative holomorphic side of that said respective Hamiltonian operator -- in such a manner, that is Poincare to the Gliosis-based topological surface, that is here to be of the so-eluded-to holonomic substrate, that is here to work to comprise the phenomenology that is of the respective Hamiltonian operator -- that we have been discussing here in this given arbitrary case.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Hamiltonian Operator Versus Lagrangian

In the following multiplicit case, one may say that the general difference that is to exist, between the Hamiltonian operator and the Lagrangian, is that the respective  Hamiltonian operator, is here to be the actual physical entity of energy that is to be transferred from one spot to another, -- whereas, the Lagrangian is the actual motion, by which the said physical entity of energy that was earlier mentioned, is to be transferred from the one respective spot to another.  Samuel David Roach.

A Basic Example Of Ward-Polarization

Here is a basic general example, of what may be termed of as a phenomenon -- in which there is to be the Ward-Cauchy-based condition of Ward-Polarization:

Let us initially say that one is to have an orbifold eigenset, that is to be undergoing a tense of conformal invariance at its internal reference-frame, that is here to work to bear a tense of what would here be at least the equivalence -- of a tense of angular momentum, that is subtended in what would here be the relative forward-holomorphic direction.  Let's next say, that over the translation of a relatively small distance, as taken in the earlier mentioned forward-holomorphic direction, from where the initially stated orbifold eigenset is to be bearing its so-eluded-to tightly-knit location of vibrational oscillation,  -- there is to be the bearings of a tense of a quantum of electromagnetic energy to be present.  However, there is here, in this general case, an orbifold eigenset, that is placed in-between the direction of the angular momentum that is of the initially stated orbifold eigenset and the so-stated quantum of electromagnetic energy -- that is here to be placed in such a manner, to where the relative holomorphic direction of the orbifold eigenset that is here to get in the way, is to be orthogonal to the holomorphic direction of the initially stated orbifold eigenset.  Such a substringular condition of such a case, may then work to partially, if not completely, block any otherwise eminent Yukawa Coupling to then to be able to be achieved, between the initially said orbifold eigenset and the so-eluded-to electromagnetic energy-based orbifold eigenset.  This general genus of a Ward-Cauchy-related condition,  is one of basically countless types of situations -- in which there is to be the phenomenon, of what may be termed of as Ward-Polarization.  Samuel David Roach.

My Current Understanding As To How Gravity-Based Cohomology Is Transferred

The cohomology that is thus formed, by those particles that I had mentioned in my last post, -- as being either "gravitons" (transversal-based) or "gravitinos" (radial-based) -- is to here be indirectly translated to the corresponding cite of the gauge-bosons, in such a manner, to where, as the said gauge-bosons act in so as to pluck the directly corresponding second-order light-cone-gauge eigenstates like a harp, there is then to exist, the general tendency, to where such a so-eluded-to tense of a set of translated cohomological eigenindices -- are to then to be transferred to the thence formed Schwinger-Indices, in so as to help at working to form those integrative set of Schwinger-Indices, that are to move in such a manner, that is simultaneously transversal and perpendicular, to where the wavelength of such a so-eluded-to wave, is to have a wavelength that is to be anywhere from and including (5*10^(-22) of a meter To 4*10^(-18) of a meter) in overall length, -- in such a manner, -- to where there is here to tend to be the transference of a translation of the cohomology of what I earlier named of as being "gravitons" and "gravitinos," to where such a so-eluded-to tense of a gravitational wave, is here to work to each bear only a wave-based knotting equation, without it working to bear a particle-based knotting equation.  The holonomic substrate of the transversal motion of a gravitational wave, works to help at describing the knotting equation -- that is related to the cohomology of a "graviton," whereas -- the holonomic substrate of the perpendicular motion of a gravitational wave, works to help at describing the knotting equation -- that is related to the cohomology of a "gravitino."
One may metaphorically think of the genetic translation of traits in biology.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

More As To The Recycling Of Relativistic Cohomology

Mass-Bearing superstrings of discrete energy permittivity, tend to form what I term of as being Gliosis-Sherk-Olive cohomology.  As eigenstates of such so-eluded-to GSO cohomology, are to be scattered in an anharmonic manner -- these eigenstates then work, to be changed into what I term of as being the holonomic substrate of particles called dilatons and dilatinos.  This just mentioned general genus of activity, is here to be happening on the relative Real Reimmanain Plane -- whereupon discrete energy permittivity, is here to continue to be both iterated and reiterated over time.  The thence formed dilatons and dilatinos, are to then to be pushed off of the said relative Real Reimmanian Plane, in the process of working to help at recycling the local presence of norm-state-projections, in so as to refurbish the holonomic substrate of those so-eluded-to point commutators, to where, such a recycling of cohomology is here to be necessary as well, for the formation of cohomology to be able to occur off of the Real Reimmanian Plane.  Without such recycling, this situation would otherwise amount to, as well, an excessive build-up of localized Hamiltonian operators, that would no longer be able to commute -- which would end-up stopping the existence of energy.  Such a relative wave-tug, that is here to push such said dilatons and dilatinos off of the relative Real Reimmanian Plane, happens, on account of the resultant Ward-Cauchy-based angling, in which the earlier inferred Rayleigh scattering of the said GSO cohomology-related eigenstates -- which was here to be scattered in such an anharmonic manner, in so as to work to form a tense of cohomology, that may be described of as being of the nature of what I term of as being Neilson-Kolosh cohomology-related eigenstates.  As these said eigenstates of a Neilson-Kolosh cohomology, are to come together at a general locus that is off of the relative Real Reimmanian Plane, the holonomic substrate of such gathered cohomology-related eigenstates, are to come together -- in so as to work to form the indistinguishably different eigenindices, that work to comprise what I term of here as being "gravitons" and "gravitinos."  The motion of the cohomological eigenstates of "gravitons" and "gravitinos," is to then to work to indirectly induce the gauge-bosons (the E(6)XE(6) strings), of which are on the relative Real Reimmanian Plane, to act in so as to pluck the directly corresponding second-order light-cone-gauge eigenstates like a harp -- in so as to work to form Schwinger-Indices.  Such a general genus of Schwinger-Indices will then act, in so as to work to influence both the general formation and the general activity of the four fundamental forces of nature, -- such as gravity.  In the meanwhile, that general cohomology of both the said "gravitons" and "gravitinos," that was here to be scattered in an anharmonic manner, due to the resultant Ward-Cauchy-based angling, in which the earlier inferred Rayleigh scattering is to occur, -- is to be recycled back into the relative Real Reimmanian Plane, -- in so as to refurbish the holonomic substrate of those norm-state-projections, that are necessary for both the formation of cohomology to occur at this said relativistic Plane, as well as to work to allow for the commutation of the multiplicit discrete quanta of energy.  My model of string theory is becoming clearer in my mind.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Mesons And The E(8)XE(8) Oscillation-Based Tendency

As is according to my present model of string theory, it is the metric-gauge-pulsation of mesons --
that works to form the E(8)XE(8) string oscillation-based tendency.  Therefore, as a minor correction to one of the things that I have stated before, -- in a way, that oscillation-based tendency, of which is here to be thought of as being of the E(8)XE(8) string (of which is one general form of a heterotic string), happens to be as well, an actual general genus of a type of superstring.
Continued later!  Sam Roach.

Beads Of Particles

What I term of as being mini-stringular segmentation -- is that inter-connective bead, that is comprised of what I term of as being second-order point particles, that exists in such a manner, in so as to come together with the multiplicit phenomenology of all of rest of such segmental entities, in a way that tends to be pervasive -- all along the arena of the substringular, -- in so as to work to inter-connect that general field, by which the Ward-Cauchy-based conditions of homotopy may transpire.  Likewise -- when such a general tendency is here to be taken at a reverse-fractal level -- each superstring, as is according to my model of string theory, is comprised of a bead of first-order point particles. Sam Roach.

A General Description Of The Vibrational Flow Of The Rarita Structure

The Rarita Structure is the multiplicit Ward-Cauchy-based structural phenomenology, -- of that general flow of vibrational oscillations, that are propagated as stemming from those initially formed Schwinger-Indices, that are here to be formed by the "plucking" of the multiplicit second-order light-cone-gauge eigenstates -- by the directly corresponding gauge-boson eigenstates -- in so as to then to be rippled forth among that mini-stringular segmentation that is in its general multiplicit path -- in so as to act as that multiplicit holonomic substrate, on account of which the four general basic forces of nature are then to have the condition-related ability, as then to act in so as to be of such a spontaneous nature, to be both formed and interdepdant upon each other, in a viable manner.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Where Mesons Are At

Wherever there are eigenstates at, that are of the centralized knotting of the Rarita Structure -- there are mesons -- of which are the respective given arbitrary bonding cites, -- whereupon subatomic particles are to come together, in so as to work to form the basic building-blocks of atoms and other matter.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Some More Information As To Metric-Related Chern-Simons Singularities

Let us initially consider a distinct given arbitrary superstring, that is perturbating over a set metric-based sequential series of instantons -- when in terms of the varying scalar amplitude of its directly corresponding Lorentz-Four-Contraction, that is acting in a Gliosis-based manner, which is here to be at the Poincare level to the topological surface of the holonomic  substrate, that is of the so-stated superstring (of discrete energy permittivity), over time.  Let us next consider, that the said superstring of discrete energy permittivity, is to be differentiating in a Fourier-based manner -- through a given Hamiltonian operand, that is to here to be spanning the space by which this so-eluded-to superstring of Hamiltonian-based operation is to be tugged, while doing so in a kinematic manner, through the set path that is correlative to its directly corresponding discrete Lagrangian, that the so-stated eigenstate of discrete energy per charge is here to be in the process of being moved into -- over the said sequential series of iteration of group-related instanton.  Let us next say that this tense, of the directly appertaining perturbation of the correlative Lorentz-Four-Contraction, that is being directly applied to the Polyakov-based mechanism in a kinematic manner -- whereby the so-stated discrete quantum of energy permittivity is to be of a harmonic-based cyclical manner -- that would here work to form an even tense of a gradual increase in the directly applicable scalar amplitude of the quantum effect, to where this will then involve an increase as to what the linear-based scalar amplitude in velocity that is of a unitary motion, of which is here to be taken in the transversal direction -- is then to effect the gradual increase in the degree as to the amount of a Lorentz-Four-Contraction that is here to be displayed, is then to take-hold upon the so-eluded-to gradual decrease in the scalar amplitude of the directly associated degree of its Polyakov-based action, in which this is to happen over a discrete number of a successive series of group-related instantons, -- to where this self-same superstring of discrete energy permittivity that is of such a case, is to then work to bear an even tense of a gradual decrease in the directly applicable scalar amplitude of the quantum effect, as to how the linear-based decrease in velocity in a unitary transversal motion in a direction, is to effect a gradual decrease in the degree of the amount of a Lorentz-Four-Contraction -- is then to take-hold upon the gradual increase in the scalar amplitude of the directly associated degree of its Polyakov-based action -- is to then happen, over a discrete evenly-gauged Hamiltonian eigenmetric that is of a successive series of group-related instantons.  Such a gradual and even fluctuation of motion, that is of the process by which an initial acceleration -- that is of a linearly-transversal-based tug, that is here to be formed by a superstring -- through the kinematic activity of a discrete unitary Lagrangian, will then tend to form a higher probability, -- as to here to be consequently of such a nature as to be potentially forming hermitian Lagrangian-based singularities -- even though this so-eluded-to acceleration of a superstring, that is here in this case to then to be cyclical in its eventual process of deceleration -- will thence form changes in the metric-related pulsation of the directly associated superstring in question, - to where this cyclical genus of a process, will then tend to consistently work to form metric-based Chern-Simons singularities over time.
I will conitnue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Fundamentals As To Why Chern-Simons Invariants Are Always Of A Minimum Of A Cotangent Bundle Of R3

Whenever one is to have a given arbitrary Lagrangian-based Trace, that is here to be curving in such a respective manner, to where it is to bear both one or more transversal-based components -- as well as to here be bearing one or more radial-based components in time and space, -- it will always be translated through the general said time and space -- via a dimensionality that is here to work to bear a minimum of two spatial dimensions plus time.  A Lagrangian-Based Chern-Simons singularity will always be able to be mapped-out through a Laplacian-related locus, at which the directly corresponding phenomenon -- that is here to be acting in so as to be in the process of working to bear such a said Lagrangian-Based Chern-Simons singularity -- will be changing in one or  more derivatives of motion, beyond what the number of spatial dimensions that are here to be pertinent to the translation of the motion of this said phenomenology, that is here to be acting in so as to work to form the earlier inferred mappable trace.  Consequently, -- this general situation of tendency will then work to infer -- that certainly if one were to be consistently to be mapping-out any given arbitrary region, over the course of a so-eluded-to Fourier Transform, in which there is to be any translation of mappable-tracing that is to be present, as taken from the initial side of such an earlier inferred trace -- that is to exist in going from Before the presence of such a general Lagrangian-based Chern-Simons singularity to After the presence of the self-same Lagrangian-based Chern-Simons singularity, -- one will deductively need to have the proximal local presence of a dimensional field, that is here to require the existence of the eminent presence of At Least Three spatial dimensions plus time.  Any respective general locus of a cotangent bundle, is here to work to mean and/or to infer, the presence of a convergent region of discrete energy-related phenomenology.  Therefore -- in any situation in which there is to exist the presence of Chern-Simons Invariants, there will always be the presence of a situation in which there is a minimum case of a Cotangent Bundle of at least R3.  Plain and simple.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Direction Of The General Forces Of Nature

Whenever electromagnetic energy is to scatter upon another phenomenology,  one or more discrete quanta of electromagnetic energy are here to be striking the externalized core-field-density of the respective coresponding light-cone-gauge eigenstates in a Gliosis-based manner, -- in so as to work to influence the general flow of the directly corresponding proximal local Schwinger-Indices.  Consequently, this general genus of an interaction that is here to be happening between discrete quanta of electromagnetic energy and the light-cone-gauge is to then to be able to work to influence the general direction in which the forces of nature are to be applied.
Samuel David Roach.

Different Distinct Tenses Of Vibration Of Majorana-Weyl-Invariant-Mode

If one is to have a mass-bearing orbifold eigenset -- that is here to exhibit the tendency to be able to work to bear a relatively high tense of a Majorana-Weyl-Invariant-Mode -- then, such a said orbifold eigenset, is then to tend to not only be superconformally invariant at an internal reference-frame, yet as well, it will then tend to bear both a tense of a harmonic vibration and a tense of an anharmonic vibration, --  as taken at the Poincare level to the proximal locus of the external topological shell of the so-stated orbifold eigenset.  The earlier mentioned harmonic vibration, will be a tense of one or more sets of oscillations -- that will more than likely tend to form a certain tense of a sound-like phenomenology; whereas, -- the earlier mentioned anhamornic vibration, will be a tense of one or more sets of oscillations -- that will more than likely tend to form a tense of a heat or infrared-like phenomenology.  Since the said tense of the directly corresponding Majorana-Weyl-Invariant-Mode of such a case, was here mentioned to be of a relatively high scalar amplitude, then, its vibrational oscillations will tend to intrinsically be of a relatively low frequency, -- if it is not perturbated by an external source, yet such a set of oscillations will tend to be able to work to bear a relatively high potential, for that orbifold eigenset that is here to be in the process of forming such a set of oscillations, -- to exhibit a relatively high resonant vibration, if the proper tense of a Yukawa Coupling is to become Gliosis to the externalized core-field-density of the said orbifold eigenset.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Willmore Energy

Any set of discrete quanta of energy, that are spontaneously confined, from within what would here be -- a fully holographic or flat space (a Minkowski-related space, that is to exhibit up to a maximum of 26 spatial dimensions plus time), to where the Ricci Flow of the pertinent topological invariants, that are here to be of such a discrete quantum of energy, may be mathematically described of, as appertaining to the nature relating to:
+ or - ((The mean Gaussian curvature of the surface, that is of the respective cotangent bundle -- that is of such a case)
MINUS (The mean mobius-based curvature of the surface, that is of the respective cotangent bundle -- that is of such a case)).  (+ "out in front," for a Reimman tense of energy, or (- "out in front," for a Nijenhuis tense of energy.)  Generally, this will call for the explication of a Nijenhuis tense of energy.
Here, the said set of discrete quanta of energy, is to spontaneously remain as being of a flat Ricci Curvature, -- to where the said condition of mobiaty, that is of this respective given arbitrary case, is to remain spontaneously superconformally invariant, -- in so long as the correlative Ricci Curvature is to remain flat -- to where the said set of discrete quanta of energy, is to remain as being of a flat space, in so long as there is no external perturbative effect upon the dimensionality of the said set of discrete energy (space-time-fabric that is of a flat Ricci Curvature, is of a purely holographic tense of space) -- that is here in this case, to potentially take upon itself, an approximation of a round-like shape.
Spontaneously means here, that such a case would here to tend to remain as such, in so long as no other non-mentioned factors are to come into play.  Such a set of discrete energy, -- that is to be spontaneously kept as being of a flat space (maximum of 26 spatial dimensions), may be termed of as being here as an example of a "Willmore Energy."  A Willmore Energy, is a manner that is to be taken at a Ward-Cauchy-related level -- by which one is to be able to work at distinguishing the difference between a given actual displayed tense of energy, versus a theoretical completely spherically round tense of energy.  Since I perceive that the space-time-fabric that is of one individually taken set of parallel universes, works to bear a total of 32 spatial dimensions plus time, I have concluded that not all confined spaces are of a flat-space or holographic nature.  Furthermore -- I perceive there are three sets of parallel universes, with one time dimension in common among these, -- since there is only one space-time-continuum.  It then makes sense to me, that Space-Time-Fabric is Volumed space overall.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Revision As To Conformal Dimension

If a given arbitrary superstring of discrete energy permittivity, that is to bear no scalar effect of a Lorentz-Four-Contraction -- is to work to bear what may be described of here as three discrete spatial dimensions plus time, over the course of any respective given arbitrary duration of BRST --  its conformal dimension will then tend to be:  2+(3^((3*10^8)/10^43)), (and anything taken to the zero-power is one), which is equal to 2+(~1) = ~3 spatial dimensions plus time. (Just a hare over the general number of spatial dimensions.)
So -- a given arbitrary superstring of discrete energy permittivity, that is to exhibit N number of general spatial dimensions, during any one given arbitrary duration of an iteration of BRST,  as a generic genus of an equational extrapolation, -- will work to bear a conformal dimension of:
(N-1)+(N^((the inverse of what the Lorentz-Four-Contraction will respectively be)/10^43)), or, in other way of exhibiting such a general idea for an equation may be written as:
(N-1)+(N^((the scalar amplitude of what the Polyakov Action will respectively be)/10^43)).
Again -- anything to the zero-power will be one, so, the conformal spatial dimension of any one given arbitrary superstring of discrete energy permittivity during BRST, will tend to always be just a tiny fraction of a scalar amplitude of numerical extrapolation -- above what its discrete spatial dimension will be.
Any discrete spatial dimensionality will always be of a specific integer value, yet, the conformal dimension will tend to always be just a basically insignificant fraction above such a general said discrete value.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sincerely, Samuel David Roach.

Immediately Adjacent Fadeev-Popov-Trace Eigenstates Of The Same Universal Setting

If one were to have the basic condition in the substringular, of there being in this case, two different distinct quanta of energy -- that are here to be of the same universal setting -- that are here to be immediately adjacent in time and space, -- then the covariant wobble that is here to be existent between the two said different distinct correlative respective Fadeev-Popov-Trace eigenstates ("Plank Phenomenon Related Phenomena") is to then to tend to be basically orthogonal, yet with a back-and-forth topological sway in this so-eluded-to vibrational oscillation, of ~1.104735878*10^(-81) degrees (~1.104735878*10^(-81)I degrees).  These said Fadeev-Popov-Trace eigenstates, are here to act as basically the particle-based nature that is of the two so-eluded-to quanta of discrete energy impedance -- that are here to be atoned to the holonomic substrate of the here inferred two overall discrete quanta of energy, that are of this particular case scenario.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Resultant Binary Lagrangian-Based Paths

If one were to initially have two different distinct orbifold eigensets, that are here to be traveling in a way in so as to be working to express two different respective unitary Lagrangian-Based paths, in such a manner, to where these two so-stated orbifold eigensets are here to spontaneously become Yukawa to one another in a symmetric way, that is both covariant, codeterminable, and codifferentiable at the Poincare level that is relative to the proximal local region in which these said eigensets are here to be transferred -- via the explication of their respective Fourier Transform, then, this may often work to help in causing these two different orbifold eigensets, that had initially been working to form their motion through space as two different distinct substringlar entities, that were here to start in so as to be forming a unitary Lagrangian-Based path, to then instead, to be working to form their motion through space, as a pair of distinct substringular entities, that are here to then form a dual tense of a binary Lagrangian-Based path, -- over the course of a relatively transient evenly-gauge Hamiltonian eignemetric.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Next As To Binary And Tertiary Lagrangian-Based Paths

If a given arbitrary tense of a cohomological stratum, that is here to be formed by the respective action of the Fourier Transformation, that is of a correlative given arbitrary bosonic orbifold eigenset, is to here to be of either a binary Lagrangian-based path or of a tertiary Lagrangian-based path -- then, such a tense of a cohomological stratum, is a bit more likely to work to then be of a Duboult (Dubeault) nature of cohomology -- than such a symplectic residue of motion would otherwise be, if that respective activity of the Fourier Transformation of the said correlative given arbitrary bosonic orbifold eigenset were to, instead, to be of a unitary Lagrangian-based path.  Consequently -- if a given arbitrary tense of a cohomological stratum, that is here to be formed by the respective action of the Fourier Transformation of a correlative given arbitrary bosonic orbifold eigenset, is to here to be of a unitary Lagrangian-based path -- then,  such a tense of a cohomological stratum is a bit more likely to work to be of a De Rham nature of cohomology -- than such a symplectic residue of motion would otherwise be, if that respective activity of the Fourier Transformation of the said correlative given arbitrary bosonic orbifold eigenset were to, instead, to be of either of a binary or of a tertiary Lagrangian-based path.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Binary And Tertiary Lagrangian-Based Paths

If an orbifold eigenset that is here of a Noether-based flow, is to bear a tense of motion that is go through the course of its translation from one spot to another in the substringular -- in such a manner, to where its transference through the fabric of space and time, may be described of by an interaction that is between two different distinct directorial-related equations, over the course of the same evenly-gauged Hamiltonian eigenmetric, to where such a motion-related path is NOT of any tree-amplitude-based nature, -- then, one may say here that the path of the said orbifold eigenset -- as it is here to be translated from one spot to another in such a manner -- may then tend to be described of as to here be moving through a binary Lagrangian-based path.  Furthermore -- if an orbifold eigenset that is of a Noether-based flow, is to bear a tense of motion that is to go through the course of its translation from one spot to another in the substringular -- in such a manner, to where its transference through the fabric of space and time may be described of by an interaction that is between three different distinct directorial-related equations, over the course of the same evenly-gauged Hamiltonian eigenmetric, to where such a motion-related path is NOT of any tree-amplitude-based nature, --  then, one may say here that the path of the said orbifold eigenset -- as it is here to be translated from one spot to another in such a manner -- may then tend to be described of as to here be moving through a tertiary Lagrangian-based path.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Unitary Lagrangian-Based Path

If the Lagrangian-based path of an orbifold eigenset, is to not only to be completely hermitian in the mappable-tracing of its covariant-based motion (in so as to be working to bear a De Rham cohomology), as well as the condition that such an orbifold eigenset is to here be moving, in so as to be displaying a trajectory-related course of motion, that is as according to only one common directorial-related equation of motion -- that is here to be translated over the span of an evenly-gauged Hamiltonian eigenmetric -- then, one may then tend to say that the Hamiltonian operand in which the said orbifold eigenset is here to be moving through, over time, may be thought of as being as a tense of what would here be a unitary Lagrangian-based path.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Tense Of Interaction Of Scattering

A Rayleigh scattering is one general tense of a Cevita interaction, -- whereas, a Reimman scattering is one general tense of a Wess-Zumino interaction.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

A Little More As To Hamiltonian Operator Versus Lagrangian

If any one given arbitrary phenomenon in the substringular, is of the nature as to being an example of a metric-gauge eigenstate -- it will then tend to act as being a tense of what may be thought of here as an example of a Hamiltonian operator,  however, -- if any one given arbitrary phenomenon in the substringular,  is of the nature as to being an example of a gauge-metric eigenstate -- it will then tend to act as being a tense of what may here be thought of as an example of a Lagrangian, that is here to happen along the fabric of space and time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The General Direction Of States Of Discrete Energy

While mass-bearing discrete quanta of energy tend to move in the direction of least resistance, electromagnetic-related discrete quanta of energy tend to move in the direction of least time, -- whereas, kinetic energy-related discrete quanta of energy tend to move in the direction that is most optimum to that interactive motion, that is here to be displayed among that motion of mass-bearing superstrings -- when this is here to be taken in its relative relationship to electromagnetic-related discrete quanta of energy.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Hamiltonian versus Lagrangian

Substringular Ward-Cauchy-related phenomenology that actually does "stuff," may be thought of as being -- in one manner or another -- examples of Hamiltonian operators.  Whereas, -- the actual superstringular motion of discrete quanta of energy over time, may be thought of as being -- in one manner or another -- examples appertaining to being of a Lagrangian.  Consequently, -- the holonomic substrate of superstringular phenomenology -- that is to perform a specific function in the substringular, may here to be considered as the general essence as to what a Hamiltonian operator is, whereas, the actual motion of such a just mentioned holonomic substrate of superstringular phenomenology, may here to be considered as the general essence as to what a Lagrangian is.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Rate Of iPI(del) Action

Let's initially consider a mass-bearing orbifold eigenset, -- that is thus, in part, comprised of mass-bearing superstrings of discrete energy permittivity.  As the here proximal local Polyakov Action is to either be increased or decreased in its scalar amplitude (magnitude), then, the directly affiliated Lorentz-Four-Contraction, is to here be respectively either to be decreased or increased.  This is because the Polyakov Action acts here, in so as to be an inverse operation -- of what is known of as the Lorentz-Four-Contraction.  For instance -- as such a said general tendency, such as the Polyakov Action, is to be increased (This is a case in which the correlative mass-bearing orbifold eigenset, is here to be slowed down), there is then to be an increase in the number of partition-based discrepancies, that are here to exist in those superstrings of discrete energy permittivity, that are here to exist in the directly corresponding orbifold eigenset, that would here be expressed to be of a correlative nature.  Consequently -- as a tendency such as the Polyakov Action, is to increase in its rate, -- then, the correlative rate -- as to an increase in the so-eluded-to Hodge-Index, that is here to be as of the number of partition-based discrepancies -- that are here to exist in those individually taken superstrings of discrete energy permittivity, that are here to work to comprise such an orbifold eigenset, will then tend to be increased in its scalar amplitude.  This increase here, will then tend to be inversely proportional -- to what will here be a decrease in the number of mass-bearing superstrings of discrete energy permittivity, that are here to work to comprise the said orbifold eigenset.  This would then work to mean, that there will here tend to be an increase in the rate of the directly correlative iPI(del) Action -- that is here to be proximal local to those mass-bearing superstrings of discrete energy permittivity, that are here to work to comprise the initially implied mass-bearing orbifold eigenset.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Partition-Based Discrepancies And Orbifold Eigensets

Let us initially consider a mass-bearing orbifold eigenset, that is here to be traveling at a constant rate -- that is here to be translated in a constant direction.  Over the whole evenly-gauged Hamiltonian eigenmetric, in which the said orbifold eigenset is to be traveling in a so-eluded-to constant velocity -- the Lorentz-Four-Contraction of the said mass-bearing orbifold eigenset is here to be maintained, when this is here to be considered as a specific scalar amplitude of a given arbitrary contraction.  This will then work to mean, that the so-eluded-to set of discrete energy quanta that are here to operate in so as to perform one specific function, will, over the proscribed metric of duration in which it is to be going at a constant velocity -- will then work here to bear a constant scalar amplitude of its directly corresponding Polyakov Action.  This will then consequently mean, that the individually taken mass-bearing superstrings that are here to work to help at comprising the said mass-bearing orbifold eigenset, will, over the course of the said Hamiltonian eignemetric, work to bear an unchanged number of partition-based discrepancies.  (Each mass-bearing superstring of discrete energy permittivity, that is to work to comprise an orbifold eigenset that is to be moving at a constant velocity -- will consistently work to bear the same number of partition-based discrepancies.)  Furthermore, since when an orbifold eigenset is to be consistent as to be working to bear the same Lorentz-Four-Contraction over a metric of duration, is to tend to neither gain nor lose mass spontaneously -- when there are here to be no other eminently pertinent considerations, that would work to help at causing an alteration in the mass of the so-stated orbifold eigenset -- then, such a mass-bearing orbifold eigenset will, over the said evenly-gauged Hamitonian eigenmetric, -- tend to be consistent at being comprised of by a constant number of mass-bearing superstrings of discrete energy permittivity. (And as an ansantz -- such a said orbifold eigenset will here, tend to be comprised of in this case, by a consistent number of mass-bearing discrete energy quanta.)  This is what would tend to be the case, in so long as there are here to be no ulterior discrete energy quanta, that would here to be becoming eminently Yukawa to the initially mentioned mass-bearing orbifold eigenset, in a Gliosisi-based manner -- to where this would then potentially work to alter the initially implied operation of the just mentioned mass-bearing orbifold eigenset.  To Be Continued!  Sincerely, Samuel David Roach.

Cohomology Of Mass-Bearing Neutrinos

When one is here to be considering the Fourier-related motion of a set of mass-bearing neutrinos, -- the cohomology that such a said phenomenology is thus to tend to form, will bear a silicone-like shape.  Please bear with me.  Consequently -- such a cohomology of a set of mass-bearing neutrinos, will bear a toroidal-like disk shape, at the general locus that is relatively most proximal to the so-eluded-to core-field-density, that is of the  respective set of neutrinos that are here to perform one specific given arbitrary function, -- that is of this given arbitrary case scenario.  Furthermore -- if one were now to take a Laplacian-related "snapshot" of the said cohomology-related eigenstate, of such a respective case, -- as one is to progress at analyzing the said eigenstate, as one is to extrapolate what is here being mapped-out in the correlative forward-holomorphic direction -- that is to be of such a given case, the correlative cohomology is to then to bear a hermitian-related decrease in its cross-sectional diameter, -- until, over a relatively transient distance, such a cohomology is then to apex to the "point" of working to bear one first-order point particle at the said forward-holomorphic tip of the respective cohomology, that is of the said set of mass-bearing neutrinos, that are of this given arbitrary respective case scenario.  This would mean, then, that the set of mass-bearing neutrinos, may work to bear a cohomology that works to bear a conical shape, that may be thought of as being configured as a multidimensional silicone-related holonomic substrate, that is here to work to bear a net abelian geometry over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Noether And Entropic Photons And Homotopic Residue

Electromagnetic energy that is not in the process of scattering, tends to maintain the condition of working to bear only one partition-based discrepancy -- per each individually taken iteration of instanton in which such a phenomenology is being kept as unscattered electromagnetic energy.  However, whenever a photon is to strike another phenomenon, in so as to scatter upon it -- the individually taken entropic photon will tend to, over the course of a total of 384 consecutive instantons upon Gliosis-based contact, toggle between gaining while then releasing, respectively one tense per individually taken instanton, bewteen 8,886,111 and 8,886,110 partition-based discrepancies, -- until such an entropic photon is to, if it will, re-quantize back into an electromagnetic beam of photons. (A phenomenon with a Yang-Mills light-cone-gauge topology that is partially Yau-Exact.)
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Tachyonic Motion And Homotopic Residue

Tachyonic activities -- meaning here, quantum leaps that are not Noether, -- work to compensate for the condition of electromagnetic energy to not be gaining nor losing partition-based discrepancies, per instanton, while such phenomenology is in the process of acting as electromagnetic energy.  The idea of homotopic residue, works to refer to the resultant of the exchange of the holonomic substate of the said homotopic residue, -- whereas, the Betti number refers to the condition of either the compactification (positive Betti number) or the decompactification (negative Betti number) of the cohomological generation or cohomological degeneration of a superstring.  When there is a discharge of cohomological eigenstates -- this often results in either the compactification or the decompactification of spatial dimensionality.  A superstring's dimensionality -- if of a cohological-related tense -- will tend to compactify during right before BRST, -- whereas, such a said superstring will tend to decompactify during the ensuing Regge Action.  Sincerely, Samuel David Roach.