Light Intensity And Orbifold Abrasion

The higher that the intensity of electromagnetic energy is, upon the proximal locus of the topological stratum of a given arbitrary orbifold eigenset, over a set group-metric of time, -- the more that there will be the potential tendency of there then being a higher density of infrared photons, that are to likely be at the said proximal locus of the topological stratum of the respective given arbitrary orbifold eigenset, over that same said group-related metric.  As said before, the higher that the intensity is, of infrared photons upon the proximal locus of the topological stratum of a given arbitrary orbifold eigenset, the more of a chance that such a tendency alone will then work to involve the resultant causation of oscillation-based distortions upon the said respective orbifold eigenset of topological stratum.  Therefore, the higher that the intensity of electromagnetic energy is, upon the proximal locus of the holonomic substrate of an orbifold eigenset of topological stratum is, the more likely that the correlative orbifold eigenset is to then to work to bear a higher tense of substringular abrasion -- since such an individually taken factor will tend to increase the tendency of working to form oscillation-based distortions upon the topological surface of the holonomic substrate of such a said respective given arbitrary orbifold eigenset --- if over the same duration of group-related metric.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Conformal Invariance And Lack Of Heat

A conformally invariant Ward-Cauchy-based setting, potentially tends to have orbifold eigensets that are to here to bear less abrasion than otherwise -- when it is to here be situated in a condition that works to bear a lower scalar amount of heat energy.  This will then work to mean, that a supercooled Ward-Cauchy-based region, will tend to potentially have less spontaneous oscillation based distortions -- if otherwise under the same Ward-Cauchy-based conditions than another similar region, that is to, instead, to bear a higher scalar amount of heat energy.  This will then mean, that the less of a density of infrared photons that are to exist from within the Ward-Cauchy-based bounds of a set substringular region, over the same duration of time -- then, the less of a tendency that there will be, if everything else were to basically be of the same general nature, that there will be the proximal local presence of oscillation-based distortions -- that would then be applied to the topological stratum of the holonomic substrate of the directly corresponding orbifold eigensets, that are to be present from within the Ward-Cauchy-based bounds of the respective given arbitrary set region that one would be discussing here. I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel Roach.

Heat And Orbifold Abrasion

A given arbitrary orbifold eigenset is said to work to bear the tense of working to form either a cohomological generation and/or a cohomological degeneration, that is of an abrasive nature -- when there is a significant scalar amplitude and/or a significant scalar magnitude of oscillation-based distortion, that is to happen to the external fringes of the topological stratum of the Ward-Cauchy bounds of the holonomic substrate, that is of such a said respective given arbitrary orbifold eigenset, over a set group-related metric.  Such a so-stated abrasive Ward-Cauchy-based condition -- is often produced, when there is a relatively high scalar amplitude or a relatively high scalar magnitude of heat energy, that is applied to the proximal locus of the topological-based stratum of such a so-stated orbifold eigenset, -- as it is to be going through a correlative Fourier Transform.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

As To Nature Of A Certain Substringular Perturbation

If an orbifold eigenset is to be altered out of a tense of Majorana-Weyl-Invariance -- into a net unitary-based holomorphic path, that is to be brought into a tense of working to bear an abrasive cohomological generation, then, such a perturbation out of the said state of Majorana-Weyl-Invariance -- is to be of a Rayleigh state of a scattering-based mode. Yet, if such an alteration out of a tense of Majorana-Weyl-Invariance -- into a unitary-based holomorphic path, is to be brought into a tense of working to bear a tightly-knit cohomological generation, then, such a perturbation out of the said state of Majorana-Weyl-Invariance -- is to be of a Reimman state of a scattering-based mode.  In so long as those eigenstates that work to form the resultant set of those complex roots, that work to form any potential either metrical-based and/or Lagrangian-based Chern-Simons singularities, are to act in so as to be of a high tense of a Ward-Caucy-related state of bearing little to no eigenindices of oscillation-based distortion, then, the so-eluded-to tense of scattering will then tend to be of a Reimman-based nature.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Substringular Jittering

Let us initially consider a given arbitrary orbifold eigenset, that is to be undergoing the physical condition of a state of superconformal invariance -- by oscillating in so as to be hovering at one general specific proximal locus -- in a state of Majorana-Weyl-Invariance, in such a manner in so as to be at both a Lagrangian-based and at a metrical-based steady-state Ward-Cauchy-based condition, -- over a set sequential series of group-related instantons.  Such a physical condition, will tend to mean, that, over the so-eluded-to group-metric -- that the composite discrete quanta of energy will be differentiating in a Fourier-based manner, in so as to work to form a set of Rham-based cohomologies, -- of which will then tend to neither spontaneously generate nor to spontaneously degenerate neither a net scalar amplitude nor a net scalar magnitude of significant cohomological residue, in so as to exhibit the Calabi-Yau behavior of then working to bear a relatively strong tense of a Yau-Exact nature, over the so-eluded-to transient duration of time in which such an orbifold eigenset is to be acting in such a so-eluded-to state of a Ward-Cauchy-based tense of "static equilibrium."  Let us next say, that an external force is to be applied to the Yukawa-based eigenindices of the topological stratum of the said orbifold eigenset -- in so as to work to perturbate the respective given arbitrary eigenset, to then move as a group of discrete energy quanta, into an overall holomorphic direction that is of a unitary-based nature, in such a manner in so as to then alter out of its state of conformal invariance -- at the so-eluded-to internal reference frame.  Such a perturbation in the sequential-based delineations of the Calabi-based eigenindices, that are of the said orbifold eigenset, will then work in this given arbitrary case, to generate a significant scalar amplitude and/or a significant scalar magnitude of cohomological indices -- in so as to then tend to, as well, to generate a genus of a Doubolt cohomology, that will then tend to form at least one set of Lagrangian-based and/or metrical-based Chern-Simons singularities, in the process of such a perturbation out of a substringular state of homeostasis.  Such a general genus of cohomological generation -- will tend to form at least one set of Lagrangian-based and/or metrical-based Njenhuis roots of singularity.  The nature of the covariant-based differentiation of such so-eluded-to complex roots, will then also tend to depend upon if the inferred scattering that is to happen here,  in so as to work to cause such a perturbation of the eigenstates of the orbifold eigenset-based Hamiltonian operand -- is to result in working to form adjacent eigenindices, that are either of an even chirality (Reimman scattering) or of an odd chirality (Rayleigh scattering).
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Poisson Integral And The Green Function

Let us consider here, a one-dimensional superstring -- of which is, over a sequential series of instantons, is to make a mappable-tracing of a flat-space cohomology, -- of which we are to here to only consider the two most directly corresponding spatially-related dimensional parameters, in this given arbitrary respective case.  Let's next say, arbitrarily, that one-thousand iterations of instanton are to  have just happened -- that are here to be involving the earlier mentioned one-dimensional superstring of discrete energy permittivity.  Let us next consider the Ward-based conditions of the so-eluded-to mapped-out two-dimensional cohomology, that is here to be most directly pertinent to the Hamiltonian operand that is to here to be most directly associated with the region that is to have been just covered by the Lagrangian-based path of the said one-dimensional superstring.  Given a relatively decent synapsis, as to the behavior of the said superstring -- as it had worked to have just formed what is to now to be a non-time-oriented world-sheet, that is to be considered here at a contextual framework, that is most explicitly in only two spatial dimensional parameters, -- as such a partially integrative cohomological texture is to now be considered in a Laplacian-based manner, in only two of its several spatial-based dimensional parameters.  Such a two-dimensional mapping-out of a cohomology, may be described of here as taking a respective Ward-Cauchy-based means of a Poisson Integral.  Furthermore, if one were to reverse the said Poisson Integral -- back into its initially translated superstring of discrete energy permittivity, that was to have just formed the region that had been mapped-out as a Poisson Integral -- such a process of taking the derivative of such a Poisson Integral, in so as to relate, in a Laplacian-based manner, the origin of such a Hamiltonian-based world-sheet in the substringular, -- may be done by utilizing what is known of as the Green Function.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Majorana-Weyl-Invariance And Cohomological Generation

The more tightly-knit that a tense of a Majorana-Weyl-Invariant-Mode is, when this is directly appertaining to the state of the conformal invariance that a given arbitrary Yau-Exact orbifold eigenset is to be going through -- the more that there is to here be a relatively even exchange of the correlative cohomological generation with the correlative cohomological degeneration that is here to be formed, over the respective given arbitrary group-metric in which such a so-stated orbifold eigenset is to be undergoing such a so-eluded-to relatively tightly-knit tense of a Majorana-Weyl-Invariant-Mode, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Yau-Exact Superstrings And Cohomologies

Yau-Exact superstrings are called Yau-Exact, in part, because such superstrings of discrete energy permittivity are utilized to work to comprise orbifold eigensets -- that are considered here to be, in fact, Yau-Exact -- because such eigensets tend to generate as much of a scalar magnitude and as much of a scalar amplitude of cohomology-based topological stratum, as these tend to work to degenerate as such, -- over time.
Again -- an orbifold eigenset is a set of one or more discrete quanta of energy, that work or operate in so as to be performing one specific given arbitrary respective function, -- at the physical cite of their correlative Ward-Cauchy bounds.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Wave Modulae And Doubolt Cohomologies

Let us say that one was to have an orbifold eigenset -- that was here to work to bear a wave modulus, that would here be of the nature of:  e^(lambda*the wave function), to where "lambda" would here be significantly greater than zero.  This would then mean, that the said orbifold eigenset would then:   1)Be of a Doubolt cohomology.  2)  Tend to work to bear an ellongated pulse.  3)  Work to bear a set of one or more Chern-Simons metrical singularities.  4)  Be generative of its external core-field-density eigenindices.  5)  Bear a Faro wave modulus.  6)  Work to bear spurious iterative Calabi-based singularities.  7)  Has more to do with a Clifford Expansion of its externalized core-field eigenindices.  8)  Will tend to bear an amplification of wave-related eigenvalues, that are of the directly corresponding Hamiltonian operation-based eigenstates.  & 9) Will tend to work to generate a significant scalar magnitude of the cohomological-based eigenindices, that are of the topological stratum that is to be Yukawa to the path of the resultant Fourier-based propagated Hamiltonian operand.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Wave Modulae And Rham-Based Cohomologies

Let us say that one is to have an orbifold eigenset -- that is to bear a tense of a wave modulus, that is to basically be of the nature of:  e^(lambda*the wave function), -- at which the "lambda" constant is to basically be zero.  This would then make the directly corresponding wave-based modulus, to be basically of a unitary nature (of the nature as to be appertaining to "one.") This would then work to mean, that the directly corresponding orbifold eigenset, is: 1) To be of a basically pure Rham-based nature.  2) To bear no spurious iterative singularities.  3)  To bear a directly corresponding cohomology, that will tend here to be heuristically Rham. 4)  To tend to bear a relatively high tense of Majorana-Weyl-Invariance -- at the immediately proximal local external-based reference frame, at the Poicare level. & 5)  To tend to neither significantly generate nor to significantly degenerate any cohomological topological stratum.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Lorentz Invariance

Let us consider one given arbitrary orbifold eigenset -- that is to here to be undergoing a respective proximal local relative state of Majorana-Weyl-Invariance.  Such an orbifold eigenset is to here to be existent under a tense of conformal invariance, that, let us here presume -- is to here to be translated via a Fourier-based Transformation, that is to here to be moving, at least transiently, at a relatively constant rate, over time.  At the Poincare level to the Gliosis-based topology of the external shell of such a said orbifold eigenset -- one may say that such an eigenset, as an eigenstate, may at least be exhibiting some sort of a transient tense of a state of Lorentz Invariance.  Next -- let us consider what is to here to be going on at the Poincare level to the Gliosis-based topology of those individually taken superstrings of discrete energy permittivity, that are to here to work to comprise the overall discrete energy quantum of the so-stated orbifold eigenset -- over that gauged group-metric, in which the said orbifold eigenset is, in and of itself, to be at least transiently Lorentz Invariant. Since such individually taken superstrings of discrete energy permittivity are to constantly to be moving the scalar magnitude of either both the Planck Length and/or the Planck Radius, per each succeeding iteration of group-related instanton -- the so-stated individually taken respective strings are to constantly be perturbating in their relative rate of Fourier-related Transform -- when this is taken in a general relation to both the existence and the motion of electromagnetic energy, per each succeeding so-stated iteration of group-related instanton.  Therefore -- at the Poincare level to the Gliosis-based topology of the holonomic substrate of any individually taken superstrings of discrete energy permittivity, -- such discrete increments of energy quanta are not to act here as being Lorentz Invariant, as such eigenindices that work here in so as to help at comprising the said orbifold eigenset, are to here to act as metrical-gauge-based Hamiltonian operators, that work together as a group, in so as to perform that specific respective given arbitrary function, that its so-eluded-to reverse-fractal-based orbifold eigenset is to operate in so as to do, as a Ward-Cauchy-based eigenstate, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

General Genre Of Cyclic Permutations

I can immediately think of three different general genre of cyclic permutations.:  1)These may be Calabi-based. -- There may be fluctuations in any one respective given arbitrary tense of a Majorana-Weyl-Invariant-Mode, that is Poincare to the so-eluded-to internal reference frame -- that is of the correlative topological stratum of the correlative holonomic substrate.  2)These may be metrical-based. -- There may be an analogous but different relatively proximal local gauging of the directly corresponding group-metrics, that may be effectual to the Gliosis-based topological stratum, that is here of the correlative holonomic substrate at the Poincare level.  &, 3)These may be Lagrangian-based. -- There may be analogous but different relatively proximal local Lagrangian-based paths, that may be attributed to the correlative metrical-gauge-based Hamiltonian activity that may be traversed, -- over the course of a directly corresponding Fourier Transformation, that would here be happening at an internalized gauged reference frame.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Cyclic Permutations Involving Ward-Supplemental-Based Paths

Let us initially consider an orbifold eigenset, that is to be traveling through an initially considered discrete Lagrangian-based path.  Let us say, that all of the sudden -- the said orbifold eigenset, is to be effected by the Chern-Simons-based condition of a Ward-Supplemental-based perturbation, upon the topological stratum of the holonomic substrate of the said orbifold eigenset.  This will then work to cause the said eigenset, to ensue at attaining an antiholomorphic Kahler condition.  Let us say that the said orbifold eigenset, is to be traveling through six spatial dimensions plus time, in this general respective given arbitrary case.  So, there are actually quite a number of possibilities as to what exactly are to be the arrangement -- of those respective complex roots, that are to here to be directly associated with the here resultant antiholomorphic Kahler-based Lagrangian path.  Let us next say, that the said eigenset is to then to reverberate back into one of its original parameters of homomorphism, in so as to then to work to attain an antiholomorphic Kahler-based condition, --  that may be attributed to it in the meanwhile.  This to, is to be associated with one of a number of a potential sets of arrangements of those respective complex roots, that are to here to be directly associated with the here resultant antiholomorphic  Kahler-based Lagrangian path.   Let us next consider this general genus of activity to repeat -- in an analogous but cyclical permutative manner -- to where, over a relatively spread-out group-metric, the same Lagrangian-based paths are Not to be identically mapped-out in the same fashion -- but in such a manner, to where there are here to be an iterative cycle of a set of similar but different combinations of complex roots, that are to work here in so as to help at working to form similar but different combinations of the resultant antiholomorphic Kahler-related Lagrangian-based paths.
 I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Degenerative Cohomologies

Any one said given arbitrary degenerative cohomology, will tend to be exclusively of a Doubolt nature.  Such a respective said general tense of a degenerative cohomological index, will tend to be both of an attenuated pulsation, as well as the condition that such a general genus of a cohomological metric -- will always tend to bear metrical-based Chern-Simons singularities, in the form of the directly corresponding complex roots, that are to be correlative to the corresponding perturbation in the Fourier translation of those eigenstates -- that have to had here just increased in the scalar magnitude of their metrical instability, over time.  Fourier-based transformations, that are to involve a degenerative cohomological index -- will often tend to also work to bear what would here be the presence of Lagrangian-based Chern-Simons singularities, that will here have more to do with an assymptotic approximation to what would otherwise be of a Rham-based cohomological index, than if the resultant Lagrangian-based path were to instead to be of a hermitian-based nature -- due to the general Ward-Cauchy-based condition, that such a degeneration will often tend to bear such a dampening of the metrical-based singularities -- that will as well help at working to cause the formation of a set of potential complex Lagrangian-based roots, via the resultant space-time translation that would here be imbued upon the holonomic substrate of the correlative Hamiltonian operand, that would thus be potentially formed over time, to where such Njenhuis singularities are here to be formed by the resultant Ward-Supplemental motion of the external core-field-density-related eigenindices of the respective Calabi-based manifold -- that had just been translated into a directly corresponding antiholomorphic Kahler condition, upon what would have initially been the presence of a relatively Njenhuis topological substrate of Hamiltonian operand space-time-fabric phenomenology.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Wave Modulae And Cohomological Generation

Let us initially consider the basic generic set-up, for the condition of the wave modulae of an eigenfunction.  What I am referring to is:  e^(lambda*the eigenfunction).  One may here come to grips with the three basic genre of the wave modulae of eigenfunctions, which would be:
1)  e^(lambda*the eigenfunction), when lambda is less than zero -- for degenerative cohomologies.
2)  e^(lambda*the eigenfunction), when lambda is zero -- for  purely Rham-based cohomologies.
&3) e^(lambda*the eigenfunction), when lambda is more than zero -- for  generative cohomologies.

Now, we will look at a specific example -- as to how this may be applied to a physical condition, at the sub-atomic level.:
One is to initially have a loose electron -- that is of a basically Rham-based cohomology -- to where the cohomological index is to neither work to bear a degenerative nor a generative cohomology.(lambda~0).
Next -- the said electron is to be magnetically pulled into the Ward-Cauchy-based field of an atom -- to where the cohomologies that the electron are to form are to now be of a net generative nature, to where lambda is here to be greater than 0.  (This is to then be related to what may be called a Faro wave function modulae.)
Next -- the said electron is to be struck by a photon -- to where there is the eminent formation of an antiholomorphic Kahler condition -- to where there will thus be the formation of a basically degenerative cohomological index.  In the process, as the electron is to be struck via a Calabi-Yau interaction, in the process of it going into an antiholomorphic Kahler condition, -- it is to first drop an energy level (towards the nucleus of its correlative atom), while then going back an energy level (away from the nucleus of its correlative atom) -- to where the said electron is to then to release a discrete quantum of energy, in the form of a photon, through the Fujikawa Coupling, via the Green Function.
I will explain cohomological generation later!  To Be Continued!  Sincerely, Samuel David Roach.

Multidimensional Kahler-Metric And Instability In Proximal Local Field

Let us initially consider an orbifold eigenset -- that is to here to be comprised of the holonomic substrate of the Ward-Cauchy-based phenomenology of bosonic superstrings, that are to here to be moving through ten spatial dimensions plus time -- through a relatively discrete Lagrangian, over time.  Let us next say, that the so-stated orbifold eigenset is to soon be perturbated into then working to bear an antiholomorphic Kahler condition.  The potential resulting Ward-Supplemental "reverberation" of the so-eluded-to topological substrate, that is of the said orbifold eigenset, may then tend to work to bear significantly more potential complex roots, as to the mappable-tracing of the resultant potential world-sheets -- that is related to what I mean of as to the potential mapping-out of the Lagrangian-based path of the so-eluded-to "reverberation," that will here be of the so-stated Kahler-Metric, -- than if the said orbifold eigenset were to, instead, be traveling through only three spatial dimensions, plus time, -- in the process of working to undergo the Kahler-Metric in a Gliosis-based manner, in such a way that would then be initiated upon those superstrings that are to here to work to comprise the said orbifold eigenset.  This  would  then work to mean, that the more spatial dimensions that an orbifold eigenset is to be traveling through -- in the process of going through an antiholomorphic Kahler condition -- the more of a tendency that there will then be, of the condition of there then being a higher scalar magnitude of the proximal local related topological instability of the directly corresponding Hamiltonian operand that is to here to be considered at the Poincare level, in the process of the perturbation of the resultant mapped-out Lagrangian-based path, than if there were, instead, to be an antiholomorphic Kahler condition that were to be traveling through fewer spatial dimensions, over time.  I will continue with the suspense later!
To Be Continued!  Sincerely, Samuel David Roach.

Reimman Scattering And Relative Lack Of Entropy

When one is to have the general premiss -- as to the correlative Ward-Cauchy-based conditions of any directly corresponding substringular situation, to be of such a nature, to where there is here to be a relative lack of entropy -- then, there is to be, in such a case, a hightened probability as to the potential presence of what would here be a higher relatively proximal local density of the sum of the correlative individually taken Reimman scatterings, -- as well as there to here be a lowered probability as to the potential presence of what would here be a lowered relatively proximal local density of the sum of the correlative individually taken Rayleigh scatterings.  The higher the scalar amplitude of the integrative sum of the intensity of the relatively proximal local respective given arbitrary Reimman scatterings -- that are to be present here, the more likely that there it to be -- at the general region of the parametric Ward-Cauchy-based stratum that is here being implied, in which such scattering is to here to be taking place, the relatively lower scalar magnitude that the general Ward-Cauchy-based conditions of entropy will then tend to be, from within the physical confines of the just mentioned Ward-Cauchy-based parametric region.  I will continue with the suspense later!  To Be Continued!
Sincerely, Samuel David Roach.

Entropy And Rayleigh Scattering

Whenever one is to have the proximal local presence of entropy, one will have at least one or more eigenmetrics of a Rayleigh scattering, that will be of the re-distribution of the holonomic substrate of the correlative Ward-Cauchy-based eigenindices -- that are here to be re-distributed.  Entropy is, most intrinsically thought of -- as a general condition of disorder.  Whenever there is a proximal local general condition of disorder, then, there will be at least one or more eigenmetrics of an annharmonic-based scattering.  An annharmonic-based scattering, is a scattering in which the adjacent scattered eigenindices are here to bear an odd chirality.  Such a general tense of an annharmonic scattering, may here be called a Rayleigh scattering.  This  is why the general condition of entropy, will always work to involve at least some manner or degree of the process or of the processes of the state of a Rayleigh scattering.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Orbifold Eigensets And Entropy

Here's a relatively simple one.  Let us initially consider an orbifold eigenset, that is to be moving through a proximal local field -- to where this said field that the said eigenset is to be moving through, is of a relatively entropic nature.  The more entropic that this said proximal local field is -- when in terms of the scalar amplitude of such a condition of the so-eluded-to entropy -- the less likely that the so-stated respective given arbitrary orbifold eigenset, that is to be traveling through such a field, is to bear a prolonged structural integrity over time.  Consequently -- the less entropic that this said proximal local field is -- when in terms of the scalar amplitude of such a condition of the so-eluded-to entropy -- the more likely that the so-stated respective given arbitrary orbifold eigenset, that is to be traveling through such a field, is to bear a prolonged structural integrity over time.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Reimman Scattering And Structural Integrity

Let us initially consider an orbifold eigenset -- that is formed, via the respective Fourier-based translation of a Reimman-based scattering.  The higher that the scalar amplitude of the Hamiltonian-based pulse is, of a respective Fourier-related Reimman scattering -- that is to work to put together the components of one respective given arbitrary orbifold eigenset, -- the higher that the tendency will then be, of the thence formed orbifold eigenset, to have a prolonged structural integrity.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Strucural Fortitude Of Orbifold Eigensets

The higher that both the combined fractal modulae and elastic modulae of the eigenindices that work to help to comprise any one given arbitrary orbifold eigenset is, as well as the higher that the combined fractal modulus and the elastic modulus of the topological-based holonomic substrate is -- of the said respective given arbitrary orbifold eigenset will happen to be -- the more likely that the said respective orbifold eigenset will then tend to bear a prolonged structural integrity, -- than if such a so-stated general Ward-Cauchy-based set of conditions were to, instead, to tend to bear a lower scalar amplitude of both of such general tenses of fractal and elastic conditions of modulae.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Two Of Holomorphic Direction Of Orbifold Eigenset

The structure of an orbifold eigenset -- when this is taken into consideration along with both the fractal modulae and the elastic modulae of its component eigenindices, as well as along with both the fractal modulus and the elastic modulus of its overall Ward-Cauchy-based topological holonomic substrate -- works to help at influencing the tendency that any said respective given arbitrary orbifold eigenset will have, -- in regards to its holomorphic Fourier-related flow, that is of the directly corresponding radial and orbital oscillations by which such an orbifold eigenset is to twist through, -- as such an oribifold eigenset is to move through its correlative Hamiltonian operand, via its Lagrangian-based path, -- over the ensuing sequential series of group-related instantons.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Holomorphic Direction Of Orbifold Eigenset

Let us consider the tendency for the holomorphic direction, of any one given arbitrary discrete energy quantum, that is of one particular genus of such a discrete quantum of energy.  (P.S.  The following is a general theoretical condition, in so as to help at eventually being able to understand what one is to be working towards, when one is here to be considering an actual case scenario).  Let us next, consider that there is to be a relatively large Hodge-Index -- as to the number of those discrete quanta of energy, that are to here to be present, from within the Ward-Cauchy-based bounds of one respective given arbitrary orbifold eigenset -- of which are to each be of that same general genus of discrete energy quanta, that the respective initially mentioned discrete quantum of energy was of, that I had brought-up at the beginning of this given post.  The influence that is to then to be attributed towards the holomorphicity of the respective given arbitrary orbifold eigenset, that is of the general genus, that is of the initially so-eluded-to genus of discrete energy quanta that I had inferred at the beginning of this post, will then tend to be the resultant average holomorphic direction, that is to then to be attributed to the net mean Lagrangian path, that one is to be able to extrapolate, -- when one is given the overall differential geometry that is to here to be related to the initial Laplacian-based Ward-Cauchy conditions -- that are here to be in correlation to the differential geometry of the initial substringular conditions, via which motion of the discrete energy quanta of the said orbifold eigenset is to be Yukawa to, over time. This will then help one to be able to then have a better ability to extrapolate the ensuing directoral-based holomorphicity of such a case, of the here said given arbitrary orbifold eigenset, over the ensuing sequential series of group-related instantons. I will continue with the suspense later!  To Be Continued! Sincerely, Sam Roach.

Electrons And Holomorphic Direction

Let us initially consider an electron.  Furthermore, let us consider the mass-bearing superstrings of an electron, -- as such Calabi-Yau-based superstrings of discrete energy permittivity are to exist here, in so as to work to come together as part of the said electron, -- to where the electron, as a unit, is to act here as an orbifold eigenset.  Let us next consider an individual mass-bearing superstring of discrete energy permittivity, that works to help at forming the said electron, to where that electron of this case is here to act as an orbifold eigenset.  The Calabi-Yau field of such mass-bearing states, is to here to bear a proximal local shell-like toroidal-shaped cohomological-based surface, at the Poincare level to its external core-field-density.  The so-eluded-to Calabi-Yau eigenstate, that is here to act as a mass-bearing eigenindex, that is of the said electron, is to theoretically act in such a manner -- in so as to work to bear a tendency of tugging to bear its relatively forward-holomorphic direction in the mean Lagrangian path, that is to exist right in-between both the directoral-based delineation of the angular momentum that is in the direction of its edge, as well as also existing right in-between the directoral-based delineation of the angular momentum that is in the direction of its anuulus.  Next, consider the integration of all of the so-eluded-to mass-bearing superstrings of discrete energy permittivity, that are to theoretically comprise the "rest mass" of the so-stated electron.  Each of such Calabi-Yau-based strings is to tend to behave in such a way, to where these are to heuristically lean-in towards the multiplicit-based earlier mentioned mean Lagrangian path -- that lies in-between the multiplicit edge and the multiplicit anuulus of the so-eluded-to Gliosis-Sherk-Olive (GSO) toroidal-based cohomological-based field.  The resultant of such a tendency, is to then to work in part, to help influence, along with the main influences of its charge and its magnetic field in relation to the general protonic field that it is attracted to, -- the Ward-Cauchy-based conditions that are related to the general manner of the spin-orbital momentum of the said electron, over time.  I will discuss more later, -- the more prominent influences of charge upon the magnetic field of sub-atomic particles, -- which happens in so as to work more at helping at producing the spin-orbital momentum of an electron.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

As To Kahler-Metric Preparation

As the Wick Action works to indirectly cause the initiation of the Kahler-Metric to become Gliosis upon that discrete quantum or quanta of energy that is to ensue, in so as to bear a Gaussian Transformation, -- once there is the presence of a viable antiholomorphic Kahler condition, that is to be attributed by the manner of the activity of either the here pertinent discrete quantum or the discrete quanta of energy -- that is to then to work to undergo the said Gaussian Transformation, -- the resulting domino effect of the Fourier-based activity that is to here to be most directly associated with the said initiation of the said Gliosis-associated Metric, will then be directed in so as to help at working to allow for the Fischler-Suskind-Mechanism eigenstate that is most associated with the respective given arbitrary discrete energy, that is to be undergoing such a so-stated transformation, to be happening at an optimum proximal locus, so that the directly associated eigenstate of the holonomoic substrate of the Klein Bottle will be delineated at such a locus, to where the ensuing Gliosis-related translation of the said Kahler-Metric eigenstate is to be positioned where it should, so  that those fractals of discrete energy may be re-attained by the here pertinent energy quantum or quanta, so that discrete energy may both persist and exist.  I will continue with the suspense later!  To Be Continued!
Sincerely, Samuel David Roach.

Antiholomorphic Kahler Conditions And Ward-Supplemntal Paths Of Energy

Let us initially consider an orbifold eigenset -- that is to here be moving in its relative forward-holomorphic direction, over an initial proscribed duration of time.  Let us next consider -- that the said orbifold eigenset, is to then to be perturbated into moving into an ensuing reverberative path, that is Ward-Supplemental to the initial so-eluded-to Lagrangian-based path, that the so-stated orbifold eigenset was initially be moving in.  The orbifold eigenset is to here be moving in perhaps as many as ten spatial dimensions plus time -- over the entire "journey" by which the so-stated eigenstate is to be moving, as a holonomic substrate that is to have here, just worked to bear an antiholomoprhic set of Kahler-based conditions.  Since the said orbifold eigenset is to here be moving in ten spatial dimensions plus time, -- the so-eluded-to perturbation-based reverberation of the said eigenset, is to not necessarily be fully backtracking in its steps, in the process of the given arbitrary respective motion of the orbifold -- to here be working to form a set of  antiholomorhpic Kahler conditions.  Just as the said orbifold eigenset is to reverse in its relative holomorphicity,  the just mentioned general genus of activity will act here, in so as to work indirectly in so as to form a Wick Action eigenstate.  Such a Wick Action eigenstate will then indirectly work, in so as to lead-up into working to help at causing the proximal local Kahler-Metric to soon be Gliosis upon the topological stratum of the holonomic substrate of that discrete energy quanta, that is to here to work to form the so-stated orbifold eigenset of this given  arbitrary case scenario.  To Be Continued! Sincerely, Sam Roach.

More As To Mass And Gravity

As said before in my blog, the gluonic force, as well as those forces that are under Ward-Cauchy-based conditions that behave in the same general manner as the gluonic force, is that general genus of force -- that is located at the relative multiplicit centralized knotting of the multivarious Rarita Structure eigenstates.  It is the multiplicit array of the Rarita Structure eigenstates, that work to act as the generic holonomic substrate, whereabout the multiplicit gravity waves are to act as metrical-gauge-based Hamiltonian operators, whereby the force of gravity is to then to be taken into effect -- when such Rarita Structure eigenstates are to indirectly act in both a covariant, a codifferentiable, and in a codeterminable manner at a multiplicit proximal locus, -- that tends to be most interactive on the general relative Real Reimmanian Plane -- with particles that may be called both gravitons and gravitinos, -- at a multiplicit proximal locus that tends to be most interactive on the general relative Njenhuis Plane.  Mass-Bearing strings tend to differentiate in a Fourier-based manner, that is of a Yau-Exact nature.  This means, that the homotopic torsioninal eigenindices, that are directly appertaining to the twisting behavior of the holonomic substrate of such mass-bearing strings -- are to move in such a holomorphic-based manner, to where their twisting-related activity, as such a so-eluded-to discrete quantum of energy is to initially be considered in so as to move as a vector-based unit in as many spatial dimensions as the number of spatial derivatives that it is changing in, is to, as well, to torque or twist as a tensor in as many spatial dimensions as the number of spatial derivatives that it is changing in.  So, when a discrete bundle of an electromagnetic quantum of energy is to act in so as to strike the externalized core-field-density of the light-cone-gauge eigenstate of a mass-bearing discrete quantum of energy, the resultant Schwinger-Indices that act as gravity waves, that are thence formed by the consequent hermitian-moving discrete energy field, will tend to form a general genus as to that Rayleigh scattering of the correlative photonic field, that will then work to bear the reaction of a Reimman scattering of the resulting fluctuating Rarita Structure eigenstates -- as the consequently formed gravity waves are to thence to bear a tendency of bearing a positive wave reinforcement, that is to be tugged into a consequent euler-delineated Clifford Expansion of the scalar amplitude of the relative gravitational force.  This is part of the puzzle as to why mass is key to gravity.  To Be Continued!  Sincerely, Samuel Roach.

The Flow Of Energy Through Time

At group-related instanton -- the correlative discrete quanta of energy are pretty-much basically at a standstill, -- even though there is still a great deal of viable activity that is to be happening to the said discrete quanta of energy, during the so-eluded-to discrete increment of time.  Right after group-related instanton, -- the superstrings go into the generally unnoticed duration of Ultimon Flow.  Right before the ensuing generally noticed duration of Ultimon Flow, -- just as the discrete quanta of energy are to then be fully encoded for, in so as to then to work to reach their next delineation, -- then, these said discrete quanta of energy are to then to iterate again at their ensuing positions, over the course of the ensuing group-related instanton.  The multiplicit successive series of group-related instantons, via the multiplicit successive series of the delineations of the discrete quanta of energy -- is, in general, the flow of energy through time.  To Be Continued! Sincerely, Samuel David Roach.

Norm-State-Projection Eigensets

Let us initially consider a set of norm-states, that work to perform one set of functional operation.  Such a Hamiltonian operator that is to here to consist of a group of cohesive norm-states, may here be called a norm-state-projection.  Furthermore, a set of norm-state-projections that operate as a group, in so as to work to perform one specific general function, may be called a norm-state-projection eigenset.  Let us next consider, in general, the array of gauge-metrics, that are here to be most directly pertinent to those sub-Fourier-based kinematic activities, that take place from a scope that takes place in less than one discrete increment of time.  None of such gauge-metrics are to here to be able to go an exact integer number into one discrete increment of instanton, to where, although any duration that is of a viable import to any living being, will tend to bear a discrete number of instantons, yet, any of such so-eluded-to gauge metrics that are here of a sub-Fourier-based tense, will tend to never bear an exact integer number of those said gauge-metrical-based durations into any viable time, to where these are here to occur at a level that takes place in less than one discrete increment of time.  Let's now consider a superstring, as it is eminent in its Yukawa-based inter-relationship with the Kahler-Metric, in a Gliosis-based manner.  Let us next consider the four general stages that such a directly affiliated discrete quantum of energy is to be involved with, over the course of one correlative individual instanton.  There will tend to be one norm-state-projection eigenset -- that is to be involved with that decompactification that is involved with the Polyakov Action.  There will tend, as well, to be one norm-state-projection eigenset -- that is to be involved with the main part of BRST, during the remainder of that said iteration of the respective proximal local Polyakov Action egienstate.  There will also tend to be one norm-state-projection eigenset -- that is to be directly associated with the eminent Yukawa-based inter-relation, that the said discrete quantum of energy is to bear with the holonomic substrate of the correlative Klein Bottle eigenstate, in a Gliosis-based manner, with the correlative increment of the Kahler-Metric -- right after the respective so-eluded-to iteration of the proximal local increment of BRST.  And, there will also tend to be one norm-state-projection eigenset -- that is to be directly involved with the directly associated discrete quantum of energy, that has been in the process of being in a Gliosis-based relationship to the Kahler-Metric, as the said discrete quantum of energy is to be going through the ensuing correlative Regge Action eigenstate -- at the relative ending part of instanton.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.