Clarity As To Scatterings

When one is to have a Reimman scattering -- the adjacent scattered eigenindices are chiral, with an even chirality-based parity, -- whereas, when one is to have a Rayleigh scattering -- the adjacent scattered eigenindices are antichiral, with an odd chirality-based parity.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Lagrangian-Based Cohomological Generation

Let us initially consider one given arbitrary orbifold eigenset -- that is in a state of superconformal invariance, -- at one respective given arbitrary proximal locus.  Such a respective orbifold eigenset, is here to be of a Rham-based cohomology -- that is here to tend to generate as much cohomological eigenindices as it is here to degenerate, over a gauged-metric, that is of an even Hamiltonian metrical function.  Such an orbifold eigenset is here to tend to be of a Yau-Exact nature, in so long as the topological stratum that works to comprise the said orbifold eigenset, is of a Calabi-Yau nature.  In this case, both the resultant formed Lagrangian-based singularities and the resultant formed metrical-based singularities, will tend to be of a hemitian nature, over the so-eluded-to proscribed guaged-metric.  Let us next say, that a group-attractor is to act upon the holonomic substrate of the said orbifold eigenset -- to where the so-stated eigenset is to then to all of the sudden act, in so as to then be generating a net of cohomological eigenindices, in the relative forward-holomorphic direction.  Now, the orbifold eigenset in question, is now to be of a Doubolt-based cohomological setting, instead of being of a Rham-based cohomological setting, -- as the said orbifold eigenset is now to no longer be of a superconformally invariant nature.  The orbifold eigenset is to then to work to bear at least one set of Lagrangian-based Chern-Simons singularities, -- to where it is to consequently to bear at least one respective set of complex roots, that may here work to describe the Ward-Cauchy-based nature of such path-related resultant changes, that are in the differential curvature that is here to be related to the perturbated motion of the said orbifold eigenset.  In so long as the so-eluded-to set of superstrings that work to comprise the one respective Hamiltonian operator of this case (the said orbifold eigenset that is here being discussed), are not be alter in the nature of their group-related pulsation -- over the duration of the so-eluded-to changed nature of the motion of the said orbifold eigenset -- then, there isn't the tendency of the formation of metrical-based Chern-Simons singularities in the overall said process.  I will continue with the suspense later!  To Be Continued!
Sincerely, Sam Roach.

Part Two Of Bundles Of Covariant Energy

Let us consider two different sets of orbifold eigensets -- that are to interact here, in a manner that is to be both covariant, codeterminable, and codifferentiable, -- as the two said given arbitrary orbifold eigensets are to act as two tenses of energy, that are to interact in an interdependent manner, over a relatively transient duration of time.  Let us next consider one of the two mentioned orbifold eigensets as being of a vector-based bundle, whereas, the other of the two mentioned orbifold eigensets is as being of a tensor-based bundle.  The orbifold eigenset that is to work to bear a vector-based bundle of cohomology, is to act in so as to exist in a tense of superconformal invariance -- to where the so-eluded-to cohomology that is thus formed by the Fourier-related differentiation of the said orbifold eigenset -- is to be of a Rham-based cohomology.  The orbifold eigenset that is to work to bear a tensoric-based bundle of cohomology, is to act in so as to exist in a tense of bearing a relative lack of superconformal invariance -- to where the so-eluded-to cohomology that is thus formed by the Fourier-related differntiation of the said orbifold eigenset, is to be of a Doubolt cohomology.  Such a dual state of the resultant activity that is here to happen, due to the interaction of the two said orbifold eigensets -- as these two sets of superstrings are to traverse through their correlative Fourier-related transforms -- may then be said to bear a tense of tending to bear a state of behaving in manner that is partially Yau-Exact, over time. I will continue with the suspense later!  To Be Continued!
Sincerely, Samuel David Roach.

Bundles Of Covariant Energy

Let us initially consider a pulse of discrete energy, that is here to be comprised of two different covariant, codeterminable, and codifferentiable sets of orbifold eigensets.  Let us next consider here, the cohomological path that the so-eluded-to pulse of energy that is to here to be considered, is to work to form.  Next, let us consider that each individually taken orbifold eigenset of this case, -- is to work in so as to form a Hamiltonian-based bundle of cohomological-related eigenindices, -- that are here to be distributed along two covariant genre of Lagrangian-based path eigenstates.  Furthermore, let us next consider that the first respective given arbitrary mentioned Lagrangian-based eigenstate, is to work to form a Hamiltonian operand -- that is of a vector bundle of cohomological eigenindices.  Next, let us say that the other respective so-eluded-to Lagrangian-based eigenstate, is here to work to form a Hamiltonian operand -- that is of a tensoric-related bundle of cohomological eigenindices.  The vector-related bundle here mentioned, will tend to bear a hermitian Lagrangian-based path, that may be described of here as existing with Real Reimmanian-related roots.  The tensoric-related bundle here mentioned, will instead, tend to bear a Chern-Simons Lagrangian-based path, that may here be described of as existing with Njenhuis or complex-related roots.  As long as there are here to be no metrical-based Chern-Simons singularties -- in the overall energy of this given arbitrary respective case, the respective hermitian Lagrangian-based path mentioned here, will tend to move in the direction of being of the Ward-Cachy-condition of having a Yau-Exact nature. Whereas, the respective Chern-Simons Lagrangian-based path mentioned here, will tend to either significantly generate or degenerate cohomological-based eigenindices -- to where it will not be as such of a Yau-Exact nature.  Furthermore, such a lack of metrical-based Chern-Simons singularities in this said overall case, would eluded-to the said overall tense of energy of this case, as either approaching and/or attaining a tense of being partially Yau-Exact.
I  will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

More As To Calabi-Based Cyclic Permutations

Let us initially consider one given arbitrary orbifold eigenset, that is moving through a Lagrangian-based path -- that is either generating or degenerating cohomology, -- over a correlative gauged-metric.  In so long as the Lagrangian-based path, that the said orbifold eigenset is to be moving through, is of a discrete nature, -- the said eigenset is to bear metrical-based Chern-Simons singularities, yet it is not to bear any Lagrangian-based Chern-Simons singularities, -- to where the directly corresponding Lagrangian-based path, is to tend to be of a purely hermitan nature, over the said gauged-metric.  Think of the following reverse-fractal case.  Do you remember the condition that, when we interact with atoms, how we tend to basically just interact with the electrons of these atoms, in our general daily experience?  Electrons may be perceived of as being the "shell" of an atom.  Next, going back to what I was saying before -- let us say that the so-stated orbifold eigenset that is of this main case scenario, were to go through a cycle of morphological permutations, over time.  Such changes in the morphology of the eigenindices of the said orbifold eigenset, are to tend to be of a change in the "shell-like" morphological eigenindices, that are of the topological stratum of the said respective orbifold eigenset.  Such a cyclical pattern of the morphological permutation of a Ward-Caucy-based phenomenon, such as of an orbifold eigenset, may be said to be of the genus or of the nature of being called a Calabi-based cyclic permutation.  I will continue with the suspense later!  To Be Continued!
Sincerely, Samuel David Roach.

Signal Fading In And Out

Let us initially consider a given arbitrary electrical signal, that is to go through a series of activity -- in which the said signal is to fade in and out, over a relatively set gauged duration of time.  As the said electrical signal is to be in the process of fading into existence -- the directly corresponding electrical energy, that is here to work to form the said electrical signal, will be in the process of being generated.  As such so-stated electrical energy is here to be in the process of being generated, -- those orbifold eigensets, that are here to work to comprise that electrical energy, that is thus to work to form the said electrical signal, is to then to tend to be in the process of working to generate cohomology.  So, as the said electrical signal is to be in the process of fading out of existence -- the directly corresponding electrical energy that is here to work to form the said electrical signal, will be in the process of being degenerated.  As such so-stated electrical energy is here to be in the process of being degenerated, -- those orbifold eigensets, that are here to work to comprise that electrical energy, that is thus to work to form the said electrical signal, is to then to tend to be in the process of working to degenerate cohomology.  I will continue with the suspense later!  To Be Continued!
Sincerely, Samuel David Roach.

As To The Generation And The Degeneration Of Cohomology

As energy is being generated over time -- those given arbitrary orbifold eigensets, that are directly corresponding to this said energy, are to then to tend to be generating cohomology. As the said orbifold eigensets are here to be generating cohomology -- these are to be traveling here, in so as to work to form a Doubolt cohomology -- in which there is to be both at least one respective correlative metrical-based Chern-Simons singularity thus formed, and/or at least one respective correlative Lagrangian-based Chern-Simons singularity thus formed.  Such a process of a generative cohomology, will tend to amplify and/or augment the scalar magnitude of the here pertinent energy, over time.  Furthermore, as energy is being degenerated over time -- those given arbitrary orbifold eigensets that are directly corresponding to this said energy, --  are to then to tend to be degenerating cohomology. As the said orbifold eigensets are here to be degenerating cohomology -- these are to be traveling in so as to work to form a Doubolt cohomology, in which there is to be both at least one respective correlative metrical-based Chern-Simons singularity thus formed and/or at least one respective correlative Lagrangian-based Chern-Simons singularity thus formed in the process.  Such a process of degenerative cohomology -- will tend to dampen and/or atenuate the scalar magnitude of the here pertinent energy, over time.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Some Substringular Activity In Laymens Terms

Let us consider the following metaphorical analogy, -- in so as to work to improve the reader's perspective, as to what is going on in the Ward-Cauchy-based bounds of the substringular realm -- by relating as to what is happening here, in pretty-much laymens terms.  Let us say -- in this analogy -- that one is to be the orbifold eigenset in and of itself.  The so-eluded-to person is to be moving in a direction-based path, in so as to reach a given arbitrary physical destination.  The person -- as a metaphorical orbifold eigenset -- is to then to be the allegorical Hamiltonian operator.  The region that is to be traversed, from the point of origin -- to the point of destination -- is to be the allegorical Lagrangian-based path.  The medium that one is to be moving through, over the course of moving along the said Lagrangian-based path, is the allegorical Hamiltonian operand.  What one is doing in the process of moving through the said allegorical Hamiltonian operand -- is the metaphorical Hamiltonian operation.  If one is to be making a straight shot from the point of origin to the point of destination, then, one may then say that the path as to where one had just traveled, is of a discrete unitary Lagrangian-based path.  Even if the path that is here to be traversed, is not of a directly straight translation over time, -- if the path that is to be traversed, is of one smoothly taken genus of motion, then, the path is of a discrete Lagrangian-based path.  And, if the path that one is to here to metaphorically take -- is to be done in a bunch of jagged motions, then, the translated Lagrangian-based path is not discrete.  Next, translate what I have just conveyed -- to what is happening at the Ward-Cauchy-based level of the substringular, and, you will then get a better idea as to some of what I have tried to teach you, about the cohomological-related mappable-tracing of the motion of orbifold eigensets, over time.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Partials As To Lorentz-Four-Contractions

Let us initially consider an orbifold eigenset, as I had described yesterday -- of which is a set of superstrings that operate in so as to perform one specific function, that goes from being of a superconformal invariant nature, to then scattering briefly into a looser mode of Majorana-Weyl-Invariance, to then scattering back into a tighter tense of conformal invariance, and back again, and so on.  Let us next say -- that as this is happening, the field of the said orbifold eigenset as a whole, is to be otherwise tending to be traveling in the relative holomorphic direction at a constant rate.  In this manner -- there are to here to be two different general partials of the correlative Lorentz-Four-Contraction, that are to be Yukawa to the so-eluded-to Fourier differentiation, that is of the said orbifold eigenset, in this just mentioned process.  There is to be that Lorentz-Four-Contraction partial, that is due to the directly pertinent tense of the scalar amplitude of the extent of the directly corresponding Majorana-Weyl-Invariant-Mode, that is to be differential in its Yukawa influence upon the so-stated orbifold eigenset, -- and, there is also to be that Lorentz-Four-Contraction partial, that is due to the directly pertinent tense of the scalar amplitude of what would otherwise be the tendency of a motion that is in the relatively metrical smooth holomorphic motion of the said orbifold eigenset, as it is here to be translated as a whole, across what may be termed of here as an approximate discrete unitary Lagrangian path, that is to bear both a codifferentiable and a codeterminable cohomological wave-tug -- across the space-time stratum of both that Hamiltonian operand that is in the direction of the region of its perturbative Majorana-Weyl-Invariant-Mode, as well as that Hamiltonian operand that is of the tendency of moving in the relatively holomorphic direction of the region of the mappable-tracing of the just mentioned discrete unitary Lagrangian path.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Perturbations In Superconformal Invariance

Let us initially consider one given arbitrary Calabi-Yau-based orbifold eigenset, that is to be initially set in one tense of superconformal invariance -- at the reference frame that is Poincare to the externalized core-field-density of the so-eluded-to mass-bearing orbifold eigenset, that is of this particular respective case scenario.  Let us next say that the scalar amplitude, as to how tight that this tense of superconformal invariance is upon the topological stratum of the said externalized core-field-density of the said orbifold eigenset, is now to be perturbated in a reiterative manner -- from initially loosening, to then relatively tightening, to then returning back to a tendency of loosening, -- etc. -- to where such a so-eluded-to reverberative cycle of reiteration, is to here to be of such a nature, to where the said loosening will tend here to be more of the nature as to approaching that of being of a Rayleigh-based scatterirng, while the said relative tightening will tend here to be of more of the nature as to approaching that of being of a Reimman-based scattering, over time.  As the said reverberative cycle ( when in terms of the correlative Majorana-Weyl-Invariance) is to loosen, then, the correlative Lorentz-Four-Contractions that are to be applied to those superstrings of discrete energy permittivity, that act in so as to comprise the said orbifold  eigenset, are to increase, -- while, as the said reverberative cycle (when in terms of the correlative Majorana-Weyl-Invariance) is to tighten, then,  the correlative Lorentz-Four-Contractions that are to be applied to those superstrings of discrete energy permittivity, that act in so as to comprise the said orbifold eigenset, are to decrease.  I will continue with the suspense later!  To Be Continued!
Sincerely, Samuel David Roach.

Superconformal Invariance And Lorentz-Four-Contractions

Let us initially consider a given arbitrary individually taken orbifold eigenset, that is to be in a proximal local state of superconformal invariance -- at a reference frame that is Poincare to the externalized core-field-density of the cohomological shell, that is of the said orbifold eigenset, -- as it is to here be undergoing a Fourier Transformation, over a sequential series of group-related instantons.  The tighter that the tense of superconformal invariance is, of what is here to be of a vibrating orbifold eigenset, that is to be basically remaining in one proximal local Ward-Cauchy-based spot -- the lower that the correlative Lorentz-Four-Contractions will be, upon those superstrings of discrete energy permittivity, that work to comprise the so-stated orbifold eigenset, -- over any correlative extrapolated gauged group-metric, that is here to be of an even function of Hamiltonian operation.  Furthermore, -- the tighter that the tense of superconformal invariance is, of what is here to be of a vibrating orbifold eigenset, that is to be basically remaining in one proximal local Ward-Cauchy-based spot -- the higher that the correlative Polyakov Action eigenstate will be, upon those superstrings of discrete energy permittivity, that work to comprise the so-stated orbifold eigenset, -- over any correlative extrapolated gauged group-metric, that is here to be of an even function of Hamiltonian operation. 
I will continue with the suspense later! To Be Continued!  Sincerely, Sam Roach.

Orbifold Eigensets And Lorentz-Four-Contractions

Lorentz-Four-Contractions are to be determined, at what is here to be at the Poincare level to the reference frame of the externalized core-field-density, of any one given arbitrary respective orbifold eigenset -- at the most internal level.  So -- consider any one correlative respective orbifold eigenset, or, any one set of superstrings that operate in so as to perform one specific operation or function over time.  Consider the correlative motion of that said orbifold eigenset, to the motion of electromagnetic energy over time, -- that is from within that medium of which, the so-stated respectively considered orbifold eigenset in question, is to be moving through at the I.U.C. that is to be considered here.  The respective Lorentz-Four-Contraction of each of the superstrings of discrete energy permittivity that are to be of the mentioned orbifold in question here, is to be based upon the just inferred relativity of the motion of the said orbifold eigenset, when relative to light.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Electromagnetic Energy As A Partially Yau-Exact Phenomenology, Part One

Orbifold eigensets that are comprised, in part, by superstrings that are of discrete electromagnetic energy permittivity, that are, when individually taken, to be continuing to move through the same medium over time, tend to behave in such a manner -- to where these may here be described of as being of such a Ward-Cauchy-based state of being partially Yau-Exact.  When a beam of electromagnetic energy is continuing to travel through the same medium over time, -- the transversal-based eigenindices of any one given arbitrary respective orbifold eigenset of electromagnetic energy, -- of which are here to tend to move in the same general direction that the correlative wave-tug of the angular momentum of the composite photons, that are here to work to comprise the said given arbitrary orbifold eigenset of such a respective case, are to be directed in  -- when this is existing in a general condition of superconformal invariance -- are here to tend to generate as much cohomology as these are to degenerate, over a set extrapolated gauged group-metric.  Yet, the homotopic torsional eigenindices, that are here to move in the same general direction as the spin-orbital momentum of the said respective given arbitrary orbifold eigenset is to be directed in, are to not to tend to be of a Yau-Exact nature.  Such said torsional eigenindices, are here to tend to either generate or to degenerate significantly more cohomology than these are here to respectively degenerate or generate -- given whether or not the directly corresponding orbifold eigenset of electromagnetic energy is to either be respectively amplified or augmented Or dampened or atenuated over time, -- as this may be extrapolated over a group-related metric, that is of a Ward-Cauchy-based Kahler condition, that is here of an Even gauge-metrical functional Hamiltonian operation over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Calabi-Yau Manifolds And Yau-Exact Strings

Mass-Bearing superstrings of discrete energy permittivity, have a tendency of behaving in a Yau-Exact manner, when such superstrings are to be set into a tense of superconformal invariance -- when this is taken at the Poincare level to a directly corresponding internal reference frame, in which any given arbitrary orbifold eigenset that is to be comprised of such respective superstrings -- is to be differentiating in a Fourier-based manner, that works here to display a Rham-based cohomology.  This is in terms, again, of the interactions of a Calabi-Yau manifold, that is of a relatively maintained Ward-Cauchy-based pulsation -- in which both the transversal-based eigenindices and the torsional-based eigenindices, that are of the correlative mass-bearing superstrings of discrete energy permittivity, are to both behave as such in a hermitian-based manner, -- in so long as the directly corresponding orbifold eigenset is to remain as behaving in a superconformally invariant manner, in which it is to here to be translated via a Fourier Transformation, that is here to be working to form a Rham-related cohomology over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Some More As To Generative Cohomologies

Let us consider an orbifold eigenset -- that is initially to be working to generate a set of cohomological indices, that are to be directly associated with a Doubolt cohomology, that is to here to be associated with a gradual increase in the tendency of working to bear an ellongated pulsation of the metrical eigenindices -- that are here to be correlative to a steadily accelerated orbifold eigenset-related oscillation-based mode.  As the said orbifold eigenset is to be generating cohomological indices at a gradually increasing metrical-based rate, -- it is to here to be in the process of this general activity to here be working to form a resultant tense of metrical-based Chern-Simons singularities, that are here to be extrapolated by a set of complex metrical-based roots.  If the development of the said integrative set of cohomological indices , that are here to be generated by the Fourier-related motion of the said orbifold eigenset over time --  is to be displaced at a kinematic-based "Sterling Approximation," as a unitary Hamiltonian operator, that is to be delineated via a Hamiltonian operand that is to here to work to involve a discrete Lagrangian-based path, that is to be traversed, then, the resultant Doubolt cohomology will not necessarily work to form any Lagrangian-based Chern-Simons singularities.  This is the tendency of this case, (to not work to bear any Lagrangian-based Chern-Simons singularities), in so long as the flow of the homotopic torsional eigenindices is to be hermitian as  a covaraint-based Hamiltonian operator -- that is to bear both a codifferentiable and a codeterminable hermitian-based transversal flow, that is here to be of an overall discrete nature as a wholistic hermitian-based Hamiltonian operator -- as the said orbifold eigenset is to both transversal-wise and torsional-wise, to flow in as many spatial dimensions as the number of derivatives that is is to be changing in, -- as this so-stated orbifold eigenset is to be delineated along the whole translation of the directly associated Lagrangian-based path, --  over the correlative gauged group-metric, that is of this particular genus of a case scenario.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

More As To Cohomological Generation

Let us initially consider an orbifold eigenset of one given arbitrary nature, that is to work to bear an ellongated pulse -- as it is to be accelerated through a Doubolt cohomology, that is to bear both a set of metrical-based Chern-Simons singularities that are to each to bear a set of complex roots, as well as to also bear a set of Lagrangian-based Chern-Simons singularities that are to each to bear a set of complex roots, -- as the so-stated Doubolt cohomology is to be able to be extrapolated as having a mappable-tracing, that is to bear a general index of Ward-Polarization, that is to be generating a respective cohomology, that is to bear a larger resultant scalar magnitude of the formation of Gliosis-Sherk-Olive ghosts than the resultant scalar magnitude of the formation of Nielson-Kollosh ghosts.  So, the general condition of a net generation of cohomological residue -- that is to be formed by discrete quanta of energy that are to work together in so as to perform one common Hamiltonian operation -- will tend to form a significantly higher scalar amplitude of a Reimman scattering, that is of the norm-state-projections that such discrete energy is to strike in a Gliosis-based manner, -- than the relative quanta of the scalar amplitude of that overall Rayleigh-based scattering, that is of the Gliosis-Sherk-Olive ghosts that are to be scattered out of the condition of cohomological generation, -- that would otherwise happen if the correlative Hamiltonian-related group-related discrete energy that is to here to act as one quantum, would work to form, if it were to, instead, to act as a group-attractor of cohomological degeneration.
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.