As To Oribifold Eigensets And Curved-Space

The closer that a phenomenology that is of a lower mass-based genus, moves towards a phenomenology that is of a higher mass-based genus, in this respective given arbitrary case  -- the less that the Lagrangian-based path that was of the initially so-stated orbifold eigenset, will move as if it was moving in a discrete unitary-based manner, -- since the hightened gravitational-based index will then tend to here, move in the "direction" of as having a more curved-like Hamiltonian operand.  This is as the phenomenology of a lower gravitational -based index is propagated towards the phenomenology that is a higher gravitational-based index.
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

More As To Rham And Doubolt Cohomologies

Let us initially consider an orbifold eigenset, that is moving through a discrete unitary Lagrangian -- over a sequential series of group-related instantons.  Let us next say that the said orbifold eigenset, is to be moving toward a phenomenology that works to bear a much higher gravitational-based index -- to where the topological substrate that is being moved towards, works to bear a much higher mass than the initially so-stated orbifold eigenset does, in this given arbitrary respective case scenario.  The initially said orbifold eigenset, is to be initially moving via a cohomological mappable-tracing -- that works to bear here a Rham-based cohomology.  Space-time-fabric tends to bend, and not be of a perfectly "straight" nature.  The Fourier-based activity of gravity, is the main general course of force -- that tends to work at bending space-time-fabric.  Since the topological substrate that is being moved towards, works to bear a higher gravitational index, the Fourier-based activity of the first so-stated orbifold eigenset, that is moving towards the second said topological substrate -- will tend to form more of a bending of space-time-fabric per time -- as the said orbifold eigenset is to here be moving closer and closer to the so-eluded-to holonomic substrate, that is of a higher mass-based index.  This will then tend to mean, that as the initially so-stated orbifold eigenset is to be moving towards the so-eluded-to mass that is of a higher genus of Hodge-based index, the more that the initially said Rham-based cohomology will then tend to convert into a Doubolt-based cohomology.  This will then mean, that the closer that the holonomic substrate that is of a lower genus of mass moves towards the holonomic substrate that is of a higher genus of mass -- there is more of a likely-hood of the Hamiltonian operand that is of its initially hermitian-based nature, will then tend to form both at least one Lagrangian-based Chern-Simons singularity and/or one metrical-based Chern-Simons singularity.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Two of Chern-Simons Singularities And Ghost-Inhibitors

Let us say that one is to have an orbifold eigenset -- that is to initially be moving in what may here be thought of as the relative forward-holomorphic direction.  Let us next say that one is to here be observing the said orbifold eigenset -- as a topological substrate, that is to here be in the process of being translated as a metrical-gauge-based Hamiltonian operator, that is to here be propagated via a unitary Fourier Trasformation of a relatively cohesive set of eigenindices, that will work to help form the kinematic activity of being propagated through an elementary mean Lagrangian path -- that is of a relatively "straight" directoral-based wave-tug -- as the resultant cohomological-based mappable-tracing, is to here be propagated as a tense of the here resultant generation of a set of harmonically scattered Reimman spaces.  Let us then consider that the resultant general cohomological eigenbase, that is to here be thus formed by the physical memory of the projection of the trajectory of the so-stated kinematic-based activity that is of the so-stated orbifold eigenset, is to be of a Rham-associated nature -- since the homotopic-based torsional eigenindices, that are to here be formed by the propagation of the said orbifold eigenset through space-time-fabric, that is proximal localized at the Yukawa-based range-related cite of the functioning of the eluded-to Hamiltonian operation -- are to here bend in as many changes in derivatives as the number of spatial dimensions that the so-eluded-to set of superstrings that are to here be operating in so as to perform one specific function, are to be translated through.  All of the sudden, there is to here be a Lagrangian-based Chern-Simons singularity, that is to be formed by the initial general Fourier-related activity of the said orbifold eigenset, that was initially working to form a Rham cohomology, is to act in a directoral-based flow, that is to be propagated in so as to form a Rayleigh scattering of the cohomological eigenbase that is of the ghost-based pattern of the initially said Rham cohomology.  This will often be the result of a relatively forward-holomorphic-directed ghost-based inhibitor. This will then tend to cause a spontaneous turn of the Lagrangian-based pattern, that is of the said orbifold eigenset -- to the relative Njenhuis-to-reverse-holomorphic direction.  I will continue with the suspense later! To Be Continued!  Samuel David Roach.

Chern-Simons Singularities And Ghost-Based Inhibitors

Let us initially say that one is to have a metric-gauge-based Hamiltonian operator, that is to here be in the form of an orbifold eigenset that is to be translated via a Fourier Transformation -- in what is here the relative forward-holomorphic direction.  Let us next say that this given arbitrary respective holomorphic direction, is being observed of as to here be moving via a Lagrangian-based Hamiltonian operand -- that is of a relatively "straight" directorial-based path.  Let us next consider that there is to here be a sudden Lagrangian-based spike -- that is to happen to the said respective orbifold eigenset, that was, up until now, being propagated as a unitary Hamiltonian operator that was moving in a hermitian-based manner, in so as to bend in as many derivatives as the number of spatial dimensions that the so-stated metric-gauge-based eigenset was to here be moving through, as a parametric operator of a respective topological substrate.  Let us here say that the course of the activity that was here to be involved with the result of the said Lagrangian-based spike -- was to work to cause the said orbifold eigenset to then turn in the relative Njenhuis-to-forward-holomorphic direction -- at the cite of the so-eluded-to Lagrangian-based Chern-Simons singularity.  Part of what would tend to work to cause such a singularity, would be the motion of a ghost-based inhibitor, in the relative reverse-holomorphic direction to the initial motion of the orbifold eigenset of this given respective case, that would act in so as to work to form an initial Rayleigh scattering of the cohomological mappable-tracing of the projected trajectory of the ghost-based pattern that was being formed by the said orbifold eigenset.  Just as this so-eluded-to inhibitor is to begin in its Yukawa-based influence upon the said orbifold eigenset, this will then tend to pull the so-eluded-to cohesive set of superstrings, to then pull to what will here be the relative "left."  (This is if the forward-holomorphic direction is to here be considered as going relatively "straight.")
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Two As To Consecutive Chern-Simons Singularities

Let us here consider an orbifold eigenset, that is moving in the relative forward-holomorphic direction.  Let us next consider that the just mentioned orbifold eigenset, is to all of the suddenly spike into what is to here be the relative reverse-Njenhuis to forward-holomorphic direction -- to where this said activity is to here, work to form a Lagrangian-based Chern-Simons singularity -- that is of a genus of one.  Let us next say that the just mentioned orbifold eigenset, is to ensue, in so as to just about immediately spike again, into a Fourier-based activity that is to all of the sudden -- veer into what is to be the ensuing motion of that self-same orbifold eigenset, into what is now to be the relative reverse-Njenhuis to forward-holomorphic direction.  Again, this general type of a Fourier-based activity, is to here work to form another Lagrangian-based Chern-Simons singularity -- that is again to be of a genus of one.  This general type of activity -- that is to here involve the cohomological mappable-tracing of two consecutive Lagrangian-based Chern-Simons singularities, of which are to happen almost immediatley ensuing Lagrangian-based spikes -- will tend to often work to form what will here almost ensuredly work to form an antiholomorphic Kahler condition.  Such an antiholomorphic Kahler condition, will here tend to initiate the proximal localized condition -- of what here may called the Wick Action, via a group-related metric that is called the Kahler-Metric.  The Fourier-based activity of the Kahler-Metric, tends to always work to ensue the presence of the activity of what may here be termed of as a Gaussian Transformation.  A gauge-transformation is always an example of a genus of a Gaussian Transformation, yet, not all Gaussian Transformations are of  the general nature of what I have just termed of as a gauge-transformation.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Consecutive Chern-Simons Singularities

Let us initially consider an orbifold eigenset, that is to work to bear a Lagrangian-based Chern-Simons singularity that is of a genus of one -- after the said initially considered orbifold eigenset has just finished at working to bear only hermitian singularities, over the so-eluded-to subsequent compilation of a Rham-based cohomological mappable tracing, that had just happened over the so-eluded-to subsequent sequential series of group-related instantons.  The so-stated activity, that had been involved in the formation of the said Lagrangian-based Chern-Simons singularity -- will have here worked to form, in this given arbitrary case scenario, a Ward-Caucy-based condition -- that will work to cause the Lagrangian-based path of the here mentioned orbifold eigenset, to then veer from the initial relatively forward-holomorphic direction, into the relative forward-Njenhuis to holomorphic direction -- over the initially so-eluded-to immediately ensuing duration, of what will here be the Fourier differentiation of the said orbifold eigenset over the so-eluded-to group-related metric.  Let us next say, that there will then be an almost immediately ensuing Lagrangian-based Chern-Simons singularity of a genus of one, that will now work to ensue upon the self-same orbifold eigenset -- of which will then work to form what will here amount to another changing of holomorphicity, that will as well veer into what will now be the relative forward-to-Njenhuis to hololmorphic direction, relative to the immediately subsequent Fourier-based directoral flow of the said orbifold eigenset.  This will then tend to work to form an antiholomorphic Kahler Condition -- of which will then work to cause a proximal localized initiation of a Wick Action eigenstate.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Calabi-Yau Manifolds Versus More Spurious Manifolds

A Calabi-Yau manifold is a set of one or more orbifold eigensets, that are of a mass-bearing nature.  Calabi-Yau manifolds tend to be directly appertaining to orbifold eigensets, that are to -- at any specific respective instant under consideration -- be differentiating over a metric that is of the nature of a Fourier Transformation, in such a manner, in so as to be translated through time, as a set of eigenstates that are of a Noether-based flow, of the directly associated discrete quanta of energy, that are Gliosis, at that so-eluded-to group-related metric, of a mass-bearing nature, that is here to not be of a tachyonic-related nature.  Any given arbitrary set of eigenstates that are to spike in the course of their delineatory translation, as a metrical-gauge-based Hamiltonian operator, that is to here tend to change relatively abruptly, in either its Lagrangian-based flow and/or in its metrical-based flow, over a sequential series of group-related instantons, -- may form Chern-Simons singularities that can here be of either a Lagrangian-based nature and/or of a metrical-based nature -- to where the cohomological mappable tracing, that is of the projected trajectory that is of the physical memory of the kinematic-related activity of such so-stated given arbitrary eigenstates, will then tend to act through the basis of the spike, that is to here be related to the thus formed singularity, in such a manner as to here be not of a Yau-Exact nature.  This will occasionally be the case, whether the set of eigenstates that are here to be translated through, are what is here to be of either a Lagrangian-based Chern-Simons-related spike, and/or of a metrical-based Chern-Simons-related spike.  Yet, a Calabi-Yau manifold is said to tend to always be of a Yau-Exact manner, in the following way, when this is taken as a set of orbifold eigensets that are of the Lagrangian eigenbase of a Noether-based flow:  Discrete quanta of energy that are of a nature of the topological substrate of a Calabi-Yau nature, will always tend to bear holomorphic-based torsional eigenindices, that will bend in a hermitian-based manner, in all of the spatial dimensions that the said eigenstate that is here of a Calabi-Yau nature is moving through, as a holonomic substrate that is here to be projected through its directly corresponding Hamiltonian operand -- as a set of what will here tend to be Yau-Exact quanta of discrete eigenindices of energy -- whether or not the whole so-eluded-to topological substrate that is of the said holonomic eigenbase, that is to here be delineated through space over time, is to spike in a Chern-Simons-based nature or not, in either a Lagrangian-based nature and/or in a metrical-based nature. This is what tends to be the nature of the delineation of the Fourier-based translation, of what are to here be mass-bearing orbifold eigensets -- in so long as the directly affiliated Calabi-Yau manifold, that is kinematic in this case in its displacement, is of a Noether-based flow, over the correlative eigenbase of time.

More As To Calabi-Yau Manifolds And Worm-Holes

Just as a Calabi-Yau manifold has exited from a given respective arbitrary worm-hole, it (the respective Calabi-Yau manifold) will go back from working to bear a Yang-Mills light-cone-gauge topology, to working to then bear a Kaluza-Klein light-cone-gauge topology -- once again.  As the light-cone-gauge topology of the mass-bearing orbifold eigenset of this case returns from working to bear a non-abelian light-cone-gauge topology to then working once again to bear an abelian light-cone-gauge topology, -- the dimensional parameterization of the spatial-based Ward-Caucy bounds of the core-field-density, that is Gliosis to the so-eluded-to orbifold eigenset at the Poincare level, will then work to compactify from that added dimensionality-based condition that it had had in the worm-hole that it had just exited, -- to then simply bearing those initial d-fields (for electrons) and f-fields (for nucleons) that the directly corresponding Calabi-Yau manifold of that respective tense of an orbifold eigenset that had here just traveled thru a worm-hole, was to initially work to bear, as a Noether-based tense of a set of substringular eigenindices that are to tend to be Yau-Exact, for all intensive purposes -- once the said orbifold eigenset has finished bending through space amongst the immediately prior venue of those critical cusps that had eluded-to the process that is here of the transfer of physical phenomenology, along a contorsioning delineatory-based Lagrangian displacement, that is of that Hamiltonian operand that had here acted as the previous translated worm-hole eigensbase.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Calabi-Yau Manifolds And Worm-Holes

Let us say, that an initially mass-bearing topological substrate -- of which would inherently be of a Calabi-Yau manifold -- is to be altered from its initial tense of a Fourier differentiation as a Hamiltonian operator that is moving via the process of Noether Flow, into being translated into an ensuing tense of a Fourier differentiation as a Hamiltonian operator that is to then be moving via the process of a tachyonic flow, -- over a relatively transient duration of a sequential series of group-related instantons.  Just as the said set of mass-bearing orbifold eigensets that work to comprise the so-stated Calabi-Yau manifold, that is to then travel through the so-eluded-to worm-hole -- the dimensional context of the so-eluded-to metrical-gauge-based Hamiltonian operator will then tend to work to decompactify -- from being of the spatial parameter-related nature of working to bear six or less spatial dimensions plus time (six spatial dimensions that would initially be related to the directly corresponding d-fields, and four spatial dimensions that would initially be related to the directly corresonding f-fields), into next working to bear at least twelve spatial dimensions plus time -- as the overall composite of the said Calabi-Yau manifold is to here be translated as a set of torsional-based indices, that are to here travel through a worm-hole, -- as the said worm-hole is to here work to bend two different Njenhuis-based Gaussian eigensets of mass-bearing topological substrate, in so as to allow for a relatively immediate spatial translation that will here work to inter-bind two relatively far reaches of space in a relatively transient period of time.  Even though a vast portion of the relative speed of a worm-hole is directly related to the contorsioning or the bending of space-time-fabric -- this particular worm-hole of this case is to here bear a certain degree or a certain scalar magnitude of working to bear a tense of a tachyonic propulsion.  This will not disobey the needed tense of Lorentz-Four-Contractions -- since the directly corresponding light-cone-gauge topology of the mass-bearing superstrings that are to here be translated via the so-eluded-to tachyonic-based worm-hole, are to alter from working to bear an inital Kaluza-Klein topology, into then working to bear a Yang-Mills topology.  As the said Calabi-Yau manifold that is to travel through the said worm-hole, is to then be both traveling through twelve or more spatial dimensions, of which it is to tend to change in the number of spatial derivatives that are to equal the number of spatial dimensions that it is traveling through, the worm-hole will tend to always -- at the critical cusps of the bending of space via the worm-hole -- change in more derivatives than the number of spatial dimensions that it is moving through.  This will then mean that any Calabi-Yau manifold that is to travel through a worm-hole, will tend to not be Yau-Exact at the critical cusps of the contorsioning of space, where the directly corresponding bending of space is to here be relatively maximized, as a Hamiltonian operand by which the said Calabi-Yau manifold is to here be Yukawa to it, as it is being translated in such a tachyonic manner.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Lagrangian-Based Alteration and Doubolt Cohomologies

Let us here initially consider an orbifold eigenset, that is moving in a Noether-based manner -- through a set number of spatial dimensions -- in such a manner, by which the so-eluded-to metrical-gauge-based Hamiltonian operator is to act as a Calabi-Yau manifold, that is to here be working to form a Rham cohomology, that is of a proximal localized tense -- from within a Real Reimmanian context.  This would then involve the conditions, that the so-stated orbifold eigenset is to here be changing in the same number of derivatives as the number of dimensions that it is moving through, as well as that the holomorphic-based torsional eigenindices that are of such a so-eluded-to orbifold eigenset, are to also bend in the same number of derivatives as the number of spatial dimensions that it is moving through -- over the set group-metric, by which the said Hamiltonian operator is to be functioning in so as to move through a discrete Lagrangian of space, via a Fourier Transformation that is of a Noether-based flow, that is of the directly corresponding spatial eigenindices, that are to here be Gaussian to that Hamiltonian operand that is Gliosis to the topological substrate that is Yukawa to that flow of motion by which the so-eluded-to disturbance of space is being propagated through, over time.  Next, consider that the said orbifold eigenset of such a respective given arbitrary case, is to then, all of the sudden -- move in so as to change in two more derivatives than the number of spatial dimensions that it is moving through.  This will then work to tend to form that Ward-Caucy-based conditions of a set of Lagrangian-based Chern-Simons singularities, in such a manner, that, since that the said Hamiltonian operator is to suddenly change in two more spatial dimensions than it is moving through instead of in only one more spatial dimensions than it is moving through, then, to where such a set of superstrings that are to here work to perform in so as to operate as one unit that is to function in so as to do one specific task -- then such an abrupt change as I have just described here, will as well tend to form at least one set of roots, as to what will here tend to be the formation of metrical-based Chern-Simons singularities.  As I have implied earlier, in so long as the orbifold eigenset is to here remain in so as to only form a Noether-based flow in the meanwhile, it will, over the course of being commuted through the so-eluded-to spike in the flow of the said Hamiltonian operator -- via the course of its translation through its directly corresponding Lagrangian over time, the pulse of the so-stated set of superstrings will then be altered here in its general commutation -- in what will here tend to be either an attenuation or an ellongation of the flow of its transmutation, over time.  This will then work to tend to alter the flow of that cohomology -- that is Yukawa to the flow of the said orbifold eigenset, from being of a Rham-related ghost-based pattern to then being of a Doubolt-related ghost-based pattern -- in the process of the said Hamiltonian operator being translated through the said Lagrangian -- over the directly corresponding sequential series of group-related instantons.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Tendency Of Rham Versus Doubolt

If an electron is moving through a d-field, that is to here be involved with the translation of the said electron to be delineated here via six spatial dimensions plus time -- then, it will tend to both be Yau-Exact, as well as such a so-eluded-to discrete metrical-gauge-based Hamiltonian operator to here be working to form a Rham-based cohomological mappable tracing, -- since the said electron will here be changing in only as many derivatives as the number of spatial dimensions that it will be going through, in such a case, over the directly corresponding sequential series of instantons, by which the said electron will be translated through.  Yet, if the said electron is to either spike in either its Lagrangian-based translation and/or in its metrical-based translation, and/or if the said electron is to increase in the number of spatial dimensions that it is to here be traveling through -- then, such a so-stated tense of a discrete Hamiltonian operator, will often be altered in so as to then be working to spontaneously form the course of a Doubolt-based cohomological mappable tracing, -- over the ensuing metrical-based grouping of such a sequential series of instantons.  This will then work to form an occasional mode, as to what would tend to be of a Yau-Exact phenomenology -- to then work to bear at least one set of Chern-Simons-related index-based roots. Such Chern-Simons affiliated roots, will tend to be of an Imaginary-based eigenbase, -- If the spike that works to form such a tense of a so-eluded-to aberation -- is of a Njenhuis nature, over time.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Tense Of Cohomological Genre

Let us initially consider a superstring that is partially Yau-Exact -- such as a photon, that is being propagated along a discrete Lagrangian as a metrical-gauge-based Hamiltonian operator, over time.  The said superstring is to here -- in this given arbitrary respective case -- be traveling through at least ten spatial dimensions plus time, over the course of the respective metric, by which the said photon is to be traveling over, yet, the so-stated photon is to not be fully Yau-Exact, since it is not of an eigenbase that is as to mass-bearing superstrings.  Let us next stipulate that the so-eluded-to discrete quantum of electromagnetic energy, is to be both moving in ten spatial dimensions, as well as the so-eluded-to discrete quantum of energy to here be changing in ten spatial-based derivatives -- as it is being propagated along the so-eluded-to Lagrangian, over a sequential series of instantons.  Let us say, that the holomorphic-based torsional eigenindices that are of the said discrete quantum of electromagnetic energy, are to only be hermitian in six of the ten spatial dimensions that it is moving through -- over the course of such a so-eluded-to Fourier-based translation, which is to here exist -- as the said photon is to function as a unitary Hamiltonian operator, that is of such a respective genre as to here being of a partially Yau-Exact nature.  This would then work to mean, that the six holomorphic-based torsional eigenindices that are of a hermitian nature, will then tend to work to form a partial integration of a Rham-based cohomological mappable tracing, while the four holomorphic-based torsional eigenindices that are instead of a Chern-Simons nature, will then tend to work to  form a partial integration of a Doubolt-based cohomological mappable tracing. A hemitian cohomological mappable tracing tends to only bend in as many derivatives as the number of spatial dimensions that it is traveling through over time, yet, a Chern-Simons cohomological mappable tracing bends in more derivatives than the number of spatial dimensions that it is traveling through over time. 

I will continue with the suspense later!  To Be Continued! Sincerely Samuel David Roach.

Part Two As To Rate Versus Magnitude

The relative codifferentiable rate of one given arbitrary respective tense of a second-ordered light-cone-gauge eigenstate, is to be taken to the sixth power -- while the relative codifferentiable comparison as to the scalar amplitude of the amount of mini-stringular segmentation, that is here to be fed-into the self-same said second-ordered light-cone-gauge eigenstate -- is to be taken to the first power. So, how does this work to compare the condition, as to how many times as many Schwinger-Indices or gravity waves are to here be produced by the plucking of one respective given arbitrary second-ordered light-cone-gauge eigenstate, of a discrete quantum that is of a Kaluza-Klein topology, versus the condition as to how many times less Schwinger-Indices or gravity waves are to here be produced by the plucking of one respective given arbitrary second-ordered light-cone-gauge eigenstate, that is of a discrete quantum -- that is of a Yang-Mills topology?
Let us say that a given arbitrary second-ordered light-cone-gauge eigenstate that is of a Kaluza-Klein topology, is to work to bear one-half of the scalar amplitude of mini-stringular segmentation -- that is to be fed-into its immediate Ward-Caucy bounds, than a covariant-based comparitive second-ordered light-cone-gauge eigenstate that is of a Yang-Mills topology, yet, the said eigenstate of a Kaluza-Klein topology, is to here vibrate at twice the relative rate as the said eigenstate of a Yang-Mills topology. (This would probably not happen literally, yet, this is just to give you an idea.)  Two to the sixth power is 64.  Two to the first power is 2.  This would mean, in this given metaphorical case, that the said eigenstate of a Kaluza-Klein topology of this case, would then tend to form 32 times as many Schwinger-Indices -- than the said eigenstate of a Yang-Mills topology of this case.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Rate Versus Magnitude

The rate at which any respective given arbitrary second-ordered light-cone-gauge eigenstate is to vibrate -- over the course of BRST -- has a lot more to do with the Hodge-Index as to the number of Schwinger-Indices or gravity waves, are to be produced by the topological substrate of the directly corresponding first-ordered light-cone-gauge eigenstate.  The second-ordered light-cone-gauge eigenstates, that are to be directly affiliated with the condition of a Kaluza-Klein light-cone-gauge topology -- tend to vibrate a lot quicker over the course of BRST, than the second-ordered light-cone-gauge eigenstates that are to be, instead, directly affiliated with the condition of a Yang-Mills light-cone-gauge topology.  This is why phenomenology that is correlative to the Ward-Caucy-based conditions of a Kaluza-Klein light-cone-gauge topology, will always tend to produce more Schwinger-Indices or gravity waves -- than that phenomenology that is correlative to the Ward-Caucy-based conditions of a Yang-Mills light-cone-gauge topology.  Mass that is not tachyonic, will always tend to be of a Kaluza-Klein topology, and, such so-eluded-to manifolds of mass will always work to bear more of a direct association with gravity waves -- than a phenomenology that is instead of a Yang-Mills topology.  I will continue with the suspense later! Sincerely, Samuel David Roach.

Torsioning Of Second-Ordered Light-Cone-Gauge Eigenstates

Any discrete quantum of energy, will either have an abelian light-cone-gauge topology, or, it will have a non-abelian light-cone-gauge topology -- over the course of any one respective given arbitrary iteration of BRST, during the course of any one given arbitrary respective iteration of instanton.  Any discrete quantum of energy that has an abelian light-cone-gauge topology, will tend to have more of a Laplacian lay-out -- of working to bear supplemental second-ordered light-cone-gauge eigenstates.  The lay-out of these just inferred eigenstates, will basically be of a linear eigenbase -- that is being fed-in mini-stringular segmentation, over the course of that Clifford Expansion that is to here be directly involved with the Fourier-based translation of that Polyakov Action eigenstate,  that is to happen to any respective superstring that is of a Kaluza-Klein light-cone-gauge topology.  In contrast -- the lay-out of those second-ordered light-cone-gauge eigenstates that are of a non-abelian light-cone-gauge topology, -- that work to comprise the wave-based format of any given arbitrary discrete quantum of energy impedance, is placed in a Laplacian-based sinusoidal manner -- during the directly associated iteration of BRST, which is of the correlative respective iteration of instanton.  This so-stated genus of light-cone-gauge topology, is also being fed-in mini-stringular segmentation, during the course of that Clifford Expansion that is correlative to the Polyakov Action eigenstate -- that is to here be directly appertaining to any respective given arbitrary iteration of instanton.  Since any so-eluded-to Yang-Mills light-cone-gauge topology (non-abelian), works to involve a distinctly sinusoidal tense of core-field-density, that is Gliosis at the Poincare level to the topological stratum of the directly corresponding second-ordered light-cone-gauge eigenstates -- this will then work to cause the condition, that such wave-based eigenstates, that are correlative to discrete quanta of energy impedance, will likewise tend to cause the condition, that, superstrings that are of a Yang-Mills nature, will tend to bear light-cone-gauge eigenstates that are more prone to being torqued -- than superstrings that are of a Kaluza-Klein light-cone-gauge topology.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Domino Effect Of Light Scattering

Let us say that an initial beam electromagnetic energy, this is to where, let's just say that this electromagnetic energy it here to be light, has just struck upon a given arbitrary set of orbifold eigensets.  As the said light is to here be absorbed to an extent, into the holonomic substrate of the said set of orbifold eigensets -- a certain amount of electromagnetic energy is to then be released by the so-eluded-to atoms, that will have here needed to release their excessive energy that these said atoms have had here, just taken into their Ward-Caucy-based bounds.  This will then work to help in causing the so-eluded-to Calabi-Yau manifold -- the so-eluded-to atoms of such a case, -- to both absorb and radiate a certain scalar magnitude of electromagnetic energy, over time.  As the so-eluded-to group of atoms are to here be both absorbing and releasing a certain amount of electromagnetic energy, much of the electromagnetic energy that has scattered here, is to keep scattering among some of the other groupings of atoms -- that are proximal localized to the general field at which the source of the so-stated electromagnetic energy is being propagated into.  (This general proximal localized field, is the overall set of orbifold eigensets of this given arbitrary case, that are being at least partially bombarded with light.) To an extent, much of the resultant electromagnetic residue -- that is here to be scattered from within the Ward-Caucy bounds of those mass-related superstrings, that work to comprise the Calabi-Yau manifold of such a case -- is in the form of infrared energy, or, in other word, in the form of heat-based photons.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Electromagnetic Energy Striking Upon Phenomenology

Often, when light strikes a Calabi-Yau manifold (a manifold that is based upon the proximal localized tense of mass-bearing superstrings) -- the shining of electromagnetic energy upon the so-eluded-to respective given arbitrary mass-bearing orbifold eigenset, will then tend to absorb a certain quantum of energy, that may here be derived from the Gliosis-based impact of the initially stated electromagnetic energy upon the holonomic substrate of the electrostatic field -- that is directly associated with the electrical-based field of those electrons that are here to be orbiting around the nuclei of those atoms that have here just been struck by the inferred  electromagnetic beam.  Ensuing the said potential absorption of energy by the said Calabi-Yau field, certain of those electrons that work here to comprise the relative external-based electrostatic field, that work to form those atoms that work here to form the said Calabi-Yau field -- will tend to then need to release the excess energy that these so-stated electrons have just imbued.  This may then work to help at causing these over- energized electrons to then drop back-and-forth, in so as to then work to form photons -- that are then to be propagated away from the cite of the stated Calabi-Yau field in question.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Introductory Stuff About The Scattering Of Light

Whenever a beam of electromagnetic energy is to strike a phenomenology of mass, in a Gliosis-based manner, over time -- there will tend to be a certain amount of entropy that will here be formed by that general Fourier-based differentiation, that is of the activity of the so-eluded-to collision of the set of one or more photons, that are to here make a direct impact upon mass-bearing superstrings of discrete energy quanta, that will here work to help to form a tense of a Gaussian Transformation -- that may here be called a gauge-transformation.  A gauge-transformation is that general tense or genus of a Gaussian Transformation, that is formed as a gauge-metrical-based Hamiltonian operation, by which those so-eluded-to entropic-based eigenindices, that  are thence to here be formed by the so-eluded-to general activity of electromagnetic energy, are to have here just been struck by another physical phenomenology, to where this may bear an added tense of activity, over the course of the  needed replenishment of discrete quanta of energy -- that is to here be in the process of regenerating back their fractals of discrete energy -- so that discrete energy may be able to both persist and exist, over time.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Calabi-Yau Spaces And Light Scattering

What we normally come into contact with -- when we perceive of material phenomenology -- is the electrical field, that is directly associated with those atoms that work to comprise the molecules and the compounds of material stratum.  Whenever electromagnetic phenomenology strikes an electrostatic field, it will tend to always scatter to some degree or another.  When this general said genus of the scattering of electromagnetic energy is to happen, it often works to cause one or more electrons to drop back-and-forth an energy level -- in so as to work to form one or more respective photons.  Phenomenology of mass, exists in manifolds that may be described of as Calabi-Yau manifolds.  The activity of electromagnetic energy, acting to strike superstringular phenomenology of mass -- in so as to work to create this general genus of the scattering of the so-stated electromagnetic energy -- may be described of as the tense of a Calabi-Yau interaction.  Even if electromagnetic energy is not constantly bombarding the electrostatic field of a set of one or more atoms -- molecular structures tend to act in groups in such a manner, over time, in so as to at least release photons that are of an infrared nature, or, in other words, the activity of molecules over time -- will always tend to either absorb and/or radiate the holonomic substrate of heat, in the form of infrared photons.  An infrared photon is a discrete quantum of heat energy.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Chan-Patton Rules And Parity

The Chan-Patton conditions, that are appertaining to the Ward-Caucy relationships of the electrostatics of any respective given arbitrary atom -- that are to here appertain to the parity of an electron, will tend to work to force the correlative one-dimensional superstring and its directly corresponding counterstring -- to bend into a resultant two-dimensional superstring and its correlative two-dimensional counterstring, in a hermitian manner.  This will then work to tend to cause the said string and its counterstring, to thereby bend via the Fujikawa Coupling -- as is to here be in accordance with the Green Function.  The Chan-Patton conditions of parity, are here to be the case for the smooth energy relationships -- that exist for any discrete quanta of kinetic energy permittivity, that is to ensue as being released by an electron, when it works to drop back-and-forth an energy level.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Next Part As To Session 3 Of Course 20

The condition that an electron will bear a tendency, of not only moving in as many spatial dimensions as the number of derivatives that it is changing in, yet, it will as well tend to work to bear holomorphic-based torsional eigenindices -- that will bend in as many spatial dimensions as the number of derivatives that it is changing in -- is a condition, that is akin to some of what may here be called of as Chan-Patton rules.  An electron exists as an orbifold eigenstate, of what may here be called of as an example of a Calabi-Yau space.  A Calabi-Yau space, tends to bear eigenstates -- that are Yau-Exact.  Consequently, an electron is one general classification of a Fourier-based spatial Hamiltonian operator, that tends to bend in a hermitian manner, in so long as it is moving in a Noether-based manner -- via its translation through what may here be the traversal of a Lagrangian that may exist from anywhere between six and ten spatial dimensions plus time.  Therefore, an electron, when moving in a Noether-based manner over time, will tend to bend in a hermitian manner -- by both moving in as many spatial dimensions as the number of derivatives that it is changing in, as well as such an orbifold eigenset (an electron) -- to here be working to bear holomorphic-based torsional eigenindices, that will as well tend to bend in as many spatial dimensions as the number of derivatives that it is changing in.  This tendency is in so long as the said electron, is to here be moving as a metrical-gauge-based Hamiltonian operator -- that tends to work to form a Rham-based cohomology.   I will continue with the suspense later! To Be Continued!  Sincerely, Sam Roach.

A Little Reminder -- The Fujikawa Coupling

Electrons may be viewed of as mass that is energy that is wave that is particle, at the same time.  When an electron drops an energy level, while then returning to its immediately prior energy level -- a discrete amount of energy is then to be released from the said electron, in the form of a photon.  A photon is a discrete quantum of electromagnetic energy.  This happens, by the process of the directly corresponding one-dimensional superstring and its counterstring, that is released by the electron of such a case -- when it is tugged into bending in a hermitian manner -- to then be formed into a respective bosonic superstring and its correlative counterstring of discrete energy permittivity, -- via the Fujikawa Coupling, over a successive series of instantons.  The so-stated bosonic superstring of such a respective given arbitrary case, is more associated with the particle nature of a discrete quantum of electromagnetic energy permittivity -- while the so-stated correlative bosonic counterstring of such a case, is more associated with the wave nature of a discrete quantum of electromagnetic energy permittvity.  In the meanwhile, the respective light-cone-gauge eigenstate -- that is correlative to this given case, is altered from working to bear ten second-ordered light-cone-gauge eigenstates, to then working to bear only five second-ordered light-cone-gauge eigenstates ( as such said eigenstates are to then double-up in the Hodge-Index of the mini-stringular segmentation of their holonomic substrate, as to the cross-sectional thickness of the correlative chord-based topology of the so-eluded-to substrate, that is of the pheonomenology of such second-ordered eigenstates).  The correlative Fadeev-Popov-Trace eigenstate, is to here be torqued by this overall process -- yet, it will tend to still bear basically the same general genus of its morphological topological substrate, over the course of the process of the so-eluded-to group-metric of the Fujikawa Coupling.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Some More As To Energy Density And Cohomologies (Part Three)

Let us say that we are to consider here, a case of two different covariant orbifold eigensets -- over the course of one codeterminable and codifferentiable group-metric.  Let us say that both of the said orbifold eigensets, work to bear the same Ward-Caucy-based "volume."  Let us say that one of the two so-stated eigensets, works to bear twice the rest mass as the other orbifold eigenset -- of such a given arbitrary respective case.  Let us now say that the so-eluded-to orbifold eigenset, that is to here work to bear half of the rest-associated mass-based density than the other said orbifold eigenset, -- is to be traveling at a velocity, that is of twice the relative scalar amplitude of the velocity of the other so-eluded-to orbifold eigenset, of this respective case scenario.  The partial condition of one orbifold eigenset -- as bearing twice the mass-density of the other one, would Theoretically work to cause the so-eluded-to denser orbifold eigenset to be twice as efficient at eliminating its resultant cohomological residue, yet, since the less dense orbifold eigenset of this case, is to be traveling at twice the relative velocity as the other one, -- the less dense of the two so-stated orbifold eigensets will ironically work to bear a scalar amplitude of twice the efficiency at working to eliminate its excessive cohomological residue -- than the slower, yet denser, -- orbifold eigenset of this case.  Although faster orbifold eigensets of the same ulterior nature tend to generate more ghost anomalies -- these said faster eigensets still happen to be more efficient at working to eliminate their ghosts, or, their excessive cohomological residue.  So, the higher the energy density is of an orbifold eigenset is, the more efficient it is at eliminating its cohomological density.  This is although orbifolds of a higher energy density, will tend to generate more cohomological residue -- over time.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Energy Density And Cohomologies, Part Two

Let us here consider two different covariant given arbitrary orbifold eigensets, that are of the same Ward-Caucy mass-based density, over the course of one respective given arbitrary group-metric.  Let us next say, that one of such orbifold eigensets is moving at a faster relative velocity -- in a terrestrial-based manner -- than the other said orbifold eigenset, over the self-same said group-metric.  The faster of the two said orbifold eigensets, will tend to eliminate its cohomologies at a faster rate than the slower of the two said orbifold eigensets.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Energy Density And Cohomologies, Part One

Let us take into consideration two different covariant given arbitrary orbifold eigensets.  Both of such orbifold eigensets are moving at the same velocity, relative to one another -- over the group-metric that is to be considered here.  Both of such orbifold eigensets are, as well, of the same relative Ward-Caucy-based "volume," in this respective given arbitrary case scenario.  One of these so-stated orbifold eigensets has a greater mass than the other of such orbifold eigensets, over the course of the said group-metric.  The orbifold eigenset that is to here have a greater mass-based density (more mass per relative Ward-Caucy-based "volume"), will tend to work to bear a Rayleigh scattering of its ghosts -- that will tend to eliminate its directly corresponding cohomologies, in a quicker manner -- than the orbifold eigenset that is of a lower mass-based density.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Relative Yukawa Leverage Of Group Attractors

Let us say that there is to here be an initial tense of order with a covariant set of orbifold eigensets, that is to then be brought into a relative tense of disorder among the said set of covariant orbifold eigensets.  Let us next say that there is to soon be an ensuing set of group attractors, that act upon the initially so-stated set of disordered orbifold eigenset -- in so as to work to put the said eigensets, to go into a tense of relative order and interdependence.  The more Yukawa that the activity of the said group attractors is, at bearing upon the topological stratum of those so-stated orbifold eigensets that are to be brought into a tense of a Reimman scattering -- in so as to be brought back into a relative tense of order and interdependence, over time -- the quicker that the so-stated orbifold eigensets will tend to be brought together into a tense of relative order and interdependence.  Consequently, the less Yukawa that the activity of the said group attractors is, at bearing upon the topological stratum of those so-stated orbifold eigensets that are to be brought into a tense of a Reimman scattering -- in so as to be brought back into a relative tense of order and interdependence over time -- the slower that the so-stated orbifold eigensets will tend to be brought together into a tense of relative order and interdependence.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Whether Or Not A Specific Delineation Could Be Real

If an equation that treats a time-oriented cartesian-based quotient of mathematical expression to be equal to a time-oriented polar-based quotient of mathematical expression, to where this is solvable as an even function, -- that works to bear an eigenbase that is Gaussian for either a Real Reimmanian space or for a Njenhuis space -- in so as to initially bear a general value of setting "gnu" (pronounced as "nu") to a scalar magnitude of 1/((2)^.5)(of whatever the specific units are of the respective given arbitrary case), so that between four and ten spatial dimensions may then be solved for as being directoral-based space-time coordinates, that will thus, in such a general genus of a case, work to plot the net Lagrangian that is to be solve for, once one has the so-eluded-to tense of the so-eluded-to four to ten Noether-based space-time-coordinates to be plotted towards one general net locus, to where this will form a space-time translation that is to happen over the course of a here proscribed set of a certain integer-based iterations of group-related instantons.  (Let us say 3*10^8 consecutive of such instantons.)  If the so-eluded-to space is Gaussian in either a Real Reimmanian or in a Njenhuis manner, then, it may be properly solved for as a Calabi-related space.  Yet, if the so-eluded-to space is not Gaussian in either a Real Reimmanian or in a Njenhuis manner, then, it is of no actual potential tense as a delineation of a superstring, via a Calabi-based translation of those core-field-based indices of the topological transfer, that are of those coniaxial-based eigenstates, that come together in so as to work to make-up the holonomic substrate of a propagated superstring over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

As To The Yukawa Tug Of Ghost Inhibitors

Let us initially consider an orbifold eigenset, that is in a state of relative conformal invariance.  It is here to be in a given arbitrary tense of a Majorana-Weyl-Invariant-Mode.  Let us next consider a situation in the substringular, to where there is to suddenly be a ghost-based inhibitor -- that is to act in a Yukawa manner, upon the holonomic substrate of the topological stratum of the initially so-stated orbifold eigenset.  The stronger that the said ghost-based inhibitor is to act in a Yukawa-based manner upon the said orbifold eigenset, the sooner is to then be the tendency of the cohomological mappable tracing that is to be formed by the said orbifold eigenset -- to be scattered anharmonically out of place by the presence of what will here be the proximal localized upcoming relatively reverse-holomorphic norm-state-projections, in so as to work to form a Rayleigh scattering that is to then happen to the ghost-based pattern, that is to have just been formed by the physical memory of the projection of the trajectory of those superstrings that had just worked to form the so-eluded-to cohomological mappable tracing of the said orbifold eigenset of this respective given arbitrary case.  Consequently -- the weaker that the said ghost-based inhibitor is to act in a Yukawa-based manner upon the said orbifold eigenset, the more prolonged is to then be the tendency of the cohomological mappable tracing -- that is to be formed by the said orbifold eigenset, to be scattered annharmonically out of place, by the presence of what will here be the proximal localized upcoming relatively reverse-holomorphic norm-state-projections, in so as to work to form a Rayleigh scattering that is to then happen to the ghost-based pattern that is to have just been formed by the physical memory of the projection of the trajectory of those superstrings that had just worked to form the so-eluded-to orbifold eigenset that had formed that cohomological mappable tracing of this respective given arbitrary case.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Noether Versus Tachyonic Cohomology-Based Conditions

If an orbifold eigenset is operating as having a Noether-based flow -- the resultant cohomology that it will bear, will tend to be of a Real-Reimmanian-based nature.  Yet, if an orbifold eigenset is operating as having a tachyonic-based flow -- the resultant cohomology that it will bear, will tend to be of a Njenhuis-based nature.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Relative Velocity And Cohomologies

The slower that the relative velocity of a given arbitrary orbifold eigenset is -- the more of a tendency is of it to here be working to bear both a relatively loosely-knit resultant cohomological mappable tracing, along with the condition of the said orbifold eigenset to as well bear a relatively more prolonged resultant tense of such a cohomological mappable tracing.  Consequently, the faster that the relative velocity of a respective given arbitrary orbifold eigenset is -- the more of a tendency is of it to here be working to bear both a  relatively tightly-knit resultant cohomolgical mappable tracing, along with the condition of the said orbifold eigenset to as well bear a relatively more transient resultant tense of such a cohomological mappable tracing.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Two Of Session 3 Of Course 20 -- Calabi Manifolds And Calabi Interactions

Due to the condition that mass-bearing superstrings that are of a Noether-based flow, are of a multiplicit Calabi-Yau manifold, leads to the condition that mass-bearing superstrings tend to bear a tighter-knit cohomological-based tracing -- than superstrings that are not Yau-Exact.  This is in part, because Yau-Exact superstrings tend to bear holomorphic-based torsional eigenindices, that work to bear spatial coniaxions that bend in as many dimensions as the number of derivatives that these change in. -- Mass-Bearing superstrings do not tend to change in any more derivatives than the number of spatial dimensions that these are moving through, over any set group-metric that is to involve a respective sequential series of group-related instantons.  Consequently, superstrings that are either partially Yau-Exact, or, especially, superstrings that are simply of a Lagrangian-based Chern-Simons nature -- tend to bear a less tightly-knit cohomological-based tracing than superstrings that are Yau-Exact.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The First Part Of Session 3 Of Course 20 -- Calabi Manifolds And Interactions

Any Noether-based superstring, that is of a mass-bearing nature -- will tend to exist in a Calabi-Yau manifold.  So, if the mass-bearing superstrings of an f-field, that move through anywhere between four and ten spatial dimensions plus time, or, if the mass-bearing superstrings of a d-field, that move through anywhere between six and ten spatial dimensions plus time -- is to be pushed through such a so-eluded-to Lagrangian-based Hamiltonian operand, over the directly corresponding Fourier Transformation, it will then tend to bear those spatial coniaxions of the correlative holomorphic-based torsional eigenindices, that will tend to bend in a hermitian manner, in as many spatial dimensions as the number of derivatives that it is changing through.  Yet, in so long as such  said mass-bearing superstrings are not being propagated in a tachyonic manner, this may only tend to happen in up to the range of ten spatial dimensions plus time.  If either an f-field or a d-field is to be pulled in a Noether-based manner, through a Lagrangian-based Hamiltonian operand that will here work to involve more than 10 spatial dimensions plus time -- then, those holomorphic-based torsional eigenindices that are to thence be formed is the process of forming singularities that are cohomological-based in nature, this will then tend to form at least some Lagrangian-based Chern-Simons singularities -- over that multiplicit Fourier Transformation, in which such mass-bearing superstrings, -- as to thence be propagated, over time.
 I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Last General Part As To Entropic Photons

Let us consider what happens to an entropic photon, both during and just after the sixth set of 64 consecutive iterations of instanton -- that start upon the impact of the said photon upon another orbifold eigenset, -- as such an impact has at this point in time, scattered upon another holonomic substrate in a Gliosis-based manner. During the said sixth set of 64 consecutive iterations of instanton that I have respectively mentioned, even though the photon is still to be moving in ten spatial dimensions plus time, as it is changing in ten spatial derivatives in the process -- only five of its holomorphic-based dimensional coniaxions of torsional eigenindex, are here to be bending in a hermitian-based manner during this relatively brief group-metric.  Over the course of this self-same group-metric, the so-stated entropic photon is here to work to bear an abelian or a Kaluza-Klein light-cone-gauge topology.  Immediately after the initial 384 group-related instantons, at which the said entropic photon has scattered upon another holonomic substrate of physical phenomenology, the said entropic photon will then tend to bear both a non-abelian or a Yang-Mills light-cone-gauge topology -- and the said discrete quantum of electromagnetic energy will then work to bear a Ward-Caucy-based condition as to then have six holomorphic-based spatial dimensional coniaxions of torsional-based eigenindex, of which will tend to bend in a hermitian manner.  At this point, what was just previously an entropic photon, will then become a "regular" photon -- as it is re-quantized into a beam of electromagnetic energy.  This is the tendency, in so long as the prior scattered photon does not re-scatter in the meanwhile.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Reimman Scattering And Invariant Modes

The tighter that the tense is, of a Majorana-Weyl-Invariant-Mode is to become -- the higher that the correlative genus will tend to be -- of the directly corresponding Reimman scattering, that is here to work to push those superstrings that are to be organized into the said tense of Majorana-Weyl-Invariance, is to be of.  Consequently, -- the looser that the tense is of a Majorana-Weyl-Invariant-Mode is to become -- the lower that the correlative genus will tend to be -- of the directly corresponding Reimman scattering, that is to here work to push those superstrings that are to be organized into the said tense of Majorana-Weyl-Invariance, is to be of.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Infinite And Semi-Infinite Wells

An "infinite well" may often be of a Rayleigh scattering, that is in static equilibrium -- that will not alter in such a tense of static equilibrium spontaneously (in and of its own self-accord).
A "semi-infinite well" may often be of a Rayleigh scattering, that is in static equilibrium -- that may alter in such a tense of static eqilibrium spontaneously (in and of its own self-accord), yet, it may only do as such with a certain tense of reluctance.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Invariant Modes And Transiency Of Ghosts

The tighter that the Majorana-Weyl-Invariant-Mode is of an orbifold eigenset -- the longer that those directly corresponding cohomological-based tracings, that are formed as the ghosts or the physical memories of the motion of the directly associated orbifold eigenset -- that is of the so-eluded-to given arbitrary respective Majorana-Weyl-Invariant-Mode, tends to be.  Likewise, the looser that the Majorana-Weyl-Invariant-Mode is of an orbifold eigenset -- the shorter that those directly corresponding cohomological-based tracings, that are formed as the ghosts or the physical memories of the directly associated orbifold eigenset -- that is of the so-eluded-to given arbitrary respective Majorana-Weyl-Invariant-Mode, tends to be.  So, the tighter the Majorana-Weyl-Invariant-Mode is -- the less transient that its correlative ghosts tend to be, and, the looser the Majorana-Weyl-Invariant-Mode is -- the more transient that its correlative ghosts tend to be.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Here Is The Next Part As To Entropic Photons

Furthermore, in so long as an "entropic photon" does not directly strike another orbifold eigenset in the meanwhile -- it will (the said photon that is entropic), during its fifth set of 64 consecutive iterations that are directly appertaining to those group-related instantons by which it is being scattered  -- bear four coniaxions that will here work to bear holomorphic-based torsional eigenindices, that will tend to bend in a hermitian-based manner, -- as the so-stated entropic photon is to here be tending to change in ten spatial derivatives as it is to here be moving through a p-field, of which works to involve a Fourier Transformation, that is to here be translated via ten spatial dimensions plus time.  Thus, although the so-eluded-to scattered photon is to here still be of a partially Yau-Exact Ward-Caucy-based condition, it will here be of less of a Lagrangian-based Chern-Simons nature.  This is because, instead of seven of the coniaxions of its ten holomorphic-based dimensional torsional eigenindices being here of a tendency of bending in a manner that is not hermitian, only six of the coniaxions of its ten-dimensional holomorphic-based torsional eigenindices are to here be of the tendency of bending in a manner that is not of a hermitian manner.  So, as the here scattered photon becomes of more of a partially Yau-Exact condition, it likewise works to become of less of a Chern-Simons condition.  Also, during this said fifth so-stated set of 64 consecutive iterations of group-related instantons, by which the said photon has been in the process of scattering -- from the point of the impact that had worked to form the so-eluded-to scattering of the directly corresponding entropic photon, the said scattered photon will still be of a Kaluza-Klein, or of an abelian light-cone-gauge topology, instead of being of a Yang-Mills or of a non-abelian light-cone-gauge topology. -- (Photons tend to usually work to bear a non-abelian, or, in other words, a Yang-Mills light-cone-gauge topology.)  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

The Nature Of Dimensionality And The Transiency Of Ghosts

Let us initially consider an orbifold eigenset, that moves in a p-field.  A p-field is a substringular field, that exists -- over any respective given arbitrary Fourier-based translation -- in a minimum of ten spatial dimensions, plus time.  Consider the physical memories that are to be formed as those cohomological-based tracings, that are formed by the projection of the trajectory of those superstrings that act in so as to behave as the orbifold eigenset-based Hamiltonian operator, that is of any of such a respective p-field.  These so-eluded-to ghost anomalies that are thence formed, will initially be formed in the organization of one Reimman-based scattering -- to where these so-eluded-to coholomogical-based tracings are to later be broken down by an ensuing Rayleigh-based scattering, that will eliminate the initially said formed ghost-based pattern.  Next, consider a d-field.  A d-field is a substringular field that exists -- over any respective given arbitrary Fourier-based translation -- in a minimum of six spatial dimensions, plus time.  Consider the physical memories that are to be formed as those cohomological-based tracings, that are formed by the projection of the trajectory of those superstrings that act in so as to behave as the orbifold eigenset-based Hamiltonian operator, of any of such a respective d-field. These so-eluded-to ghost anomalies that are thence formed, will initially be formed in the organization of one Reimman-based scattering -- to where these so-eluded-to cohomological-based tracings are to later be broken down by an ensuing Rayleigh-based scattering, that will eliminate the initially said formed ghost-based pattern.  The Fourier-based translation of a p-field, will tend to work to bear the elimination of its ghost-based pattern in a quicker manner -- than the Fourier-based translation of a d-field will tend to work to bear the elimination of its ghost-based pattern.  The tendency is -- that the higher the dimensionality is of any respective given arbitrary  Fourier-based translated field -- the quicker, timewise,  that their directly corresponding ghost anomalies or cohomological-based patterns will be annharmonically scattered out of existence.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Ensuing Part As To Entropic Photons

You can probably see the pattern of what happens to a photon, that has just become entropic -- for the immediately ensuing iterations of group-related instanton, if the said photon does not once again scatter upon another holonomic substrate of physical phenomenology in the meanwhile.  For the fourth set of 64 consecutive iterations of instanton that the said entropic photon is going through, starting upon its direct impact upon another phenomenology, it will work to bear what may be described of as having holomorphic torsional-based eigenindices that will bend in a hermitian-based manner, in up to three of the ten correlative coniaxions that are related to the spatial dimensionality that the said photon is moving through.  This is because the so-stated entropic photon will tend to bend here in ten spatial derivatives as it is moving in a minimum of ten spatial dimensions, plus time, over the course of the said entropic photon being in the process of being delineated through time and space.  This will then work to decrease the degree of the genus of the so-eluded-to Chern-Simons nature of the so-stated entropic photon -- seeing that it will, during the said fourth consecutive set of 64 said iterations of being "entropic," be Chern-Simons now, in a Lagrangian-based manner, in only seven of the ten spatial coniaxions that it is moving through, instead of being Chern-Simons in a Lagrangian-based manner in eight of such covariant and codifferentiable Fourier-translated coniaxions that are directly related to the ten spatial dimensions that such a given arbitrary photon is going through, as a metrical-gauge-based Hamiltonian operator, as it is tending to change in this Fourier-based process in up to ten spatial derivatives, over time.  This will work to cause such an entropic photon to still be partially Yau-Exact.  Such a photon will still work to bear here -- what may be deemed of as an abelian or as a Kaluza-Klein light-cone-gauge topology.  This will be the tendency of such, during the 193rd to the 256th of such consecutive iterations -- upon colliding with another physical phenomenology, in a Gliosis-based manner at the Poincare level -- if such a photon does not directly strike another orbifold eigenset in a direct manner in the meantime.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Next Part Of "Entropic Photons"

Let us consider what tends to happen, over the course of the third set of 64 consecutive iterations of group-related instanton, that start from the moment that the respective given arbitrary photon acted in so as to strike another holonomic substrate-based physical phenomenology, in a Gliosis-based manner, at the Poincare level -- up to the ensuing so-eluded-to iterations of group-related instanton, by which I am about to describe as happening.  In so long as the so-eluded-to "entropic photon" does not act in such a Fourier-based manner, in so as to strike another orbifold eigenset -- from the instant that the directly associated respective photon has worked in so as to make a direct and immediate contact with another orbifold eigenset-based phenomenology, up to the so-proscribed and the soon to be described set of what are to here be mentioned, as being of the successive series of iterations of group-related instanton, -- that go from the 129th consecutive iteration of such a successive series of instantons that start from the moment of impact, up to the 192nd consecutive iteration of the self-same successive series of instantons, that had started from the moment of impact -- the same "entropic photon" will be mildly partially Yau-Exact -- since only two of the holomorphic-based coniaxions of the torsional-based eigenindices, that are to here be related to the contorsioning of the holonomic substrate of the said "entropic photon," will bear a bending that is of a hermitian-based nature.  The rest of the holomorphic-based coniaxions of the so-eluded-to torsional-based eigenindices are here to bend in a Lagrangian-based Chern-Simons nature.  The light-cone-gauge topology of the said "entropic photon," will here be of an abelian or of a Kaluza-Klein nature, instead of being as a Yang-Mills nature.  This is in contrast to the light-cone-gauge topology of a non-entropic photon -- of which is of a Yang-Mills nature.

More As To "Entropic photons"

After the initial 64 consecutive iterations of group-related instantons that have happened to a given arbitrary photon -- as had happened over the course of here starting with that instanton at which the respective given arbitrary photon of this case, had struck another holonomic substrate of physical phenomenology in a Gliosis-based manner -- in a manner that would here be at the Poincare level to the two respective eluded-to orbifold eigensets that had just been brought into a direct impact, the so-eluded-to "entropic photon" will then work to bear one of its ten parametric spatial dimensions, to bear the holomorphic tendencies, that will bear torsional eigenindices that may bend in a hermitian-based manner -- to where such a discrete quantum of electromagnetic energy will then be barely partially Yau-Exact -- since one of the ten spatial dimensions of the said photon will be Yau-Exact, while nine of the ten spatial dimensions of the said photon will, at this point in group-metric, be of a Lagrangian-based Chern-Simons nature, -- as the said photon is to then be traveling through a Lagrangian-based Hamiltonian operand that will be moving in a minimum of 10 spatial dimensions plus time.  This is as the said "entropic photon" will here work to bear a tendency of changing in ten spatial-based derivatives -- in so as to make such a discrete quantum of electromagnetic energy to basically be of a Chern-Simons nature, during this so-eluded-to transient duration of group-metric.  This will proceed, over the ensuing 64 iterations of group-related instanton.  To Be Continued!

Photons And Entropy, Part One

How about if I am to compare and contrast the characteristics of a photon undergoing Noether Flow, to a photon that is entropic -- right after such a Sterling-based quantum of discrete eletromagnetic energy has just struck another tense of an orbifold eigenset, in a Gliosis-based manner, at a level that is Poincare to the Yukawa-based tense of the so-eluded-to two tenses of orbifold eigensets -- that are to have here collided in a relatively direct manner, -- over the duration of that group-related metric, that would span from just before the so-eluded-to impact, up to just after the so-eluded-to impact.  What you will have here, at starts, is a discrete quantum of energy -- that is partially Yau-Exact, as it travels thru what would tend to be a Hamiltonian operand of ten dimensional space, -- because the holomorphic-based torsional eigenindices, that are of the so-eluded-to illumination-based photon, are to only bend in a hermitian manner -- in six of the ten coniaxion-based back-and-forth degrees of spatial parameter-based freedom, by which such a discrete electromagnetic particle is moving thru, over time.  As the respective photon moves in ten spatial dimensions plus time, over a correlative Fourier Transformation, it will here tend to pervasively continue to alter in ten spatial derivatives, in a systematically cyclical manner, over the proscribed duration in which it is moving through its given arbitrary Lagrangian, via the process of Noether Flow.  Such a discrete quantum of energy, is to here be of a Yang-Mills nature, since the correlative second-ordered light-cone-gauge eigenstates are to here be of a Laplacian-based sinusoidal-related nature, during the whole duration of each successive iteration of BRST,  in which the said discrete quantum of energy is as that of a photon.  This works to make a photon of a partially Yau-Exact nature in the substringular realm.  Such a superstring will work to bear a non-abelian light-cone-gauge topological geometry.  Just as the said photon is to strike a different eigenstate of an orbifold eigenset-based phenomenology, the light-cone-gauge topology of the said photon is to then convert -- as like the fractal of a "spring-like nature," -- into then temporarily bearing a Kaluza-Klein or an abelian light-cone--gauge topology.  From that iteration of the just eluded-to correlative group-related instanton -- up to the ensuing 383 iterations of group-related instantons, what was initially to be a discrete quantum of illumination-based electromagnetic energy, will at this point in group-metrical duration, act as an "entropic photon."  Initially from this point in duration, and for the ensuing 63 iterations of group-related instantons, the holomorphic-based torsional eigenindices, that are here to be formed by the said "entropic photon" are to then be of a completely Chern-Simons nature.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

A Fascinating Interim

Here is a brief synapses as to  the general tendency, as to the differences between a neutrino that moves via Noether Flow, as compared to a neutrino that moves via tachyonic flow.  A neutrino that moves via Noether Flow has an abelian, or in other words, a Kaluza-Klein light-cone-gauge topology.  Such a neutrino that moves via Noether Flow, alters in its holomorphicity, in such a manner that is only of a hermitian-based nature,  in all ten spatial dimensions that it is moving through.  This means -- that a Noether-based neutrino works to bear its torsional eigenindices in such a manner, to where such eigenindices tend to change in as many derivatives as the number of spatial dimensions that such a torsional-based activity is moving through in a Fourier-based manner, over time.  This works to make neutrinos that move in a Noether-based manner, to be of a Yau-Exact nature.  Yet, neutrinos that move in a tachyonic manner, work to bear a non-abelian, or, in other words, a Yang-Mills light-cone-gauge topology.  Such a neutrino that moves via a tachyonic flow, alters in its holomorphicity in such a manner, that is only hermitian in ten of the twelve overall spatial dimensions that it is moving through.  A tachyonic neutrino moves in twelve spatial dimensions, yet, the torsioning of the holomorphic-based eigenindices of a neutrino, tends to only work to alter in up to ten of such twelve of its so-eluded-to spatial dimensions.  This means -- that a tachyonic-based neutrino, works to bear its torsional eigenindices in such a manner, to where such eigenindices tend to change in two more derivatives, than the number of spatial dimensions that such a torsional-based activity is moving through, in a Fourier-based manner, over time.  This works to make neutrinos that move in a tachyonic-based manenr, to be of a partially Yau-Exact nature.

The Second Interim In-Between Sessions 2 and 3 of Clourse 20 -- Calabi Interactions and Calabi Manifolds

Neutrinos are comprised of one general genus of mass-bearing superstrings (and therefore Yau-Exact), that are of discrete energy permittivity.  Neutrinos are thereby comprised of, in part, by a certain type of Calabi-Yau bosonic string -- that is existent in a Gliosis-based manner, from within the Ward-Caucy bounds of the so-eluded-to orbifold eigenset, that works to operate as the manifold of the  said respective individually taken neutrino -- as a genus of a superstring, that is of a p-field that works to alter in its holomorphicity in what would only tend to be in a hermitian manner, over time.  This would then mean, that the mass-bearing superstrings that work to comprise the so-stated neutrino, are closed-loops that act as two-dimensional superstrings of discrete energy permittivity, that are configured to the correlative ten-dimensional spatial environment that the said p-field is to here be going through, over time, in a Yau-Exact manner.  This then means, that the torsional eigenindices of those mass-bearing superstrings -- that work to comprise neutrinos, tend to always bend in a hermitian manner, over the correlative sequential series of instantons by which such a neutrino would be metrically going through.  This would then mean, as well, that if such a string as a neutrino, were to travel through or be propagated through a relatively unitary Lagrangian-based Hamiltonian operand, over time, then, the so-eluded-to neutrino, as an orbifold eigenset, will then tend to not directly bear any Lagrangian-based Chern-Simons singularities -- via any directly corresponding Yukawa-based manner.  This would mean, that, the Real Reimmanian-based propagation of any given arbitrary respective neutrino -- will tend to not work to directly form any spontaneous Doubolt cohomologies of a Njenhuis-based nature, in and of themselves.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Interim One In-Between Sessions 2 and 3 Of Course 20 -- Calabi Manifolds And Calabi Interactions

Let us consider two general types of mass-bearing superstrings of discrete energy permittivity. The first general category of mass-bearing superstrings of discrete energy permittivity that I will discuss, is that of nucleons. These mass-bearing superstrings, are bosonic strings that exist in f-fields.  Superstrings that exist in f-fields -- act in a Fourier-based manner, in so as to move thru a minimum of four spatial dimensions plus time.  Mass-Bearing strings, that are of f-fields -- are closed-looped or two-dimensional phenomenology -- that are configured to a four-dimensional spatial field.  The next general category of mass-bearing superstrings of discrete energy permittivity that I will discuss here, are those of d-fields.  Superstrings that are of d-fields, exist in a minimum of six spatial dimensions plus time, as these travel thru a successive series of instantons.  Such bosonic superstrings, tend to be those that are generally associated with electrons.  The mass-bearing superstrings of electrons -- are closed-looped superstrings -- that are to acts as two-dimensional strings, that are configured to the format of a six-dimensional-based spatial field.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Partially Yau-Exact Superstrings

Let us take into consideration, the motion of one given arbitrary photon -- over time.  A photon exists in a p-field. A p-field works to appertain to a superstring, that moves through a minimum of ten spatial dimensions plus time.  This would then work to elude to the condition, that there may here be a ten spatial dimension-related coniaxion, that may be mapped-out -- in the directoral-based Lagrangian of the holomorphic direction that the said photon is to be moving through, over a sequential series of instantons.  As the interconnective mini-stringular segmentation that works to inter-bind both the correlative counterstring of such a respective given arbitrary case, to its directly corresponding superstring, as well as the interconnective mini-stringular segmentation that is to here be of that holonomic substrate of a light-cone-gauge eigenstate -- that works to inter-bind the directly corresponding superstring to its correlative Fadeev-Popov-Trace eigenstate, is to here work to bear a torsioning of its directly appertaining eigenindices, over time -- to where the intrinsic tendency will here be, that six of the ten spatial-related coniaxials-- as appertaining to the perturbative torsional eigendindices that are to here be of the overall ten of the so-eluded-to spatial-related coniaxials, that are to here be directly associated with the Hamiltonian-based motion of the said photon through space, will bear a bending through space that is of a hermitian-based nature, while, the other four of the ten spatial-related coniaxials -- as appertaining to the perturbative torsional eigenindices that are to here be of the overall ten of the so-eluded-to spatial-related coniaxials, that are to here be directly associated with the Hamiltonian-based motion of the said photon through space, will bear a bending through space that is, instead, of a Chern-Simons-based nature.  It may often vary-- as to which of the ten spatial-related coniaxials are to be of a relatively Yau-Exact nature, and, which of the ten said coniaxials are to be of a relatively Chern-Simons nature.  This will then mean, that a photon that is not entropic, will tend to work to bear such resultant singularities -- that may be mapped-out from both the so-eluded-to hermitian and the Chern-Simons- related torsionings -- that will appertain to both hermitian and Chern-Simons Lagrangian-based singularities, over time.
This works to cause the condition, that photons are superstrings that tend to be partially Yau-Exact.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Perturbative Torsional Eigenindices

Let us initially consider one discrete quantum of energy -- of which is here to work to bear a wave-tug/wave-push, in one general direction over time.  Let us say that the so-stated discrete quantum of energy of this case, is to soon alter in its specific path trajectory, in so as to then alter in the genus of its respective holomorphicity.  Let us next say, that the external force -- of which is to here work to alter the directoral-based holomorphicity, that may be described of by the perturbation of the Lagrangian-based path of the said discrete quantum of energy -- is to here be of the nature of a Real Reimmanian-based charge of some kind, that is to here be delineated in a relatively Gliosis-based manner upon the holonomic substrate of the so-stated discrete quantum of energy, in what may be described of here as a relatively Rham-based cohomological-based tracing of a path trajectory, over a successive series of instantons.  The tendency of such a respective given arbitrary case, will be to where the resultant Fourier-based action, that will here be enacted upon the topological surface of the inter-connective mini-stringular segmentation, that is to here work to bind the correlative respective counterstring to its correlative resepctive superstring, of which is to bind to its correlative respective Fadeev-Popov-Trace eigenstate of such a case -- will be a tendency in which the said topological surface will end-up being bent in a torsional way, just as the said discrete quantum of energy is to here be re-delineated from one substringular displacement to the next.  If the directly corresponding superstring is to here be Yau-Exact, then, such a perturbative torsioning of the eigenindices of that said inter-connective mini-stringular segmentation, will tend to be bent in a completely hermitian manner.  Yet, if instead, the directly corresponding superstring is to here not be of a Yau-Exact manner, then, such a perturbative torsioning of the eigenindices of that said inter-connective mini-stringular segmentation -- will tend to be bent in a Chern-Simons-based manner, over the correlative successive series of instantons.
 I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Torsional Eigenindices Of Discrete Energy Quanta

Let us take into consideration, the physical conditions of a discrete quantum or quanta of energy -- that moves, under the Ward-Caucy-based conditions of having, over a correlative group-metric, the Fourier-based state as to having the presence of non-perturbative torsional eigenindices -- over the so-stated correlative group-metric.  It is the Yukawa-based Ward-Caucy-related activity of the directly corresponding Njenhuis charges, that are to here be physically applied to the holonomic substrate of a discrete quantum or a discrete quanta of energy, -- that would then tend to work to alter or to perturbate the initially so-eluded-to Jacobian eigenbase, as to the correspondence of the translation of the holonomic substrate-based eigenindices of the directly corresponding discrete quantum or quanta of energy -- that are to here be directly effected, in a Yukawa-based manner, by the so-eluded-to Imaginary set of one or more charges -- that would act here, in so as to tend to work to help, in the process of then working at forming such a genus of a flow of the said respective discrete quantum or discrete quanta of energy, to where the so-stated discrete energy is to then be "pushed" or "tugged" as a unit, in any directly corresponding holomorphicity, in which the respective given arbitrary pulse of the correlative Njenhuis or Imaginary charge or charges, that will have here been applied to the said discrete energy, will have here been proscribed for as, over a successive series of group-related instantons.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Part 5 Of Session 2 Of Course 20 -- Calabi Interactions And Calabi Manifolds

Let us initially consider the general tendency, as to the general differential geometry of the relative conglomeration of one discrete quantum of energy, to where there are here to be:  one respective given arbitrary correlative Fadeev-Popov-Trace eigenstate, its correlative superstring of discrete energy permittivity, as is to here be at a positioning that is just to the relative forward-holomorphic of a Laplacian-based distribution at the very start of BRST, and, the here correlative counterstring, as is to here be at a positioning that is just to the relative forward-holomorphic of a Laplacian-based distribution, as well, at the very start of BRST.  It is the correlative light-cone-gauge eigenstate, of the so-eluded-to discrete quantum of energy -- that acts in so as to work to inter-connect the so-stated Fadeev-Popov-Trace eigenstate with its directly correlative superstring of discrete energy permittivity.  And, it is a correlative proximal localized set of mini-stringular segmentation -- that acts in so as to work to inter-connect the so-stated superstring of discrete energy permittivity with its directly corresponding counterstring.  The most inert tendency of a given arbitrary holomorphic flow, is to here, be going in a Fourier-based manner, in a relatively "straight" manner -- from the initial relative Laplacian-based distribution of the here correlative Fadeev-Popov-Trace eigenstate, towards the initial relative Laplacian-based distribution of the here correlative counterstring, -- over a successive series of group-related instantons.  Quite often, in reality (the theorertical versus the actual), when there is any general genus of a torsioning, that is to here happen to the holonomic substrate of any of one individually taken discrete quantum of energy, it will then tend to cause a Fourier-based differentiation of a kinematic-based Hamiltonian operation, to where the interconnections, that may have here been of an initial state of linearity -- will then work to, instead, bear a tendency towards an oscillitory-based bending of the torsional-based eigenindices -- that are to here be interconnecting the proximal localized partially integrated genre, of such a said discrete quantum of energy.  Such a resultant oscillation of the kinematic-based eigenindices, that work to bind the partially integrated genus of one respective given arbitrary quantum of energy -- will work to help in the here resultant alteration of the directoral-based Hamiltonian operation, that is to here be correlative to a continued change in the here respective holomorphic direction of the said discrete quantum of energy.
To Be Continued!  Sincerely, Samuel David Roach.

A Further Interim As To Session 2 Of Course 20 -- Calabi Manifolds Calabi Interactions

If the Ward-Caucy-based Yukawa Coupling, that is of one set of zero-norm-state-projections, that are to strike one superstring of discrete kinetic energy permittivity, in so as to work to form a photon via the Fujikawa Coupling -- is to strike the just mentioned superstring at one given arbitrary angle, as would here be subtended from in-between the correlative said set of zero-norm-state-projections and the correlative Fadeev-Popov-Trace eigenstate -- the directly corresponding angle, that is to here be delineated by the directly corresponding individually taken set of zero-norm-state-projections, that are to here strike the correlative counterstring of discrete kinetic energy permittivity, by which this is to result in forming the directly corresponding counterpart of the said photon, via the Fujikawa Coupling -- this will happen, to where this is to then be subtended by the same genus of a Ward-Caucy-based angle, from in-between the correlative said set of zero-norm-state-projections and the correlative core-field-density of the directly corresponding superstring, that was here initially mentioned as working to form the so-stated photon.  If the so-eluded-to angle of Gliosis-based strike, is to be either more acute or more obtuse than it should theoretically be, in so as to work to form the initially extrapolated tense of the holomorphic pulse -- that the soon forming photon and its counterpart were to have -- in order to not veer in its directoral-based propagation, then, the holomorphic direction of the soon propagated photon and its counterpart will contorsion, as I will soon explain later!

I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

An Interim In-Between Two Parts Of Session 2 Of Course 20 -- Calabi Manifolds And Calabi Interactions

The following is the general tendency as to the relative Gliosis-based positioning, of those zero-norm-state-projections, that are to here act upon a quantum of discrete energy that is released as the excess energy of an electron -- in so as to result in working to form a photon (and its counterpart).  In one given arbitrary case scenario, as the two individually taken sets of zero-norm-state-projections, that work to form both the respective photon and the respective counterpart of the photon -- via the Fujikawa Coupling -- are acting in a Gliosis-based manner upon the holonomic substrate of both the respective given arbitrary discrete quantum of particle-based kinetic energy permittivity, and, the respective given arbitrary discrete quantum of wave-based kinetic energy permittivity -- the so-eluded-to two open loop amplitudes, that are here of the holonomic substrate of both the respective one-dimensional superstring of discrete kinetic energy permittivity, and, the respective one-dimensional counterstring of discrete kinetic energy permittivity, are here to be closed, via the duration of a successive series of group-related instantons, in a hermitian manner -- in so as to work to help in the forming of the resultant respective said photon and the resultant respective counterpart of the so-stated individually taken photon.  This said Fourier-based tense of differentiation, is to here work to form both a resultant bosonic superstring of discrete electromagnetic energy permittivity, that is completed in its formation -- at having the superstring that is to here be formed as such, to be knotted at a spot, that is here be be Gliosis to the said formed bosonic superstring, at a general locus that is proximal localized at the relative central index of curvature that is Njenhuis to the forward-holomorphic positioning of both that respective so-stated resulting two-dimensional superstring, and, at that respective so-stated resulting two-dimensional counterstring that will have here just been formed by the so-stated Fujikawa Coupling via the Green Function. This would then mean that, over the course of the Fourier-based activity of the said eigenmetric of the Fujikawa Coupling -- that the hermitian-based closing of the two said loop amplitudes, that will here result in the formation of both the here formed photon and its counterpart, will happen as a radial-based delineation of the initially so-eluded-to open-loop amplitude, in a directoral-based curvature that is here to work to bear a wave-tug based motion, that is to here be flush in the said relative Njenhuis to forward-holomorphic direction, in both of these so-stated cases.  This is in so long as there is to here be no contorsioning, in what is to here be the directoral-based Lagrangian affliliated propagation of the initially so-eluded-to holomorphic direction, that is of the motion of the here formed photon and its counterpart, over the course of the said eigenmetric of the Fujikawa Coupling.
I will continue with the supsense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Four Of Session 2 Of Course 20 -- Calabi Manifolds And Calabi Interactions

Do you remember me mentioning the two sets of zero-norm-state-projections that work upon that discrete quantum of kinetic energy permittivity, in order to allow for that process that may be called the Fujikawa Coupling via the Green Function?  This involves one of such sets of zero-norm-state-projections, that is to here act upon the pointal-based quantum of discrete kinetic energy permittivity (the respective given arbitrary superstring) -- and one of such sets of zero-norm-state-projections, that is to here act upon the wave-based quantum of discrete kinetic energy permittivity (the correlative respective given arbitrary counterstring).  The angle that exists in-between the locus of Gliosis-based contact, in which the initially so-stated set of zero-norm-stated projections is to be working to form an abelian-related Fourier-based Yukawa Coupling upon the said superstring of discrete pointal-based kinetic energy permittivity, in so as to undergo a successive set of iterations of group-related instantons, in so as to work to allow for the correlative activity of the Fujikawa Coupling via the Green Function -- in so as to help the said discrete quantum of kinetic energy permittivty to subsequently work to form a photon -- and the Laplacian-based position-based iterative delineation at which the correlative respective Fadeev-Popov-Trace eigenstate is to here be in the process of being "tagged-along," is of a Ward-Caucy-based inter-relation of 22.5 degrees. As well, the angle that exists in-between the locus of Gliosis-based contact, in which the secondly so-stated set of zero-norm-state-projections is to be working to form an abelian-related Fourier-based Yukawa Coupling upon the said counterstring of discrete wave-based kinetic energy permittivity, in so as to undergo a successive set of iterations of group-related instantons in so as to work to allow for the correlative activity of the Fujikawa Coupling via the Green Function -- in so as to help the said discrete quantum of kinetic energy permittivity to subsequently work to form the counterstring of a photon -- and the Laplacian-related position-based iterative delineations at which the correlative respective superstring that is of the pointal-based nature of discrete kinetic energy permittivity, is to to here be in the process of being "tagged-along," is of a Ward-Caucy-based inter-relation of 22.5 degrees.  Due to the trivially isomorphic assymetry that is to here exist, in both of these two said general cases, of a proximal localized Ward-Caucy-based torsioning, that -- due to the just mentioned manner of assymetry -- works to form an abelian eigenbase of a general Fourier-related activity, in spite of the non-abelian nature of the Laplacian-related delineation of such a respective torsioning.  In both the case of the superstring, and in the case of the counterstring -- the correlative individually taken set of zero-norm-state-projections, will then work to form the equivalence of a supplemental-based wave-tug upon the Gliosis-based locus as to where the so-eluded-to discrete quantum of kinetic energy permittivity is to bear its so-eluded-to Yukawa Coupling, as to the ensuing activity of what is here to be the activity of the said Fujikawa Coupling, to where, in spite of the so-stated angling of the Laplacian-based Hamiltonian curvature that is to here be pushed at an angle that is not actually supplemental, -- the resultant Hamiltonian-based operation of the wave-tug that is to be applied in both of the eluded-to cases of a Yukawa-based thrust -- will then work to form a propagation that is to here happen to both the superstring and to its counterstring simultaneously via the vantage-point of a central conipoint, that is of a relative Wilson linearity to, what would be in both cases, in the relative forward-holomorphic direction as to the directoral tug of the then forming photon and its correlative counterstring.  I will continue with the suspense later! To Be Continued! Sincerely, Sam Roach.

The Third Part Of Session 2 Of Course 20 -- Calabi Manifolds And Calabi Interactions

The light-cone-gauge topology that is directly associated with a photon, is of a Yang-Mills, or, in other words, is of a non-abelian light-cone-gauge topology.  This works to mean -- that those second-ordered light-cone-gauge eigenstates, that work to form the holonomic substrate of the light-cone-gauge eigenstate, that works to inter-bind any one respective given arbitrary Fadeev-Popov-Trace eigenstate to the directly correlative superstring of discrete electromagnetic energy permittivity of any respective case, will tend to bear a Laplacian-based Ward-Caucy condition -- as to working to bear a sinusoidal delineation -- when this is taken as a Fourier-translated standing wave basis, via which there is a Clifford Expansion as to the scalar amplitude of the correlative mini-stringular segmentation, that works here, in so as to work to form such so-eluded-to second-ordered eigenstates, during the immediate Ward-Caucy condition that is related to the here proximal localized eigenstate of the correlative Polyakov Action. Yet, think about the Ward-Caucy-based conditions of the delineation of a superstring, during the course of any one respective iteration of BRST, in which the discrete particle-based quantum of energy permittivity is here to bear a relatively Laplacian-based displacement relation to the discrete wave-based quantum of energy permititvity, of which is to here bear a relatively Laplacian-based displacement relation to the discrete particle-based quantum of energy impedance, of which is to here bear a relatively Laplacian-based displacement relation to the discrete wave-based quantum of energy impedance.  This would then work to mean, that the Laplacian-based inter-relationship of those zero-norm-state-projections -- that are to here act as two different sets of individually taken mini-stringular segmentation, that is upon both the respective superstring of discrete particle-based permittivity and upon the respective counterstring of discrete wave-based permittivity, is to bear a Fourier-translated Ward-Caucy delineation, that is to work in a smooth-curved nature at the region that is most proximal localized at the Gliosis cite of contact, by which there is to here be a Yukawa-based contact of each said set of zero-norm-state-projection upon the two so-eluded-to tenses of discrete energy permittivity, -- in such a manner to where such a hermitian tendency of contact is going to then tend to bear a local wave-tug topology, that will then be of a non-abelian nature, over those correlative sequential series of group-related instantons, by which the Fourier-based activity of the Fujikawa Coupling via the Green Function is to happen -- so that discrete electromagnetic energy permititivty is to here be formed from discrete kinetic energy permititvity, that is bent in a hermitian-based manner, as may be extrapolated by the said Green Function, over time.  Such a so-eluded-to torsioning upon the holonomic substrate of the so-eluded-to eigenstates of zero-norm-state-projection, may then here work in so as to act, via the said Fourier-based activity of the Fujikawa Coupling, via the Ward-Caucy-based Laplacian condition of a trivially isometric assymetry, by which the earlier stated non-abelian geometry of the so-stated zero-norm-state-projections, that are proximal localized at that substringular region that is Yukawa to that motion that is Ward-Caucy to the said superstring and its couterstring, of which tends to work here, in so as to form a tense of a supplemental wave-tug/wave-push, that will then operate in such a Hamiltonian-based nature, by which the resultant Gliosis-based push of the said zero-norm-state-projections will then be able to work to bear a Yukawa-based torsion that will ironically act in an abelian-based manner.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.