Part Four of the Fourth Session of Course 16

The specific regions in which a Calabi interaction happens is known of as a Calabi Manifold. The set of activities or metrics that happen from within the Ward-Caucy bounds of where a Calabi Manifold is occurring -- when such a given arbitrary region is undergoing the eluded to Calabi interaction -- is known of as a Calabi-Metric.  The activity, or, in other words, the metrical activity, of the Klein Bottle -- as the just mentioned Klein Bottle (which is made in the structural format of a Schotky Construction) is facilitating the operation of a given arbitrary Gaussian Transformation eigenstate -- is the metrical duration that is known of as the Kaeler Metric.  When a Kaeler Metric involves a specific genus of a Gaussian Transformation that is known of as a gauge-transformation, the said genus of Kaeler Metric that is then here in the process of occurring is known of as the eluded to Calabi Metric.  A gauge-tranformation is that genus of a Gaussian Transformation of which directly involves those changes in norm-based conditions that have to do with the scattering of electromagnetic energy. Whenever electromagnetic energy scatters to any degree, such a scattering forms discrete units of what is known of as entropy, or, in other words, such an activity has to do with the formation of discrete units of that genus of physical disorder of which works to allow for certain things -- such as the ability of physical states to change from one format of physical state to another, to occur. (For instance, things are only able to melt if there is, at least to some degree, some amount or level of local  entropy existent.)  As I will later mention and describe in course 20, gauge-tranformations differ in their format of Gaussian transformation due to a torsioning in the Klein Bottle that I will get to describing more when I write-out that specific course material.  World-Sheets that directly appertain to ghost anomalies that work to map-out a Calabi Manifold are known of as a Calabi cohomology. The more homogeneous, or, in other words, the more smoothly distributed, a Calabi cohomology is, the better chance that there is for a less perturbative anharmonic scattering of relatively forward-holomorphic norm-states -- by relatively reverse-holomorphic norm-states, in the process of the breaking-down of ghost anomalies.  So, a Noether-based flow of superstrings works to bear more of a chance of a homogeneous distribution of ghost anomaly-based indices than a tachyonic-based flow of superstrings.  Again, this appertains to the condiiton that a relatively abelian pull upon those norm-state indices that work to be harmonically delineated, in so as to form ghost anomalies, will tend to bear more of a hermitian-based anharmonic scattering -- when the eluded to ghost anomaly-based indices are broken-down by relatively reverse-holomorphic norm-state projections.  Part of this tendency is due to the condition that substringular activity tends to bear a Noether-based flow.  The varied degrees of Noether-based flow, that involves virtually all motion, are due to the varied degrees of increase and/or decrease in the activity and the capacity of the conformal invariance that phenomena exhibit.  Tachyonic motion happens a lot, yet, it is relatively rare -- compared to the tendency of Noether Flow.  The condition of a relatively small amount of scattering of the ghost anomalies of the substringular encoders per time works to help allow for the tendency of an adequate amount of the spontaneous  "Gaussian ellimination" of excessive ghost anomalies -- to the amount that is necessary.  Yet, a certain amount of the scattering of the ghost anomalies of the substringular encoders is necessary in order for the various superstrings of discrete energy permittivity to be able to sufficiently branch-out along the Ultimon.  I will continue with the suspense later, by starting the fifth session of this course!  Sincerely, Samuel David Roach.

A Little Bit As To The Anharmonic Scattering of Ghost Anomalies

In all cases, when relatively reverse-holomorphic norm-states initially collide with relatively forward-holomorphic norm-states, there will be both a metrical and a Lagrangian based spike -- due to the perturbation that will happen for sure when antiholomorphic norm-states and antiholomorphic norm-state projections strike in a Gliossi manner.  Yet, in certain cases, the overall process of the anharmonic scattering of ghost anomalies is relatively hermitian, while, in other cases, the overall process of the anharmonic scattering of ghost anomalies is relatively Chern-Simmons.  This is in both the cases of metrical delineation and of Lagrangian delineaton, that is incured by the format-bases of Yakawa wave-tug/wave-pull that are brought into action when antiholomorphic-based norm-states and norm-state projections are altered in the multivarious manners that such activity may occur when there is a divergence from the initial path-based Lagragian eigenstates of two reverse-chiral phenomena at the Poincaire level.  When a superstring is traveling via a Noether-based flow, the activity of the Gliossi contact that exists in-between the said given arbitrary superstring and the norm-states that theses "bump into" bears a relatively abelian geometry, over a relatively transient duration of a sequential series of iteration of group instanton -- in which ghost anomaly-based indices are formed.  This just mentioned genus of a harmonic scattering of norm-state projections works to form an equal and opposite reaction of those relatively reverse-holomorphic norm-state projections to bear a topological sway that is homotopically of an even chirality -- relative to the relatively static delineatory basis of those ghost anomaly-based indices that the eluded to reverse-holomorphic norm-states strike at a later metric, in so as to anharmonically scatter the said ghost anomalies that are pertainant here.  This means that, here, the parity of the correlative reverse-holomorphic norm-states that strike the correlative forward-holomorphic norm-states of this given case will bear a trivially isomorphic symmetry, that is curved with a congruent basis of concavity -- when in terms of the respective Ward-Caucy bounds that is inherent to this given arbitrary case. The general flow of the Lagrangian of the directly related forward-holomorphic norm-states will bear an even symmetry with the general flow of the Lagrangian of the directly related reverse-holomorphic norm-states, in either case, though.  Yet, if a given arbitrary superstring is tachyonic at any given locus in which it is kinematically differentiating over time, the superstring will have a Yang-Mills light-cone-gauge topology -- a non-abelian topology.  Via the activity of the Rarita Structure, in this case, the non-abelian topology of the said superstring of this case works to cause the topological curvature of the relatively reverse-holomorphic norm-state projections -- that later anharmonically scatter those ghost anomalies that the eluded to superstrings had just formed -- to bear a non-abelian wave-tug/wave-pull upon those ghost anomaly-based indices that these strike.  This means that the eluded to ghost scattering Hamiltonian operators will bear an odd chirality that is of a non-trivial isomorphic genus -- that is also of a reverse Ward-Caucy-based concavity.  The angling of the Gliossi-based contact of ghost scattering Hamiltonian operators will always bear some sort of a Ward-Caucy supplimental angling of 22.5 degrees upon the directly corresponding ghost anomaly-based indices that these strike.  As an ansantz, if the Hamiltonian operation of a ghost anomaly index is of a relatively cross-product basis, then, the Hamiltonian operation of the norm-state projections that scatter the eluded to ghost anomaly will be of a relatively dot-product basis.  This is more of a full explanation as to why a tachyonic-based flow of substringular activity forms more of a perturbative and Chern-Simmons-based anharmonic scattering of ghost anomalies, while, a Noether-based flow of substringular activity forms more of a hermitian-based anharmonic scattering of ghost anomalies.  I will continue with the suspense later!  Sam Roach.

The Third Part of the Fourth Session of Course 16

Ghost anomalies build up when the norm conditions of superstrings do not force these to cancel via the Gaussian geometry of the Planck-like phenomena and the superstrings that exist in any viable given arbitrary region. When the Gaussian norm conditions of the superstringular phenomena cause the directly corresponding ghost anomalies to cancel, the relatively reverse-holomorphic norm-states smoothly build up in an exponential manner just as the relatively forward-holomorpohic norm-states diminish in an exponentially smooth manner.  This is as there is, in a hermitian anharmonic scattering of ghost anomalies, a euclidean-based deterence of ghost anomalies -- as the directly corresponding mappable tracing that is comprised of a harmonic scattering of relatively forward-holomorphic-based norm-states is elliminated, as a physically emminant entity, in a relatively homogeneous manner in this given arbitrary case scenario. Yet, often, the scattering of ghost anomalies -- via an anharmonic ellimination of the physical memory as to the existence and the differentiation of superstrings -- happens in a more perturbative manner, particularly when the motion of the directly corresponding superstrings that works to form such a sequential series of traceable mapping, is pulled-out from a Noether-based flow into a tachyonic-based flow.  When what I have just mentioned happens, there tends to be more of a tendency for the formation of Chern-Simmons singularities in the mappable regions in which tachyonic flow is activated.   So, as superstrings go from a Noether-based flow into a tachyonic-based flow, the Chern-Simmons-based singularities that are thus formed work to form a lack of symmetry in the cyclic permutations that these directly corresponding superstrings imbue upon the norm-states that these harmonically scatter upon in a Gliossi manner, as the eluded to forward-holomorphic norm-states form the eluded to ghost anomalies.  Such a genus of anharmonic cyclic permutation that still involves a harmonic genus of Yakawa wave-tug/wave-pull often works to form a Clifford Expansion in the surrounding loci as to where the superstrings have perturbated in terms of their format of substringular flow.  This eluded to divergence in euler-based format that  involves a ghost-based "dominoe effect" tends to converge, when there are ghost inhibitors that work to supplement the format of Expansion in so as to work to bring the corelative spatial mappings into a tendancy of most rest.  This works to allow for the general tendancy of Noether-based flow.  Such a convergent group operation, that may be applied in so as to ease a relatively divergent Hamiltonian cohomological operation, may be viewed of as a Dirac operation that works in the direction of hermicity.  When there is entropy being formed, there are gauge-transformatons.  When there are gauge-transformations, the scattering of ghost anomalies by the anharmonic reverse-holomorphic norm-state projections will here involve what may be called a Calabi Manifold.  Whenever there is an antiholomorphc Kaeler condition that is involved with the scattering of ghost anomalies that has any direct relationship with the scattering of electromagnetic energy, such a scattering involves such a Calabi Manifold. I will continue with the suspense later!  To Be Continued. Sincerely, Samuel David Roach.

Part Two of the Fourth Session of Course 16 -- About Cohomologies...

Certain world-Sheets may often directly involve low-energy quanta that work to define a stead-state phenomenon that exists in a tightly proximal region, or, certain world-sheets may often directly involve high-energy quanta that work to define a perturbative state -- that has both a radial and a transversal kinematic differentiation, that may be mapped-out through a given arbitrary format of tracing -- from a significant starting point to a significant ending point. Often, too, certain world-sheets may involve both low-energy quantum-based indices and high-energy quantum-based indices -- in the process of what would here involve a sequential series of group instantons -- in which the mappable tracing of the directly corresponding ghost-based loci will then have tracked upon the trajectory of a superstring that has gone from going into a conformally invariant Noether-based flow into a tachyonic-based flow.   Often, world-sheets track the motion of superstrings that are Noether, yet, are not relatively conformally invariant, relative to the steady-state conditions of a low-energy-based quanta.  Any of such combinations may occur for certain world-sheets that may work at tracking a superstring that is quite varied -- in terms of either a metrical-based and/or a Lagrangian-based perturbation.  Ghost anomalies of any given arbitrary region must be eventually dis-assembled in order for these to not accumulate to the extent that these just eluded to phenomena would bear if these were to otherwise block the necessary Hamiltonian operands in which other substringular phenomena must move through.  These just mentioned ghost anomalies will tend to accumulate, unless these so-stated phenomena are acted upon.  The convergence of relatively reverse-holomorphic norm-states upon the multiplicit regions in which ghost anomalies exist, is that sort of activity that works to allow this to be so.  One may word this as naming the so-stated ghost-based anomaly as a group attractor -- in this given case, and, then naming the just mentioned relatively reverse-holomoprhic flow of norm-state projections that work to dis-assemble the so-stated ghosts as ghost-inhibitors (since the dis-assembling of ghost anomalies works to inhibit the overcrowding that excessive ghost anomalies would otherwise cause).  It is the supplementation of two geni of norm-state projection-based divergences that works to form a physically plotted convergent sequential series of wave-tug/wave-pull that works to cause the eluded to Gliossi-based interaction of opposite formats of norm-state-based holomorphicity upon each other at the Poincaire level.  This is what works to allow for that anharmonic scattering of ghost anomalies that allows for part of the process of the recycling of norm-based conditions.  Ghost anomalies tend to build up when the main conditions of superstrings do not force these said physical memories of the so-stated superstrings to cancel their mappable region that these are imbued upon, via the directly related Gaussian geometry of both those Planck-like phenomena and those superstrings that are to flow in the general given arbitrary region in which the eluded to mappable tracings have been formated to being in.  I will let you ponder this little "nugget" for now.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Tenses of Gaussian Transformations

Often, there are adjacent orbifold eigensets from different universal settings that are each in a relative transit to undergo their respective Gaussian Transformations, in so as to readjust their norm-based conditions.  When this happens, often, the specific mechanism that works to activate the process of the directly corresponding Kaeler  Metric eigenstate is multiplicity utilized -- over consecutive iterations of Gaussian Transformation eigenmetrics --  on the behalf of different orbifold eigenset-based regions that each, individually, appertain to different universal settings that are spatially proximal in the substringular.  This often means, in this case anyhow, that, only one Gaussian Transformation eigenmetric will here be inactivated for the specific locus that would here appertain to each individual universal setting, that is of the just eluded to general substringular neighborhood.  This appertains to the so-stated orbifold eigensets that are of the same universe, when in terms of a relatively transient duration of time for spatial Hamiltonian operators that are each only of the same universe.  This happens as any one of the eluded to specific orbifold eigensets, that are to alter in their norm conditions via the so-stated Gaussian Transformation eigenmetrics,  is to readjust its norm-based spatial conditions.  This is to where the other mentioned orbifold eigensets, that are each of different respective universal settings -- of which are proximal to each other at the Poincaire level, which is true even though these different orbifold eigensets are not Yakawa to each other in a Gliossi manner that is viable, are sequentially being acted upon in a consecutive manner in so as to spontaneously make the necessary changes in norm conditions that are allowed to change -- due to the said activity of the said group metrics of the said Gaussian Transformation eigenstates.  The difference in universal setting is due to the manner-based geni of the directly related intrinsic vibration and angling of both the directly related Planck-like phenomena and the directly related superstrings of discrete energy permittivity.  I will continue with the suspense later!  Sam.

Orbifolds and Kaeler Conditions

Let us take into consideration three given arbitrary sets of orbifolds -- each set of which works to define three different unique physical sets of spaces, that here appertain to three different sets of Hamiltonian operators that each are of different universal settings.  Let us now say that there is one respective orbifold, out of each of the three so-stated sets of orbifolds, that bears an antiholomorphic directoral-based trajectory -- when in terms of the ghost anomalies that work to indicate a physical memory of the world sheets that exist as the trajectory of the directly associated superstrings.  The here eluded to antiholomorphic Kaeler condition that may be then surmised by the kinematic existence of the tritiary-based one orbifold out of each set of orbifolds, is a cue for the activation of three respective Wick Action eigenstates -- one Wick Action eigenstate so formed for each set of orbifolds, that, here, bear an antiholomorphic Kaeler condition during the group metric that I have here eluded to.   Let us now also say that the three so-stated sets of orbifolds are spatially proximal, yet, with a Yakawa index that is not viably Gliossi to any significant extent.  This so mentioned activity works to form three spatially proximal Gaussian Transformations, that are allowed to happen on account of the activation of the Kaeler Metric -- indirectly by the initiation of the Wick Action by the kinematic activity that was due to the activity of the mentioned Kaeler condition in the first place. This would thus result in three discrete changes in norm conditions, that would here appertain to three different unique respective universal settings -- each.  So, even though the activity of all of the three eluded to Gaussian Transformations are relatively near each other in a spatially local manner, since the directly corresponding changes in the respective norm conditions are of different universes, the abelian format of the Yakawa Coupling that would here be involved with the wave-tug/wave-pull of the individual eluded to cohomologies upon each other would not bear an even function of a Gliossi-based genus of substringular torsion in term of topological sway.  This would then here mean that the interdependence of the so-stated three different universal settings would bear a condition of relative substringular independence --  when in consideration of the pull of the permittivity of the three eluded to integrative Hodge-based index of the Hamiltonian operations that appertain to each of the three so-stated sets of orbifolds that I have mentioned here.  I will continue with the suspense later!
Samuel David Roach.

A Little Bit of a Heads Up as to the Ensuing Portion of Course 16

When there are many world-sheets differentiating upon a relatively general locus -- that would here involve, in this given arbitrary scenario, different sets of world-sheets that would here correspond to individual sets of world-sheets that each involve kinematic mappings of different parallel universes that are of the same set of parallel universes -- then, what would work to entail the individual antiholomorphic Kaeler conidtions that apply to one antiholomorphic Kaeler condition per set of world-sheets that each directly correspond to different universe-based conditions per stratum of the said individual antiholomorphic Kaeler conditionality, would involve what is here to be the substringular status of different respective Gaussian Transformations that are to occur -- one Gaussian Transformation per each set of world-sheets that would each concur to different parallel universes, per each of the so-stated individual sets of world-sheets that work to form cohomological ghost anomalies that work to map out the tracing as to the existence and the activity of superstrings that act upon the stratum of the here eluded to indices of the here respective universes that comply to one universe per set of world-sheets that I have eluded to here at the said general locus of activity.  So, in this given arbitrary case, one has each individual set of world-sheets that each bear an antiholomorphic Kaeler condition, of which works to activate an individual Wick Action eigenstate for each of the said bases of cohomological index -- in so as to indirectly work to cause the activity of an ensuing Gaussian Transformation.  There is at least one index of holonomic substrate for each universe of one set of parallel universes that is kinematic from within the Ward-Caucy bounds from within -- say one to three millimeters from wherever one may extrapoltate these to be at.  So, it is possible for one to have, at a general locus, many sets of world-sheets -- that each form a viable bearing for one parallel universe that is unique to all of the other respective individual sets of world-sheets that are here kinematically being traced as a mappble  holonomic substrate as ghost anomaly-based indices -- in so as to allow for a conglomerate set of individual set of Wick Action eigenstates that each work to indirectly form what is here to be the respective sets of individual sets of respective Gaussian Transformation eigenstates that are all happening in a general locus.  Yet, individual eigenstates of Gaussian Transformation that are proximal, yet, are of different  universal settings, are not Gliossi in terms of cohomological index in any Yakawa manner that is viable to any abelian format of direct wave-tug/wave-pull leveraging -- in so long as none of the eluded to superstrings that are directly involved here do not synchronize in their intrinsic vibrations.  Superstrings that synchronize in their intrinsic vibrations become of the same universal settings when and if this is done.  Either way, each respective antiholomorphic Kaeler conditon that is to happen works to form one individual Wick Action eigenstate -- that indirectly works to form one individual Gaussian Transformation eigenstate.  Such an activity works to form the respective individual basis of specific Landau-Gisner Action eigenstates, as well as the respective individual basis of specific Fischeler-Suskind Mechanism eigenstaes, as well as each set of Gaussain Transformations that comply to unique universal settings that each work to involve different respective Higgs Boson eigenstates and different respective Klein Bottle eigenstates. So, in such a genus of a general locus that would here involve the changing of norm conditons of different indices of universal settings that are proixmal at the Poincaire level would here involve different individual Kaeler Metric eigenstates each, respectively.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Part One of the Fourth Session of Course 16

The activity of the kinematic spatial differentiation of superstrings, in the process of their delineations and re-delineations is what works to form the world-sheets that exist in the substringular -- the sequential series of the re-delineations of superstrings, as these are projected over time through their respective Hamiltonian-based operands, is what works to form those physical memories of the so-stated superstrings, of which is what works to form ghost anomalies in so as to form the respective given arbitrary cohomologies.  Ghost anomalies are formed by the harmonic scattering of relatively forward-holomorphic-based norm-states, that are applied to the correlative differentiation cites by zero-norm-state projections that are forward-holomorphic in nature.  The format of norm-states that work to comprise the majority of the respective Hodge-Index of ghost anomalies, are the composite of Campbell-states, Hausendorf-states, and/or Campbell-Hausendorf-states.  Zero-Norm-States -- even though these are essential for the process of ghost anomalies to become static enough in composition to be superconformally invariant over time upon the activity of the harmonic scattering of any given arbitrary path operand that may be integrable -- in so as to allow for the delineation of the eluded to genus of any type of ghost anomaly-based pattern that may be Yakawa to any local cite in which such ghost anomalies may possibly be formed -- are that format or genus of projection that makes it possible for the other format-types of norm-states to be able to behave as these do when these said ulterior-type of norm-states and norm-state-projections are harmonically scattered upon by the sequential series of motion that superstrings imbue upon Fock Space as these so-stated superstrings are being delineated and re-delineated upon over time.  All world-sheets that are defined by the harmonic scattering of forward-holomorphic norm-states are directly existent, due to the existence of Fock Space.  Fock Space is that general bearing of region-based genus that is outside of both superstrings, their counterstrings, and Fadeev-Popov-Trace eigenstates.  All ghost anomalies, and thus, all cohomology, is the result of the condition of Fock Space as acting as the holonomic substrate that works to define the physical memories of both the existence and the activity of superstrings over time.  Such loci of Fock Space works to exist as the Hamiltonian-based operands of superstrings, as such superstrings are distributed and re-distributed throughout the Ultimon over those sequential series of the iterations of group instanton that work to act as the metrical path of discrete energy over time.  The result of the ensuing anharmonic scattering of Gliossi-Sherk-Oliove-based ghost anomalies over time by reverse-holomorphic norm-states -- which is imbued upon by the respective interaction of reverse-holomorphic zero-norm-states and reverse-holomorphic zero-norm-state-projections that work to settle the Ward-Caucy bounds of the perturbations that are caused in part by the ellimination of what were the respective ghost anomalies -- works to form the physical entities that act as gravitatonial-based particles that thence kinematically differentiate off of the Real Reimmanian Plane -- in so as to allow for the existence of gravity, while, the ellimination of what I will later describe of as Neilson-Kollosh ghosts works to form the basis of the replenishment of Real Reimmanian-based norm-states and norm-state projections.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Ensuing Kaeler Metric Eigenstates

As I will discuss in much more detail over the course 24 about conformal and superconformal invariance, a specific discrete Gaussian Transformation eigenstate is directly effectual over the course of 384 consecutive group instantons -- the discrete Kaeler Metric portion of which is comprised of 191 consecutive of the so-stated 384 consecutive group instantons.  When a substringular region bears relatively little need for a change in norm conditions in its local substringular neighborhood -- due to a relatively mild genus of a here given arbitrary antiholomorphic Kaeler condition -- then, immediately after one discrete format of a local Gaussian Transformation, the activity of the directly corresponding Fischler Suskind-Mechanism eigenstate will be varied to an ensuing spatial delineation, that would here operate upon superstrings that are of a different universe. Again, all of the universes of one given arbitrary set of parallel universes are within about 3 millimeters of each other.  The activity of the genus of the angling of the directly involving Fischler-Suskind-Mechanism eigenstate is what functions in so as to propagate the motion of the so-stated mechanism-based eigenstate towards the eluded to "new" locus, that here works to form a bearing upon a different universal setting.  Yet, if a given arbirtary substringular locus needs a more vast alteration in norm conditions, then, there may be up to many consecutive discrete eigenstates of Gaussian Transformation that are Gliossi upon the same universal setting at the Poicaire level over time.  Again, different universes are not Real Reimmanian -- when this is considered relative to one another.  This basis of relativistic Gaussian Format is based upon the directly correlative basis of substringular angling of vibration.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Part Seven of the Third Session of Course 16

Kaeler cohomology may be Rham, Doubolt, or both -- depending upon the specific locus in which one is extrapolating a mappable tracing of where a given arbitrary ghost anomaly is differentiating, in either a time-wise or a timeless basis of co-determination.  If a ghost anomaly is Chern-Simmons at an extrapolatable locus in which there is such a format or genus of traceable singularity or traceable singularities, then, the genus of such corresponding cohomology -- that is latent to such a type of conditionality -- will definitely be of a Doubolt format of cohomology.  This is true, whether the directly corresponding Kaeler condition is of a holomorphic genus and/or if the directly corresponding Kaeler condition is of an antiholomorphic genus.  Part of as to why Kaeler Metric eigenstates exist as these do is due to perturbative fluctuations in the corelative world-sheets that kinematically differentiate over a relatively transient sequential series of iterations of group instanton -- to where those given arbitrary positive-norm-states that work to define the respective ghost anomalies, that work to bear the directly associated given arbitrary tense of cohomology, are anharmonically pulled out of a conformally invariant tense of harmonics.  This format of perturbation is in the respective regions that work to define the traceable mapping of the respective superstrings, of which have kinematically differentiated over the immediately prior duration of time that had come before the mappable tracing of the physical memory of both their existence and activity.  The activity of the scattering of the respective positive-norm-states by negative-norm-states -- that works to form the eluded scattering of ghost anomalies -- in the genus of an anharmonically scattered Gliossi-Sherk-Olive-based field in which Gliossi-Sherk-Olive ghosts are altered from their previous delineation -- works to define the basis of the probability of where and how the directly corresponding eigenstates of a Kaeler Metric are to happen, in the process of the interaction of the corelative world-sheets that are kinematic in a Yakawa manner in the given arbitrary Ultimon region.  If the eluded to cohomological interaction is anharmoically perturbative in a Gliossi manner over a transient period of time, then, the resulting effect with tend to form an antihomolorphic Kaeler condition, of which will work to form a Wick Action eigenstate that will indirectly cause a relatively local Kaeler Metric.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Part Six of the Third Session of Course 16

The set of iterations of instanton in which a set of one or more first-ordered point particles -- in the form of norm-states and/or norm-state projections, may initially flow through the general region of a kinematically-based world-sheet, that is in the form of multivarious delineated ghost anomalies -- in such a manner in so that the so-stated norm-states and/or norm-state projections are not mapped in a traceable manner from within the Ward-Neumman bounds of what may be extrapolated as the topological stratum of the Gliossi-based field of the said given arbitrary ghost anomaly.  This is a condition that eludes to a local tensor towards  the said given arbitrary adjacent world-sheet activity that is of a relatively antiholomoriphic/reverse-holonomorphic Kaeler condition.  Again, an antiholomorphic Kaeler condition works, as stated in my previous post, to initiate the activation of a Wick Action eigenstate.  An antiholomorphic Kaeler condition works to then indirectly activate what is known of as the Kaeler Metric.  The Kaeler Metric happens through a region of space that is open to the operation of that functioning of any given arbitary Klein Bottle eigenstate, that is directly affiliated with its given arbitrary Wick Action eigenstate that had preceded it -- of which would then here be the Hamiltonian operand of the said given eigenmetric of the corresponding Kaeler Metric.  This operand that is worked upon over a relatively limited span of group instantons may be extrapolated as being the here local Kaeler manifold.  The interaction of world-sheets that are applied upon and/or apply upon the just eluded to topological stratum, that would here work to allow for the operation of the said eigenstate of Kaeler Metric, inter-bind in so as to form what could be called a Kaeler cohomology.  A Kaeler cohomology is a direct reaction of the reassembling of norm-conditions that tends to be just perturbative enough to allow for the passage of the mechanisms that operate in so as to cause the activity of the directly associated Gaussian Transformation to happen.  A Kaeler cohomology may bear both a Real Reimmanian-based cohomological set of ghost-based indices, and/or a Kaeler cohomology may bear a Njenhuis-based cohomological set of ghost-based indices -- over the duration that would here involve those activities that are involved from the initializing of the directly corresponding Wick Action eigenstate, up to the ending of the directly corresponiding Gaussian Transformation that is Gliossi to the specific locus in which a holonomic substrate that is to be operated upon, in order to change in its norm conditions, is undergoing the general format of the corelative Kaeler Metric eigenstate. Any given arbitary Kaeler Metric eigenstate would here be needed at the said locus of substringular operation, in order for Gaussian Transformations to be able to occur.  The operation of any given arbitrary Gaussian Tranformation is comprised of a set of more subtle substringular operations that integrate here in so as to allow for the appropriate change in norm condtions at a set given arbitrary locus in so as to allow for both the needed reassortment of substringular distributions that are needed in order for phenomena to not be too bunched up, and, in order for the directly corresponding superstrings to reattain enough of a fractal of discrete permittivity in order to act as what acts as a discrete unit of energy permittivity, and, in order for the directly corresponding Fadeev Popov Trace eigenstates to attain enough of a fractal of discrete energy impedance in order to be discrete units of energy impedance -- so that both a decent delineation of energy may be spontaneous, and so that the existence of energy itself may be both spontaneous and perpetual.

More About Kaeler conditions

The center state of the perturbation of a cohomological set of indices that exists during the metrical duration that occurs right as the Wick Action eigenmetric is initiated, is the path operand as to where the center state of the ensuing relatively local directly corresponding Gaussian Transformation is to happen.  So, when there is a Kaeler condition that is antiholomorphic -- to where it is initiated upon a general substringular region -- in which a directly associated Wick Action is activated in the primal-based locus of the said general locus -- there will be an alteration in the morphological index of the eluded to corresponding cohomology, of which is comprised of interconnected ghost anomaly-based indices that are kinematic upon the on-shell topological stratum of the corelative substringular neighborhood.  Such an alteration in the morphological index will here be associated with a streaming of divergent Minkowski-based norm-state indices that bear Njenhuis norm-state projections that are tied together into what may often be an integrative Hilbert space that is annharmonic in terms of topological sway.  The center state of the eluded to perturbation of cohomological bearing is here comprised of the relative peak in topological Clifford-based divergence -- in terms of the sway of the here eluded to peaks and troughs of Gliossi-Sherk-Olive substringular field covariance.  The just eluded to Majorana-Weyl covariance will here be annharmonic in terms of both the metrical and the Lagrangian-based flow of Chern-Simmons singularites that are imbedded upon the holonomic substrate of the directly corresponding cohomological stratum.  The Laplacian-based coniaxial that may be extrapolated from one endpoint of the said general cohomological index of the here given arbitrary topological ebbing to the other endpoint of the said general cohomological index of the here given arbitrary topological ebbing -- at the conimetrical onset of the directly corresponding Wick Action that is being considered in this scenario -- is the traceable mapping as to where the center state of the ensuing Gaussian Transformation is to occur.  This  is to happen during the ensuing Kaeler Metric eigenmetric.  The higher the genus of the directly associated Chern-Simmons singularity-based perturbation is at the onset of the activation of the here eluded to Wick Action eigenstate, the more iterations that the directly affiliiated format of Kaeler Metric eigenmetric is to occur at the general substringular cite, as to where the eluded to perturbation is to occur.  Each of such iterations of Kaeler Metric that I have eluded to here will be at slightly different specific loci from within the general cohomological locus of index that I have here brought to the attention of the reader -- each of which will be centered at the specific locus that bears the best angular momentum to handle the readjustment of the substringular change in norm conditions best, via the appropriate centralization of the Hilbert gauge quantizaton that is structured kinematically along the previously discussed "longitude" of the eluded to format of a coniaxial-based Lagrangian of traceable mapping.  I will continue with the suspense later!
Sincerely, Samuel David Roach.

Part Five of the Third Session of Course 16

The ability of a specific region of a world-sheet that works to form ghost anomalies may be either propagated in the relatively forward-holomorphic directoral Hamiltonian path-integral, or, are propagated in the relatively reverse-holomorphic directoral Hamiltonian path integral, or, are propagated in a relatively antiholomorphic directoral Hamiltonian path integral -- given the tense of the directly associated kinematic-based flow of the accompanying Lagrangian that the said world-sheet is being propagated through over time -- in relation to the general directoral-based-flow of the eluded to Hamiltonian holomorphicity.  This is when in terms of the genus of the said condition, that could thence be called a Kaeler condition.  So, if a world-sheet of a given arbitrary scenario is moving in either a reverse-holomorphic directoral Hamiltonian-based path flow, or, in an antiholomorphic directoral Hamiltonian-based path flow -- in terms of the given arbitrary  Sterling approximation of the kinematic mappable tracing of the respective local divergence-based covariance or local scattering-based covariance.  Such formats of covariant-based modes are often Yakawa to the eluded to perturbation of one given arbitrary world-sheet relative to its immediately surrounding world-sheets, that are propagated in a metrical-based Dirac manner -- that is either euclidean-based in expansion mode or Clifford-based in expansion mode.  On account of what I just mentioned, this may be a Kaeler condition of an antiholomorphic divergence that may be extrapolated by the mapping of either a perturbative reverse-based covariance and/or a perturbative scattering-based covariance of the directly associated ghost anomalies -- that act here as physical memories of both the existence and the activity of the directly corresponding superstrings that behave in the format of the said manner.  If the given arbitrary world-sheets of a general locus are all kinematically covariant in terms of the genus of a convergent-based mode, then, the corresponding condition of holomorphicity may be considered as a holomorphic Kaeler condition. If a Kaeler condition is of a relatively antiholomorphic mode, and/or is of a relatively reverse-holomorphic mode, then, such a format of either a respective perturbative scattering-based condition or of a perturbative divergent-based condition is of a Kaeler condition that works upon the activity of a unique set of specific Njenhuis Rarita Structure indical projection eigenstates -- to form the metrical-gauge eigencondition of a Wick Action eigenstate.  The Wick Action is multiplicitly performed by a genus of a Hausendorf Projection that is applied through a mechanism of corroborative norm-state projections, that operates in such a manner in so as to activate the activity of Gaussian Transformations -- via the general basis of the operation of the Kaeler Metric.  The Kaeler Metric is applied by the interaction of a local Higgs Boson eigenstate with a local Klein Bottle eigenstate.  Please read my previous writings for some more detail about this.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Part Four of the 3rd Session of Course 16

The activity of the formation of ghost anomalies, via the activity of superstrings being projected as world-sheets, that form a mappable tracing as to the extrapolation of the Ward-Caucy bounds of the physical memory of the so-stated given arbitrary superstrings -- these of which have kinematically been redelineated over a sequential series of group instantons -- often have an adjutant distributioinal proximity to norm-states that are in the general path of the directoral index of the Hamiltonian-based adjutant norm-states. In this given case scenario, this does not necessarily bear a partial integration into the eluded to mappable tracing of the eluded to ghost anomaly-based propagation -- in which the more Gliossi-based norm-states that work to come together in so as to form those indices of physical memory of the said superstrings, that work to tie together to form a cohomological path operand that adheres to a specific Hamiltonian-based ghost operator,  operates in so as to bear a specific functional group-metrical-gauge.  This is a Laplacian condition of cyclic permutations that are physically imputed within the Ward-Neumman bounds of the projection of the said given arbitrary world-sheet -- this of which operates as a ghost-inhibitor-based genus of norm-state indices that are incorporated into the general cohomological region of the formation of a ghost anomaly, in a manner that is not Yakawa to the basis of the operation of the general holonomic substrate of the said ghost anomaly in a Gliossi manner -- in any spontaneous viable way.  This works to cause the directoral Hamiltonian parametric capacity of the loci of the so-stated norm-states, that act as kernel-based indices of cyclic permutations, to behave kinematically in a manner that is not holomorphic with the delineatory kinematic operation of the propagation of the Fourier-based transformation -- of the cohomological index that is chiral to the euclidean-based expansion of the said given arbitrary ghost anomaly that is here being transversed through a discrete Lagrangian over a traceable mapping,  this of which is formed over a sequential series of iterations of group instanton. This would then bear a condition of directoral-based distributional index that would be either in a relatively steady-state holomorphic delineation that is relatively non-holomorphic, or, this would bear a condition of directoral-based distribution index that would be relatively antiholomorphic to the kinematic topological sway of the here given arbitrary propagation of the cohomological Hamiltonian-based ghost operator of the so-stated scenario.

Part Three of the Third Session of Course 16

The norm-state indices that work to comprise the given arbitrary ghost anomaly one may consider here is both a specific case of a physical phenomenon that works upon its immediate environment, and also a specific case of a physical phenomenon that is worked upon by its immediate environment.  This would make the norm-state indices that here integrate to form the so-stated ghost anomaly index both a holonomy and a substrate that is Yakawa to its physical environment of substringular neighborhood -- in a Gliossi manner at the Poincaire level, that atones a bearing at the genus of substringular region that is tantamount to the here adjoining integration of superstrings of discrete energy permittivity -- that work to form a locus of the immediate locus of directly interacting orbifold eigensets.  This is here a situation in which the eluded to orbifold eigensets are behaving in a kinematic environment that is prone to vear in the relative forward-holomormphic directoral wave-tug/wave-pull over time.  So, as the so-stated given arbitrary orbifold eigensets of the said scenario are pulled into the genearal directoral Hamiltonian operand -- that bears a path of Lagrangian that is unimetrical over the course of a successive series of group instantons, in such a manner in so that the mappable tracing of their physical memories works form a cohomology-based build-up that effects the concertive directly adjacent orbifolds -- that bear a local import of adjacent operations that perform different discrete functions that act within the premises of a local substringular neighborhood, both the activity of the eluded to orbifolds and the activity of the eluded to adjacent orbifolds forms a respective set of kinematic delineation that act as a holonomy.  This being of the initially mentioned orbifold eigenset -- that is acted upon as a substrate -- due to the so-stated activity that the said adjacent orbifold eigensets bear upon the initially stated orbifold eigensets. This may work to form an assymetric chirality of a consideration as to what the given arbitrary holonomy and substrate are, when the given arbitrary holonomy and substrate are acting via an eluded to Hamiltonian Fourier Transformation that bears a kinematic-based mappable tracing that is extrapolated respectivitly inward.  (The holomorphically dot-product-wise condition versus the holomorphically cross-product-wise condition, in this case.)  The basis of the here eluded to interaction is actually meant as the interaction of the physical memories of the so-stated orbifold eigenset.
P.S.:  Actually, what I meant by "holonomy" is "holonome."  A holonomy is the condition of a physical phenomenon being a holonome.  I will continue with the suspense later!  Sincerely, Sam Roach.

Compactification Formats of Ghost Anomalies

When a Gliossi-Sherk-Olive-based genus of ghost anomaly is formed, the directly corresponding set of point commutators that are harmonically redistributed -- in so as to form the associated traceable mapping of the just eluded to format of ghost anomaly -- in such a manner in so that the so-stated first-ordered point particles that work to form the said anomaly are brought relatively toward each other.  This forms a manner of compactification at the Poincaire level of each local cite in which the corresponding ghost anomalies are thus formed.  This genus of compactification forms a cite, in which the striking of relatively reverse-holomorphic norm-states upon the general locus of a ghost anomaly of such a format -- in what would here be an anharmonic Gliossi wave-tug/wave-pull upon the holonomic substrate that is here comprised of redistributed first-ordered point particles -- works to more readily be scattered by the eluded to Yakawa push of the here so-stated reverse-holomorphic norm-states upon the Poincaire region in which the mentioned ghost anomaly had originally occupied, in this given arbitrary genus of mappable tracing.  The thence caused anharmonic scattering of the initially stated ghost anomaly, that is here pulled apart at the indices at the Poincaire level, is here more likely to be spontaneous -- in the process of the just mentioned eliminiation of the eluded to condition of ghost-based indices, that here had initially comprised a condition of bearing a physical memory as to both the activity and the existence of the directoral Hamiltonian path-operand of a set of superstrings that operated -- in so as to perform a specific physical function.  The just eluded to anharmonic scattering thus acts in so as to form a decompactification of the directly corresponding first-ordered point particles that had existed as sets of norm-states.  Norm-States that work to comprise a ghost anomaly may either be a composition of zero-norm-states that were relatively forward-holomorphic, Campbell-norm-states that were relatively forward-holomorphic , Hausendorf-norm-states that were relatively forward-holomorphic , and/or Campbell-Hausendorf-norm-states that were relatively forward-holomorphic.  The initial harmonic scattering that works to form a set of ghost-based indices -- that work to form a ghost anomaly -- works to "steady-out" the initial kinematic motion of the directly corresponding eluded to set of norm-states, into a more static phenomena of holonomic substrate.  So, when a ghost anomaly is scattered by reverse-holomorphic norm-states, the ghost anomaly is spread outward, in a multivaried  basis of Lagrangian, that ends what was initially a ghost anomaly.  So, the initial physical condition of compacitfication that I had described works to allow for the multiplicit Clifford Expansion that happens when a ghost anomaly is struck by a reverse-holomorphic set of norm-states and/or norm-state projections.  Another wary of putting it is that the act of the formation of a ghost anomaly bears a dot-product Jacobian eigenbasis, that, when struck by a relatively reverse-holomorphic set of norm-states, works to form  a cross-product of Jacobian eigenbasis.  This works to allow for both the spontaneous and the perpetual existence of a continued tendency of Hamiltonian-based path operands -- so that both the physical memory of superstrings, as well as plenty of region for superstrings to be able to move, may be thus facilitated.  I will continue with the suspense later!
Sincerely, Samuel David Roach.

Part One of the Third Session of Course 16

If you will, I am going to start with the simple.  Superstrings have fields.  Superstrings kinematically differentiate in the substringular in such a manner in so that these are detectable as these are extrapolated in the manner that these are in the globally distinguishable.  When superstrings spatially differentiate in a given arbitrary trajectory that these are projected in, through the spectrum of the Ultimon, after a successive series of an iteration of instantons, the said given arbitrary superstrings work to form what may be logically deduced as world-sheets -- whose physical memory of such may be thought of as ghost anomalies.  World-Sheets often allow the first-ordered point particles -- that may often here be point commutators -- to flow within the substringular neighborhood of the directly corresponding Sterling Approximations.  This genus of extrapolation is as to the locus of where the correlative superstrings had been over the course of an integration of the Lagrangian-based extrapolation -- in such a manner in so that the harmonic scattering of the so-stated point commutators, that are in the relatively direct path of the so-stated superstrings of discrete energy, forms, to a degree, some sort of  "anatomical" mappable tracing as to the potential whereabouts and activity of the directly corresponding superstrings of discrete energy that are here under question.  The mapping of ghost anomalies tends to pull the directly corresponding point commutators, that are moved by the so-stated harmonic scattering, inward at the outer edges of the related tracing.  This happens here, while yet working to pull the directly corresponding point commutators that are moved by the so-stated harmonic scattering outward at the relatively more interior general format of locus as to those regions that ghost anomaly-based indices are formed.  This happens over the correlative sequential series of instantons in which the motion of superstrings are being delineated and redelineated into the Gliossi Ward Neumman bounds of the said point commutators.  Such a scattering -- when happening in the same time-wise directoral format of path-wise Lagrangian genus of directoral sway -- is said to happen in what may be termed of as the forward-holomorphic directoral Hamiltonian path operand, when in relation to the directly corresponding distribution format of superstrings that are not perturbated from a constant metrical direction.  So, when a superstring is reversed from what was its initial delineation of time flow, its directoral Hamiltonian path operand is said to be altered into what may be termed of as the relatively reverse-holomorphic direction.  The forward-holomorphic direction may be arbitarily chosen as the relative left and/or counterclockwise direction, and, the reverse-homorphic direction may be arbitrarily chosen as the relative right and/or clockwise direction.  Phenomena that are worked upon in the substringular at the Poincaire level are considered to be substrates.  Entities that act upon their substringular region at the Poincaire level are holonomes.  So, a holonomic substrate is a substringular phenomena that both acts upon and is also acted upon by another substringular entity at the relative Poincaire level.  I will continue with the suspense later!  Sam Roach.

Ghost Inhibitor Eigenmatrices

Gliossi-Sherk-Olive fields inter-bind Rarita Structure-based field eigenstates via group attractor field eigensets that here act as ghost inhibitor eigenmatrices.  Individually, such an eigenmatrix, when involved with a common Gaussian format for these directly associated orbifolds that I have just eluded to, forms a field network that inter-twines the eluded to directly corresponding orbifolds into being of the same universe.  This works to make these discussed eluded to orbifolds to be of a trivial Li Algebra genus -- that is then causing these so-stated orbifolds to be of the same universal setting.  The said genus of ghost inhibitor eigenmatrix discussed here bears chiral Njenhuis Campbell-Hausendorf tensors that help work to form a Jacobian eigenbasis at the locus of the cite of the field network that ties together the so-stated Rarita Structure field eigenstates with the so-stated Gliossi-Sherk-Olive field eigenstates. This brings these given arbitrary orbifolds into then being of the same gravity-based universal setting.  This would then mean here that the corresponding eluded to gravitational indices will, in this case, bear a Yakawa-based interconnection that is field-wise Gliossi at the Poincaire level.
I am gradually building up the suspense.  To Be Continued!  Sincerely, Samuel David Roach.

Activity Associated With Chern-Simmons Genus

The higher the genus of a Chern-Simmons Lagrange-based singularity is, the more likely that the directly corresponding superstring, or, orbifold of one or more superstrings, is at being pulled out of its initial spatiality of Gaussian-based format.  So, if an orbifold moves through a Lagrangian in a kinematic manner over time in such a manner in so that  there is a change in eight more derivatives than the dimensionality of its initial euclidean Real Reimmanian arc, then, the said given arbitrary orbifold is more likely to become of a Li Algebra-based pretense -- subsequent to the eluded to metric of Chern-Simmons-based perturbation that would be along what is here then its Njenhuis-based Lagrangian kappa scattering -- than an orbifold that only changes in one more derivative than the number of spatial dimensions that it is traveling through over time, to become of a different universal setting of Gaussian format and/or of a different layer of reality.
I will continue with the suspense later!  Sincerely, Samuel David Roach.

How Gauge-Bosons Move

As the Polyakov Action occurs multiplicitly, in a simultaneous manner that hereby coincides with the activity of the Bette Action -- that is also here multiplicit in operational index --, the directly corresponding gauge-bosons that work at plucking second-ordered light-cone-gauge eigenstates in so that the corresponding second-ordered Schwinger-Indices may form, bear both a relatively "steady-state" kinematic topological sway & a sort of "back-and-forth" kinematic wave-tug/wave-pull, that works to unleash those vibrations from the light-cone-gauge that fuel those ghost inhibitors of the Rarita Structure -- so that there may be a direct relationship between discrete phenomena of both energy permittivity and energy impedance & discrete phenomena of metrical-based-Gliossi gravitational Hodge Index.  The so-stated "steady-state" kinematic operation is a mobility that topologically sways outward -- in functional parity with that given arbitrary genus of Clifford Expansion that happens to a first-ordered light-cone-gauge eigenstate, when a Polyakov Action eigenmetric occurs -- in an ellipto-inverse-hyperbollic curvature-based motim.  This happens as the so-stated gauge-bosons move "anatomically" in a sort of "back-and-forth" manner, in so as to pull the directly related second-ordered light-cone-gauge eigenstates -- in so as to form discrete vibrations that are known of as second-ordered Schwinger-Indices.  These just stated indices come together in multivarious combinations, in order to work to trigger the motion and the mobility of the Rarita Stucture.  Schinger-Indices -- as well as forming the link between discrete energy of detectible motion & discrete gravitational Hamiltonian operation, in that collaboration that works to form Ricci Scalar eigenstates, also form a tying of substringular fields that functions as an operational group attractor, that bears the mobility to work to activate the operation of the multiplicit Wick Action.  The Wick Action is the phenomena-based Hamiltonian operator that initiates Gaussian Transformations.  This functions in so that any shear reversal in the holomorphic-based directoral-pull of a substringular region puts the neighboring Wick Action eigenstates into motion, so that norm-conditions of substringular holonomic substrate may be able to alter in genus -- so that the flow of the kinematics of the substringular may perpetuate in the process of re-establishing the Jacobian eigenbasis of the mappable extrapolation of continual substringular energy.  I will continue with the suspense later!
To Be Continued.  Sincerely, Sam Roach.

About Electromagnetic Wavelengths

A photon that is propagating in a line that is straight -- when in multiconsideration of the condition of space-time-curvature -- bears both a spin-orbital momentum and an angular momentum that is operational during each succeeding propagation index of the said photon, as it travels in the so-stated straight manner in a vacuum.  Any photon and/or beam of photons that is traveling in an unperturbated manner through a vacuum over time moves in a manner that is straight -- when one considers the euclidean Ward-Caucy conditions of a propagated beam of electromagnetic indices that exists here as a quantized set of one or more photons that operate in so as to perform a given arbitrary function -- of the propagatorial delineations that work to allow for electromagnetic energy to behave as it does.  As a partial index of a beam of light, in this here given arbitrary scenario,the index acts as a photon that is pulled in a manner that is terrestrially straight over time at an even velocity (this photon, in this case, is transmitted linearly over time), the said photon -- although bearing no Lagrangian-based Chern-Simmons singularities due to the condition of here not being perturbated from its direct path -- by neither scattering, torsioning, nor a relatively circular wave-tug/wave-pull, does bear a partially hermitian tense of delineation.  This is due to the condition that the pulse of the individually so-stated photon -- per each static-based considered coniaxial settings of the said photon -- at each smoothly metrical locus to where the pulse of the said photon goes from increasing in the speed of its spin at certain even intervals, at the directly corresponding group instantons, in which both the coniaxial-based spin-orbital momentum and the coniaxial-based angular momentum at the directly corresponding instanton-based intervals, into altering in so as to be decreasing in the speed of its spin at certain even intervals at the directly corresponding group instantons.  This is to which both the coniaxial-based spin-orbital momentum and the coniaxial-based angular momentum at the directly corresponding instanton-based intervals forms a spurious condition of cetain respective elongated to decremented pulsations, while then doing a similar spin-orbital operation at an isometrically stable set of intervals -- yet, with the direction of the angular momentum bearing a directoral wave-tug/wave-pull that is then directed in the relatively reverse holomorphic direction of the here continued holomorphic directoral-pull of the so-stated photon.  The whole distance as to the even increase to decrease of static Hamiltonian thrust, that then bears the same even increase to decrease of static Hamiltonian thrust, yet, with the alteration of the angular momentum pull of the mentioned photon going from pushing in the direction of the photons permittivity into pushing in the direction of the photons impedance -- is the distance of the wavelength of whatever the wavelength of the given arbitrary photon is.  The wavelength of a beam of light is a measurement of the fluctuation of the electric field that is directly associated with a given arbitrary genus of electromagnetic energy.  So, if a form of electromagnetic energy was, for instance, 159nm, for one-fourth of this distance -- the photons that work to comprise the eluded to beam, that goes detectibely straight to our observation in a vacuum -- each partial of photonic basis, each of such photons, gradually -- in an even manner -- increase in their Hamiltonian-based thrust over the course of 3*10^8 iterations (yet over a set of group actions that each are comprised of very many group instantons), each of which happen over many actual instantons.  This increase in thrust bears no Lagrangian-based topological sway of the photons, and, this, as well, does not alter the so-stated condition of the photons hermicity.  Then, for the second quarter of this wavelength, the Hamiltonian-based thrust is gradually and evenly calmed by a factor of 3*10^8 -- in so as to go back to is most relaxed condition of spin-orbital momentum.  For the second half of the activity that the here given arbitrary photon works to complete its wavelength, the difference in the pulsation of the photons at the Poincaire level of their kinematic differentiation is only different, due to the direction of the angular momentum being pulled in the direction of the impedance of the photon, instead of the initial directoral-based angular momentum pull being directed in the direction of the permittivity of the just mentioned photon.  For this whole wavelength, the so-stated photon is moving, as a whole, in the relatively forward-holomorphic direction.  For any other electromagneitc wavelength, such a tendency is similar, but, the distance to complete such a cycle here would alter -- in proportion to the difference in so as to what the other given arbitary wavelength of the electromagnetic energy here is. The increase of Hamiltonian-based thrust in the pulsation of a photon forms infinite Chern-Simmons singularities, while, the decrease of Hamiltonian-based thrust in the pulsation of a photon forms infinitessimal Chern-Simmons singularities. To be Continued.
I will continue with the suspense later!  Sincerely, Samuel David Roach.

The Last Part of the Second Session of Course 16

When electromagnetic energy quantizes, a certain degree of what was a Doubolt cohomology due to the physical memory of scattered photons -- works to redefine a quantitative Rham-like cohomology, when in terms of a lack of Lagrange-based Chern-Simmons singularities.  The latter mentioned condition is due to the fact that light, or, electromagnetic energy, tends to go in what appears to be straight in a vacuum.  (Light tends to only bear metrical-based singularities over time.  Yet, if a beam of light were to be an   harmonically perturbed at two or more covariant axials simultaneously, then, such electromagnetic energy that was initially quantized will also bear Lagrange-based Chern-Simmons singularities -- that are directly affiliated with the corresponding given arbitrary p-field eigenlocus that is here being enharmonically perturbated.  Such coniaxial entities that work to comprise the Ward-Caucy bounds of what is here the holonomic substrate of a photon that here works to quantize into a beam of electromagnetic energy work to define the mapping-out of the premise of both the existence and the motion of the given photon that we are here discussing as being a partial discrete increment of a beam of light that is being propagated over time.  The coniaxial-based anharmonic perturbation of a local field of electromagnetic energy is known of a a Tesla effect.  When a beam of electromagnetic energy is perturbating, the electrical field cohomology tends to be more Rham in nature than its directly associated magnetic field, and, when such a perturbation of the here given arbitrary electromagnetic field is happing, the magnetic field tends to be more of a Doubolt cohomology in nature than that of the directly associated electrical field.  This is if the scattering that is here taking place bears no Njenhuis Hamiltonian-based tensors that are being applied in an abelian manner to the said given arbitrary beam of light.  This also goes for fractals of such indices of an electric field, and, this also goes for fractals of such indices of a magnetic field.  The fractals of electric field, and, the fractals of magnetic field that here appertain to the existence and motion of superstringular phenomena are eigenstates that kinematically operate in the substringular in so as to provide for both the respective Hamiltonian-based permittivity and the Hamiltonian-based impedance of discrete energy -- that exists in the multiplicity arrangements of the respective substringular eigenstates.  The fluctuations of both the electric field and the magnetic field of any extrapolation of electromagnetic energy that may be worked with, in one way or another, as well as the fractals of these said holonomic substrates -- in the form of the interactions of the angular momentum of superstrings with the spin-orbital momentum of their respective Fadeev-Popov-Traces -- works to form a multiplicity physical memory of the pseudo-pulsation that allows for the actual functioning of Hamiltonian operations.  This physical memory tends to take the shape of the traceable mapping of ghost anomaly indices that are of a Doubolt nature.  This is  due to the condition that the orthogonal torque of a basis of substringular momentum with the basis of sustringular spin-orbital momentum works to form orthogonal Hamiltonian operations that are primordially local to each other, in so that there is then here an almost certain chance of Chern-Simmons singularities that are basically Gliossi at the Poincaire level of discrete substringular units of energy.  The angular momentum dynamics of an electromagnetic fluctuation is strictly Rham in nature, since this said fluctuation is propelled by what tends to be a kinematically differentiating normalized set of indices -- that linearly project in a relatively straight trajectory (based upon the natural curvature of space-time-fabric, yet, not as straight as a Wilson Line.)  The projection of electromagnetic energy -- although relatively straight, bears a fluctuation that works to form metrical-based Chern-Simmons singularities.    This  makes light, or, electromagnetic energy, the basis of both Rham and Doubolt cohomology.  The source of the change of rate of the pulsation of a photon is due to the interaction of the fractal of its electric field with the fractal of its magnetic field.  The manner of this alteration of pulse works to form the wavelength of electromagnetic energy.  To Be Continued.  Samuel David Roach