A Little Bit Of A Tutorial About Chern-Simmons Singularities

If a superstring is traveling through a given arbitrary Lagrangian that has a path-based spike that not only changes in three more derivatives than the number of spatial dimensions that the said superstring is traveling through over time -- to where, via the directoral-based path of the superstring going through its directly corresponding Hamiltonian operand, works to form a synchronous set of singularities that are each of a factor of infinity -- yet, the superstring at the locus of Chern-Simmons spike bears an elongated pulse, the genus of the unitary basis of the said Chern-Simmons spike would be infinity^3*infinity, or, in other words, infinity^4.   Yet,  if one were to trace the said given arbitrary mappable tracing of the eluded to Lagrangian path of the superstring in the relatively opposite direction (here, instead, in the relatively reverse-holomorphic direction), then, the genus of the eluded to Chern-Simmons spike would be of (0+)^3*infinity, or, in other words, (0+)^2.  Yet, if the Lagrangian-based singularity was infinity^3, and, the pulsation of the directly corresponding superstring was truncated at the locus of Chern-Simmons singularity, in the relatively forward-holomorphic direction of the Hamiltonian operation of the said superstring, then, the genus of the Chern-Simmons spike would be infinity^3*(0+), or, in other words, infinity^2.  In the opposite mappable tracing, the genus of the eluded to Chern-Simmons spike would be (0+)^3*(0+), or, in other words, (0+)^4.   This is if the given arbitrary said conditions of Chern-Simmons spike were to be both non-hermitian and spurious.  The ghost anomalies that work to form the directly affiliated cohomologies would here be of the respective genus formats of a correlative set of displays of Doubolt cohomologies.  This is a little reminder from before.  To Be Continued!
I will continue with the suspense later!  Sincerley, Sam Roach.

The Seven Deepest General Physical Stratum

7)  Particles that work to comprise, for instance, nucleons and electrons -- such as quarks and leptons.

6)  Superstrings.

5) First-Ordered point particles.

4)  Second-Ordered point particles.

3) Third-Ordered point particles.

2)  Sub-Mini-String (The ultimate fractal of pressurized vacuum).

1)  The Logos.

Part Five of the Second Session of Course 16

Often, when one considers a region within the parametric scope of a Doubolt cohomology, there is a region of either both the Lagrangian-based delineation and/or the metrical-based delineation of the so-stated Doubolt cohomology in which the sequential series of the re-distributions of the directly affiliated superstrings -- whose trajectory works to form inter-connected ghost anomalies that come together in so as to form the said cohomology -- bears a general substringular locus of traceable mapping in which the said cohomology that had been initially considered Doubolt appears through extrapolation to be of a Rham-based cohomological nature.  Such an extrapolation may be determined by approximating a line of trajectory within the Derichlet region of the directly assoiciated field in which such a cohomological path-based projection exists in such a manner in so that the world-sheets of the superstrings that form the eluded to inter-connection of physical memories differentiate in the smooth-curved partial locus at which the region that is here relatively more limited in terms of both a Lagrangian-based scope and a metrical-based scope are being considered within a more constrained Ward-Neumman parametric delineation-based extrapolation.  This causes the detection of a relatively smooth-curved trajectory of the given arbitrary superstring that is here being discussed -- that is of a relatively high Hamiltonian-based Hodge-Index of perturbative-based indices -- to bear a comparabley thick linear and/or hermitian approximation to what a Rham-based hermitian-based cohomological curvature would behave as, if delineated as an integration of ghost-based indices that bear no Chern-Simmons singularities over both any viable Lagrangian format and/or metrical format that occurs over a discrete sequential set of iterations of group instanton in which any actual Rham cohomology may be formed in any given arbitrary case that is to be considered.  Such an approximation of a constrained parametric region of a Doubolt cohomology that bears a region that acts as a curt simulation of a Rham cohomology -- since the here Ward-Caucy bounds of what would initially be a Doubolt cohomology are here condensed from their initial Ward-Neumman bounds, without any fractal inter-relation of either the Lagrangian-based nor the metrical-based Hamiltonian-based function of the larger scale cohomology that is Doubolt at the so-stated larger delineation of its parametric said Ward-Caucy bounds.  Such a cohomology will here tend to be formed by the kinematic activity of a bosonic or closed superstring of discrete energy permittivity. This Doubolt approximation, that eludes to the simulation of a Rham cohomology is often a tense of an electromagnetic wave fluctuation that is -- from outward "appearances" a manifestation of scattered light that is here being considered within  the beginning of a Gausian Transformation.  Sam Roach.

Part Four of the Second Session of Course 16

Often, a Doubolt cohomology approximates a Rham cohomology.  This is due to a condition that a cohomology that has only one or so Chern-Simmons singularities, but is otherwise of a Rham nature -- when in terms of its cohomology -- is basically a Rham-based cohomology that has only a limited spike in the nature of the harmonics of either the Lagrangian-based and/or the metrical-based flow of the Hamiltonian wave-tug/wave-pull of that physical memory of the substringular trajectory that works to comprise the said given arbitrary cohomological traceable mapping.  This is if the interconnection of world-sheets that works to form the so-stated extrapolation-based depiction of the directly corresponding cohomology is mapped over either a Lagrangian and/or a group metric in which the said given arbitrary cohomology goes from first bearing a purely hermitian harmonic-based flow, while then converting into having the bearing of a Chern-Simmons spike in the harmonics of its flow (whether such a spike is a spur in the path of the Lagrangian that the given superstring is projecting through over time, and/or, whether such a spike is a spur in the metrical delneation of the said superstring over the time in which such a directly corresponding superstring is kinematically differentiating in as it is reiterated from a sequential series of redistributions), while then re-converting back into bearing a purely hermitian-based flow in both the Lagrangian-based path of its motion and the metrical-based pulse of its harmonics over time.  Especially if a Chern-Simmons-based spike is low in its Hodge-Index over that sequential series of iterations in which the directly related cohomology is delineaeted, then, what may otherwise be termed of as a Rham-based cohomology that is instead Doubolt may appear to have a relatively insignificant spur in either its permittivity of path-based projection and/or its harmonic-based pulsation over time.  Likewise, a cohomology that is very perturbative over either a path-wise and/or a metrical-wise traceable mapping of its projection, may appear as basically a Doubolt cohomology, yet, if one were to extrapolate the basis of the directlty corresponding cohomology in-between the spikes in its cohomological path, the perception of the directly corresponding singularities that would otherwise work to determine a Doubolt cohomology may appear as a Rham-based cohomology.  Yet, this so-stated latter mentioned tendency may often break down into so few iterations of group instanton, that it may be too impractical to conceive of certain cohomologies to be considered as Rham at all -- over certain delineations of certain superstrings that are extremely perturbative in both Lagrangian-based and/or metrical-based anharmonic-based flow over time.  So, although a Doubolt cohomology may be basically Rham in terms of a relative lack of Chern-Simmons singularities over time -- when given a relatively more vast range of mappable tracing, no Doubolt cohomology is basically Rham, since any Chern-Simmons singularities that may work to define an extrapolation of the motion and the metrical-basis of a superstring in the course of its path would here cause the so-stated mapping to be of a purely Doubolt nature instead of Rham in nature.  The latter tendency is especially true if both the mappable trace of a superstring is perturbative and/or if the metrical flow of the said given arbitrary superstring is very perturbative -- due to many anharmonic spikes in either the path of its flow and/or the pulsation of its metical delineations over time.  To Be Continued.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Some More Material About Session 2 of Course 16

Due to the need for the perturbation that happens to every superstring eventually, since Gaussian Transformations and gauge transformations eventually happen to every superstring -- every Rham cohomology eventually becomes a Doubolt cohomology.  Yet, since there is the physical need for every superstring to move in the direction of most relative stability, every unfrayed Doubolt cohomology eventually becomes a Rham cohomology.  This is also due to the condition that any superstring that moves in a hermitian-based trajectoral path -- that is not only hermitian in terms of its Lagrangian-based delineation, yet, is also hermitian when in terms of the harmonics of its pulsation -- must eventually bear a spur in either its Lagrangian-based delineation and/or its metrical-based delineation.  This works to cause the mappable tracing of the trajectory of the projection of any given superstring that is initially stable -- in terms of the harmonics of both the integration of the harmonics of its path, and also in terms of the harmonics of its pulse -- to eventually become of a Doubolt-based cohomolgy.  This is due to the condition that, any superstring that bears either a Lagrangian-based spike and/or a metrical-based spike in its trajectory, will work to form a physical memory of its trajectory that is of what may be termed of as a Doubolt cohomology.  This is also due to the condition that every superstring that -- at any given arbitrary metrical-based local delineation -- is undergoing a Chern-Simmons effect upon the cohomology, that is directly related to the mappable tracing of the trajectory of it projection, both in terms of its Lagrangian-based path delineation and/or the harmonics of its pulsation over time, if unfrayed, will eventually stabilize into a hermtian-based effect that is upon the cohomology that is directly related to the mappable tracing of the trajectory of its projection.  Again, all Doubolt-based cohomology that is unfrayed must eventually alter back into a Rham-based cohomology.  This is why the condition as to whether or not a cohomology is considered to be Rham, or, as to the condition whether or not a cohomology is considered to be Doubolt, is to be based upon both the Lagrangian-based span and the metrical-based span that may be worked into any given arbitrary extrapolation that is to be used in so as to quantitatively determine whether or not a mappable tracing of the physical memory of the trajectory of a superstring is of a purely hermitian nature (Rham), or, of a Chern-Simmons nature (Doubolt).  A cohomology that is to be extrapolated in a regional locus that starts out as either Rham or Doubolt, while then converting into a cohomololgy that is respectively either Doubolt or Rham -- may be considered as either partially Rham or partially Doubolt in nature.  Or, if a cohomology bears only Lagrangian-based spurs or only metrical-based spurs, but not both -- may be considered as Doubolt in terms of its Lagrangian-based format and Rham in terms of its metrical-based format, or, respectively, it may be considered as Rham in terms of its metrical-based format and Doubolt in terms of its Lagrangian-based format.  I will continue with the suspense late!  To Be Continued!  Sincerely, Samuel David Roach.

Certain Means of Yakawa Coupling

When a given arbitrary Wick Action eigenstate initiates a Gaussian Transformation via its Yakawa interaction with its directly corresponding Landau-Gisner Action eigenstate, the just mentioned Yakawa interaction is of a Gliossi nature.  As the just so-stated Landau-Gisner Action eigenstate initiates the activity of the directly corresponding Fischler-Suskind Mechanism, the initial locus of the eluded to and affiliated wave-tug/wave-pull is of a Gliossi manner, at the Poincaire level of kinematic interaction.  As the leveraging of the just mentioned Fischler-Suskind Mechanism is occurring -- in so as to produce that activity of a Kaeler-Metric eigenstate that works to allow for a directly associated Gaussian Transformation, the activity of the so-stated leveraging is of a Yakawa nature that is not Gliossi at the relatively central framework of such a genus of substringular "mechanics."  Yet, at the Poincaire level as to the interaction of the said Fischler-Suskind Mechanism upon the directly affiliated Higgs Action eigenstate, such a leveraging is here actually of a Gliossi manner.  The activity of a given arbitrary Higgs Action eigenstate upon its directly affiliated Klein Bottle eigenstate is a Yakawa Coupling that is of a Gliossi manner.  The activity of superstrings of discrete energy permittivity interacting with a Klein Bottle eigenstate -- in so as to undergo a Kaeler Metric eigenmetric -- is Gliossi with the contents of the said Klein Bottle eigenstate, yet, it is not Gliossi to the "chasis" of that part of the Shotky Construction that acts as the structure of the Ward-Neumman bounds of the directly affiliated Klein Bottle eigenstate.  The Yakawa interaction of superstrings of discrete energy permittivity -- entering their respective Klein Bottle eigenstates -- is what works to re-initiate the said superstrings with those critical cusps of discrete energy perimttitivity that are needed so that superstrings may sustain the drive that these need, so that discrete energy may be able to persist at all.

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

General Types of Ghost Anomaly-Based Interconnections

When two or more ghost anomalies are interconnected via a Yakawa Coupling into a given arbitrary cohomolgy that is interconected, yet, not in a Gliossi manner, then the two or more sets of ghost anomaly-based indices mentioned are bound in a Ward-Caucy manner that is homotopically integrated as a cohomological phenomenon via simply an eigenmatrix of substringular field that I term of as mini-string segments.  The directly prior stated condition that I have just mentioned would then here not be an interconnection that is via first-ordered point particles -- as to what I term of as first-ordered point particles that are of the substringular level.  Yet, if two or more sets of ghost anomaly-based indices are inter-bound into a respective cohomology that bears a condition of two or more sets of respective first-ordered point particles that are physically touching at the Poincaire level, then, such a homotopic integration of the Ward-Caucy interconnection that works to connect the just eluded to ghost anomalies into a given arbitrary cohomology, would then be a Yakawa Coupling that would here be of a Gliossi manner.  So, when a cohomology is a composition of one or more ghost anomalies that are each interconnected via a physical touching of first-ordered point particles, that are Ward-Caucy bound at the respective Poincaire level -- even though there would here also be a mini-string interconnection that would work to bind each of the two so-stated point particles at the respective centers of the coniaxials of their eluded to locus of holonomic substrate -- then, the just mentioned cohomologies that would here be formed would be of a Yakawa nature that is also Gliossi in terms of physical interconnection.  Yet, if there is only a tense of mini-string segment format of phenomenology that works to interconnect one or more ghost anomalies to form a given arbitrary cohomology, then, the interconnection that would then here work to inter-bind the ghost anomalies -- in order to form the said interconnection -- would be of a Yakawa nature that would not be Gliossi.  This format of description would be a determination for each partial of interconnection that works to bind each set of ghost-anomaly-basis of harmonically scattered physical memory of substringular trajectory -- with whatever the cohomological binding cite of ghost anomaly-based indices is, that would here work to form the holonomic substrate that the initially eluded to ghost anomaly would work to interconnect with, in order to form an eigenbasis of cohomological phenomenology.  So, if a cohomology bears some partially derived holonomic cites that bear a substrate that is not Gliossi, in terms of Yakawa-based Coupling, while the eluded to cohomology would then also bear some other partially derived holonomic cites that would bear a substrate that is Gliossi, in terms of Yakawa-based Coupling, then, the said cohomology may be described of as being of a Yakawa-based interconnection that is partially Gliossi in nature.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

An Ensuing Part of the 2nd Session of Course 16

A cohomology that is considered to be of a Doubolt genus is one that starts out at a relatively reverse-holomorphic end of the traceable mapping of the trajectory of its projection, in a relatively hermitian manner, prior to the existence of those one or more Chern-Simmons singularities that work to make the eluded to cohomology Doubolt instead of Rham.  So, as one traces the delineation of the eluded to cohomology from the relatively reverse-holomorphic end of its distribution to the relatively forward-holomorphic end of its distribution, that is, from the initial delineation of its general Lagrangian path, toward the continuation of the ensuing path of its general Lagrangian, this eluded to tracing happens in a manner that tends to sway homotopically  in a propagation that may be traced by static ghost anomaly indices -- that may be mapped-out in a non-time-oriented manner.  This happens in a format of smooth-curvedness, afterwhich, following a traceable mapping of one or more points of singularity, in the here discussed given arbitrary scenario, the initial contour of the mapped-out tracing of the Lagrangian of any of such initally Rham cohomologies will then here becomes a Doubolt cohomology.  This works to proceed to bear a trajectory of the eluded to projection that is affiliated with either a Lagrangian-based, and/or a metrical-based spike, that works to form both a codifferentiable and a codetermineable genus of Chern-Simmons spuriousness. This acitivity operates to form the basis as to why the overall here considered cohomology acts as a Doubolt-based cohomology, instead of a Rham-based cohomology.  This is the case here, as the said tracing of the projection of the eluded to Lagrangian -- that the eluded to Yakawa-based interconnection of ghost-anomaly-based indices is translated through space, in what is here to be considered as the relatively forward-holomorphic directoral sway.  This is what is considered as a tracing of a cohomology that has a directoral-based bearing that moves in an arbitrarily relatively forward-holomorphic general direction.  Whatever the general direction that a given arbitrary cohomology tends to apply its sway of permittivity towards, as the said cohomology propagates through a given arbitrary Hamiltonian-based operand, is here to be considered as the forward-holomorphic directoral topological sway of the said cohomology.  So, the distinguishment that may work to determine as to whether or not a said cohomology is a Yakawa-based interconnection of ghost-based indices that is Rham -- to where, there are here to be no extrapolation-based Chern-Simmons singularities in the path of the projection of neither the Lagrangian-based genus nor the metrical-based genus of the said cohomology, or, if a given cohomology may be, instead, of a Doubolt nature -- to where this is to bear one or more extrapolation-based Chern-Simmons singularities in the path of the projection of either the Lagrangian-based genus or the metrical-based genus of the said cohomology -- often is related to the scope of the Sterling-based approximation, that may work to determine what the endpoint-based loci are (yet, in terms of the determination of the Ward-Caucy bounds of a substringular neighborhood, instead of in terms of the determination of the Ward-Caucy bounds of a singular substringular eigenfield), that would here work to define as to where the extrapolated cohomology is to begin, and, as to where the extrapolated cohomology is to end.  So, whether a cohomology bears any Chern-Simmons and/or Njenhuis-based singularities or not is related to what region works to define what is here to be the considered neighborhood of projection that is being mapped-out.
To Be Continued.  Sincerely, Samuel David Roach.

Session 2 of Course 16, Part One

All world-sheets have either a jointal flow, a smooth-curved-based flow, or, a combination of having both a jointal flow and a smooth-curved-based flow -- when taken along the topological mapping of the Lagrangian tracing of the respective world-sheets that here may be in question.  All cohomology must then have either a jointal flow, a smooth-curved-based flow, or, a combination of both a jointal flow and a smooth-curved-based flow.  There are two basic types of Real Reimmanian cohomology that are to be considered here.  There is a general format of cohomology that may be named of as a Rham-based cohomology.  And, there is also a general format of cohomology that may be named of as a Doubolt-based cohomology.  A cohomology that is of a Rham-based genus of cohomology is traceable in mapping through the Lagrangian of the trajectory of its projection, in a manner that has a tendency of bearing a relatively straight delneation -- in so long as no exterialized Hamiltonian operation does not pull the directly corresponding mapped-out ghost anomaly-based trace of the correlative world-sheets away from a relatively linear projection over time.  Yet, more intrinsically, a Rham-based cohomology is a cohomology that is traceable, as a holonomic substrate, as a hermitian delineation of the physical mapping of the prior motion and existence of superstrings that have just moved within a relatively Real Reimmanian-based region -- over any given arbitrary scope of time in which such a residue of the projection of the trajectory of such directly affiliated superstrings have just transiently moved from within a region that may be deemed of as being within what may be thought of as a relative Real Reimmanian plane.  Such a cohomology is considered Real and not Njenhuis as well, on account of the conditionality that the formation of those ghost anomaly-based indices that work to form the directly associated ghost anomalies -- that are here the physical memory of both the motion and the existence of superstrings -- are formed over the metrical course of the iterations and reiterations of the eluded to associated superstrings that are being mapped-out, from one positioning of these superstrings during one group instanton to the next positioning of these superstrings during each succeeding group instanton.  This happens during the course of being mapped-out as a traceable memory of the time-oriented conditions of such superstrings, as these have kinematically differentiated during the generally noticed durations of Ultimon Flow.  So, even if a given arbitrary superstring is pulled out of the condition of having a relatively straight delineation, as is often the case, if the affiliated ghost-based pattern is hermitian over both the mapped-out translation of the Lagrangian, and, is also hermitian over the directly associated group metric of the said superstring over time, then, such a resulting ghost anomaly-based pattern is said to be of a Rham-based genus.  The tendency of the inertia of a physical entity that is hermitian is to move in a relatively straight delineation.  So, this is why a Rham-based cohomology is considered to have a basis of tending to move in a relatively linear projection.  So, a Doubolt cohomology -- since it is not hermitian -- tends to move in a more jointal topological-based sway, as the directly associated ghosts that work to form the correlative cohomology are here pulled out of hermicity by either a Lagrangian-based spike, and/or, are pulled out of hermitcity by a metrical-based spike.  This works to show the condition that the formation of singularities in either the Lagrangian-based projection of ghost anomalies and/or the formation of singularities in the metrical-based projection of ghost anomlies.indicates a Chern-Simmons genus that has a tendency of veering off of a relatively linear-based path.  I will continue with the suspense later!  To Be Continued!
Sincerely, Samuel David Roach.

More Stuff About The First Session Of Session One of Course 16

Higgs doublets are a dual condition of world-sheets of bosonic or closed-strings that bear a low-energy momenta in a common field band, that would  detectabley appear as two trajectoral paths of  bosons that merge at their tops.  This "merging" is the redistribution of the tops of the directly corresponding superstrings that exist as such after relatively many iterations of group instanton.  This forms a tubular world-sheet at their tops that shares a common band.  Yet, the just mentioned common band is unnormalized, seeing that the differing positions of their correlative Planck-related phenomena are not homogeneous -- when in terms of the flow of the hermicity that may be extrapolated along the eluded to path that works to trace the Lagrangian that may be mapped along the projection of the ghost anomalies that eigenstates of such world-sheets work to form.  This makes what I just termed of as a Higgs doublet to be as a unique form of a Chern-Simmons-based cohomology.  This would then make a Higgs doublet eigenstate a specialized genus of a Doubolt cohomology.  I have here described a Higgs doublet as a Chern-Simmons-based cohomology, on account of the condition that those superstrings that work to form the ghost anomalies that directly correspond to the said general phenomenology of a Higgs doublet differentiate kinematically in so as to virtually touch in a Gliossi manner -- to where any given arbitrary Higgs doublet eigenstate is an example of a Yakawa Coupling that does not directly form in the manner of a borne tangency.  This happens in such a manner in so that the directly affiliated format of cohomology that I am here discussing bears a spike in the non-time-oriented translation of the tracing of its Lagrangian, via the trajectory of its projection, due to the condition that the said genus of Ward-Neumman-bound ghost anomaly-based phenomenology bears a directoral path -- this of which may be termed of as Imaginary or Njenhuis.  This latter condition is since such a tracing of this given arbitrary genus of ghost-based projection is pulled at a general conilocus of delineation that is off of the relative Real Reimmanian plane for each of such eigenstate of the said genus of ghost anomaly-based phenomenology that may be here termed of as a Higgs doubled eigenstate.  I will continue with the suspense later!  Sam Roach.

Some More Stuff About The First Session of Course 16

Imaginary or Njenhuis cohomology may be described of as a Chern-Simmons cohomology, since this type of joining of world-sheet-based mapped-out tracings works to either inovlve one or more jointal-based permutations, one or more rounded permutations, or one or more different tenses of dimensionality to the directly corresponding world-sheets -- on either side of the multiplicit geni of singularities that may be delineated, in the process of the formation of the eluded to Chern-Simmons cohomological-based structures that are possible in the kinematic propagation of space-time-fabric. Often, when a Chern-Simmons-based cohomology is formed, the ghost anomalies that are here directly involved are formed in a propagation that is at least partially off of the relative respective Real Reimmanian plane.  Often, one may extrapolate a cohomology that is intrinsically hermitian, yet, such a binding of ghost anomalies may still be propagated over time in a Njenhuis directoral pull that is off of the relative respective Real Reimmanian plane.  On account of the necessity of a change in derivatives that is needed in order for such a tensoric directoral pull to take effect, in consideration of the directly prior said state of conditions, the latter scenario that I have just eluded to will tend to bear a Chern-Simmons spike -- in the form of a singularity that is physically delineated as a spike in terms of localized placement -- in so that this format of cohomological genus will also be a situation that is likewise Imaginary, or, in other words, this type of cohomology will be a genus of a Doubolt cohomology.  Without any Chern-Simmons spur that is either a spike in the Lagrangian-based directoral flow of a traceable cohomology, and/or a spike in the metrical-based harmonic-based flow of a traceable cohomology, such a cohomology may be described of as a Rham cohomology.  Otherwise, a cohomology -- that bears Chern-Simmons-based singularities along the mappable traceing of the directly associated flow of any ghost anomaly-based projection, may be viewed of what may be termed of as a Doubolt cohomology.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Next Part of the 1st Session of Course 16

Often, world-sheets join in a smooth and connective manner that may be described of as a hermitian pattern -- of which the ghost anomalies that are formed as a physical memory of such world-sheets may be described of as having no Chern-Simmons singularities that may be extrapolated from simply the motion of such world-sheets that are projected in the eluded to manner that I have just described.  This process is an example of a Real cohomology that bears no Lagrangian-based spurs -- since the cohomology here not only changes in only as many derivates of curvature as the number of physical dimensions that it is kinematically differentiating in over time, yet, the cohomology that is thus formed by the eluded to motion of the here stated given arbitrary world-sheets is formed in inter-connective increments over a sequential series of iterations of group instanton (during the generally noticed durations of Ultimon Flow).  Yet, often, world-sheets form physical memories that are non-connective and non-smooth over a different given arbitrary substringular situation.  Such eluded to ghost anomalies that are here formed by the just mentioned tendency of mapped-out  trajectory do not have limits that are discrete from one point of consideration that traces-out the delineation as to where a particular superstring had been kinematically differentiating, towards a given arbitrary subsequent mapped-out tracing as to the physical memory of the here mentioned superstring that is here to be considered.  The lack of a discrete limit in the mapping-out of the trace of a superstring-based physical memory works to indicate a curvature in the eluded to mapping that changes in more derivatives of curvature than the number of physical dimensions that the said ghost anomaly had been formed as over a directly corresponding sequential series of iterations of group instanton.  This not only works to reveal that the physical memory of the correlative superstring and its directly corresponding world-sheet is non hermitian in terms of the projection of the indices of the physical memories that work to show both how, where, and when the given arbitray corroborating superstring had been kinematically differentiated over time, yet, such a non hermtian condition that is thereby Chern-Simmons to a particular genus also works to indicate that the directly corresponding superstring would thereby be revealed here as being non hermitian and thus Chern-Simmons to a particular genus that is congruent to the same chirality as the particular genus of singularity that would thereby be eluded to by the condition that could then be mapped-out by the delineatory path of the projection of the ghost anomalies that would here work to show a tendancy toward a corroborating of the transient history of the directly corresponding superstrings, that are here being considered in this given arbitrary case.  When such a Chern-Simmons effect that works to show a lack in hermicity in the Lagrangian-based continuation of a given arbitrary superstring over time bears a torsioning in the eluded to physical memory of a directly corresponding superstring that is delineated off of the relative respective Real Reimmanian plane, and/or if one is here considering ghost-anomaly-based residue that is formed during the generally unnoticed durations of group instanton, then, the ghost-based indices that work to show some sort of physical memory of a given said superstring, such as is here being discussed, may be described of as Imaginary or Njenhuis in terms of the differential geometry of the directly eluded to mappped-based tracing.

Cohomology Pull

Often, a cohomology that works to inter-bind two different ghost anomaly-based patterns is pulled by a discrete substringular holonomic entity of physical substrate that is not of the phenomena-basis of either being a norm-state or a norm-state projection, that is tugged kinematically over some sort of a Lagrangian-like via homotopic residue over time.  When a cohomology is pulled kinematically through such an eluded to Lagrangian over time -- by some sort of superstring, then, it takes a different basis of either a norm-state or a different basis of norm-state projection to be able to move accordingly in a relatively reverse-holomorphic manner, in so as to anharmonically scatter the said given arbitrary ghost-like pattern in such a manner in so as to work to convert the said ghost anomalies into that substringular residue that acts as a foundation for the future formation of gravitons and gravitinos that may be able to form specific Hamiltonian-based operational-based functions via the correlative interactions with the Rarita Structure via the physical tensoric amplitude of the Ricci Scalar.  Cohomologies that are only partially anharmonically scattered via relatively reverse-holomorphic norm-states and/or norm-state projections may often interact with either discrete phenomena of substringular energy and/or other ghost-anomaly-based patterns over a relatively transient period of time -- over a sequential series of iterations of group instanton.  This often works to involve an initially Gliossi-based Yakawa Coupling that corresponds to a torsional-based wave-tug/wave-pull of one of such ghost-anomaly-based patterns with another substringular entity that has not been completely anharmonically scattered off of the relative Real Reimmanian plane.  As such a wave-tug/wave-pull tends to be relatively abelian.

General Concept As to Formats of Coholmologies

Discrete phenomena that act as holonomic substrates of both physical energy permittivity and/or physical energy impedance often act upon cohomologies of various given arbitrary conditions, while also, cohomologies of various given arbitrary conditions often act upon discrete phenomena that act as holonomic substrates of both physical energy permittivity and/or physical energy impedance.  This works to help explain the physical conditionality that actual physical entities that act as discrete energy often work upon physical memories of various other physical holonomic substrates, while physical memories of various physical holonomic substrates often work upon physical entities that act as discrete energy.  Everything that is to be accounted for is based upon the concept of the conditionality of memories, yet, the predominant physical discrete energy units of holonomic substrate act as the actual characters of any given arbitrary physical scenario.  Often, such eluded to interactions are Gliossi -- either at a Poincaire level that is in the retrospective vantage-point of either a first, a second, or a third-ordered point particle-based leveraging.  Yet, often, such eluded to interactions are Gliossi at a vantage point that is either Poincaire to an actually superstringular level, or, such a vantage point may often be more indirect at the vantage-point of a viable and relatively abelian substringular-field-based level -- on account of the condition that mini-string segments are the holonomic substrate that works to form the field density of superstrings themselves.  Cohomologies may often bear a tense of singularity that is Real at multiple ends of a substringular setting, while then not withstanding a Real Reimmanian limit at the relatively central locus of the said substringular setting, while then being extrapolated as being Real Reimmanian at the general region on the other side of the said setting.  This is an example of a Chern-Simmons spur that is here not metrical, in terms of the basis of the Lagrangian-based setting.  Such a genus of a Chern-Simmons spur in physical delineation often alters in format, as the eluded to setting is kinematically pulled into a torsional-based motion over time.  The activity of the given arbitrary local Gaussian Transformations that would be involved here would help to change the Chern-Simmons format and genus of such a locus, since the norm-conditions of physical holonomic substrates must be kinematic over time in order to free-up space, so that phenomena in general may have a place to freely move.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Course 16 About Cohomolgy, Topology, and Iterations -- Both the Spurious and the Yau-Exact Kinds, Session one, part 1

Cohomology is the inter-connectivity of world-sheets and world-sheet sectors in the Ultimon.  World-Sheets are a phenomena of iterations of group instanton that build up after a given metrical duration.  So, cohomologies are a phenomena of iterations that build up after a given set of group metrics.  World-Sheets are a phenomena that involve all superstrings that move, which would involve all superstrings that actually exist as holonomic physical substrates.  What I mean by the movement of superstrings is the displacement of a substring after individual stringular iterations of group instanton.  The trajectory of a substring after a set of motion of that said substring is a world-sheet.  World-Sheets may expand, and world-sheets may often, as well, join together in a Gliossi manner.  World-Sheets, as the trajetory of superstrings, form a physical memory as to the past motion and existence of corresponding superstrings -- in the form of ghost anomalies.  Ghost-Anomalies are the physical memory of superstrings, and, these memories work to interact and bind in so as to perform certain pseudo-Hamiltonian operations that bear respective given arbitrary kinematic functions. A cohomology always bears a Gliossi-based contact, yet, not all Gliossi-based contact is in the form of a cohomology.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Group Activity Involving Lorentz-Four-Contractions

When an orifold and/or an orbifold eigenset moves -- as a discrete unit -- in a relatively straight and transversel manner, based upon Snell's Law, through a discrete Lagrangian, for more than 384 instantons, then, the said orbifold and/or orbifold eigenset is said to behave as a holonomic substrate of physical space that is one form or another of electromagnetic energy.  When an orbifold and/or an orbifold eigenset is a quantum unit of electromagnetic energy, then, the distance between the central inter-connectivity of where the given arbitrary first-ordered light-cone-gauge eigenstates of all of the superstrings that work to form the said orbifold and/or orbifold eigenset bind with the directly corresponding Fadeev-Popov-Traces that work to form the directly correlating units of discrete energy impedance -- up to the central inter-connectivity as to where the eluded to light-cone-gauge eigenstates bind with the here corresponding superstrings that I have mentioned, is equal to pi times the Planck Length. Also, under the same conditions, the distance between the eluded to superstrings that work to comprise the said orbifold and/or orbifold eigenstate with the directly corresponding counterparts of the said superstrings will also be equal to pi times the Planck Length.  When a superstring is fully uncontracted -- due to the said superstring existing in a tense of static equilibrium as a state of superconformal invariance, then, the previous mentioned lengths of substringular field-based inter-connectivity will be shortened by one Planck Length each.  So, multiply whatever a given arbitrary Lorentz-Four-Contraction is times 10^(-43) meters, while then adding this distance to the two given respective lengths of substringular inter-connectivitiy that I had recently eluded to in this post ( onto the eluded to lengths of such field bindings that would apply for a fully uncontracted superstring), and this will work to indicate the respective lengths of the so-stated scalars of substringular inter-connectivity that work to bind both a Fadeev-Popov-Trace to its directly corresponding superstring & the distance of relativistic lengths of the directlty corresponding superstrings with their immediate counterparts.  So, when a given arbitrary orbifold and/or a given arbitrary orbifold eigenset is Lorentz-Four-Contracted by a discrete amount, each superstring that works to comprise the eluded to orbifold and/or orbifold eigenset behaves as is according to the math that I have just eluded to.  This is possible, because the condition of homotopy works to allow for mini-string segments to be ebbed into and out of the various substringular settings over time.  The reason for me stating "over 384 instantons" is because a discrete gauge-metric of any given arbitrary eigenmetric of Kaeler-Metric happens in 384 instantons -- as I will discuss more in course 24 about Conformal and Superconformal Invariance.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Some More Stuff As To Three Covariant Given Arbitrary Orbifolds

Homotopic residue has a differential symmetry that exists as indices of holonomic substrate that exist in-between the individual arbitrary conisdered instanton durations, of which involve the previously mentioned substringular groups, while also simultaneously having a differential symmetry relation that would here involve a correlation to the point-fill of the corresponding first-ordered point particles that work to comprise those superstrings that work to comprise the said orbifolds that are being considered in this scenario.  The said homotopic residue also has a differential symmetry that appertains to both the transversal and the spin-orbital superfield tensors which act upon the said two substringular groups, that here quantify as a homogeneous wave permittivity that is isomorphically bilateral.  And the here relatively invariant substringular groups mentioned -- those that are in a state of being relatively static (in transition kernel), are in this case undergoing conformal invariance in a tightly knit locus.  The said substringular group that is undergoing conformal invariance is going through the conditon of Noether Flow -- in such a manner that corresponds -- leverage-wise -- to the two substringular groups that are going through tachyonic flow, since these latter mentioned groups of superstrings are here orbifolds that are being perturbated from off of a Noether-based flow into a condition of the prior stated transition eigenstate. This would involve a spring-like torsioning of homotopic binding of the one orbifold in relation to the two tachyonic ones.  To Be Continued.  Sam.

Some Good Information as to Yakawa Couplings

What are some of the attributes of certain Yakawa Couplings?  Let us say that one, in this given arbitrary scenario, were to consider a total of three sets of one and two-dimensional superstrings that were to act in a covariant manner relative to one another, in such a manner in so that these three sets of superstirngs were to bear a relatively distinct and unique kinematic differentiation towards one another -- in a manner that could here be described of as a tritiary Hamiltonian-based function. This would arbitrarily here be three orbifolds that each had their own respective operations, although the interaction of the functions of all three substringular operations would bear an overall function that involved the activity of all three orbifolds, relative to one another, over a discrete group metric of time.  One of the eluded to orbifolds would, over the mentioned group metric, exist in a condition of transition kernel -- which would here mean that the considered orbifold would, at the given metrical point, exist in a state of conformal or superconformal invariance.  The other two eluded to orbifolds would then, over the mentioned group metric, exist in a condition of transition eigenstate -- which would here mean that this here considered orbifold would, at the given metrical point, exist in a state of unrest or perturbation.  In this particular case, the said orbifold that is here undergoing a transition kernel is kinematically differentiating in the general format of Noether Flow.  Also, in this particular case, the said other two orbifolds that are undergoing a transition eigenstate are kinematically differentiating in the general format of tachyonic propulsion.  The two orbifolds that I have just eluded to as being tachyonic bear a tense of Chern-Simmons kinematic differentiation that works to dissociate these two sets of superstrings -- that operate to perform two specific functions -- from the one given arbitrary orbifold that is here undergoing a tense of conformal invariance, over the general format of Noether Flow.  Each of the three said orbifolds, or, groups of superstrings, releases homotopic residue that is compensated by an equally fed back ebbing of substringular field indices -- in so that the said release of mini-string segments that are here eluded to work to allow for the condition that all three sets of superstrings that I have mentioned here would tend to be extrapolated as being indistinguishably different, when in terms of both the respective  Hodge-based-volumes and the respective delineations that work to comprise the three said orbifolds -- as three considered structures that are here considered in a timeless-oriented manner.  This does not discount the condition that all three mentioned orbifolds are here constantly moving over time.  This would here work to show the applied condition -- as to a more specific given functioning of the general operation of Cassimer Invariance.  Thus, since all three said sets of superstrings bear an eluded to field networking, that is interconnected via some sort of abelian mini-string-based wave-tug/wave-pull that is viable as some sort of a discrete indirect substringular touch that is here not Gliossi, this may be considered as an indirect -- but feasible -- Yakawa Coupling.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Some More As To Tenses of Singularities

Let us say that one had a substringular scenario in which a set of superstrings moved through a unitary Lagrangian, to where the genus of the directly corresponding Chern-Simmons singularity that would here appertain to the said scenario would bear a format that could be described of as being discrete relative to (1/infinity), or, in other words, the directly related singularity here would be equal to "0+".  The curvature of the said trajectoral path of the eluded to orbifold, or, set of superstrings -- that operate to perform a specific substringular function -- would then not be completely hermitian, when in terms of the overall Laplacian-based mapping of the projection of its path.  Such an attribute of a Chern-Simmons genus may be denoted by the extrapolation of the corresponding field network that could be traced by the corelative Gliossi-Sherk-Olive indices -- the said indices of which would here be physically comprised by discrete units of ghost anomaly-based residue that are left as a physical memory of the directly previous substringular motion and existence of the orbifold that is here under question.  The eluded to ghost-based indices here of which are comprised of harmonically scattered positive-norm-states, if the given arbitrary orbifold that is being considered here is moving in forward-moving time. These just eluded to indices here work to trace the said mapping as a timeless oriented differentiaion that works to show a prior-based time-oriented kinematic displacement of discrete units of energy delineation.  Yet, the said perturbation of time-oriented substringular pulse -- the scattering of ghost anomalies -- that is here the anharmonic scattering of the eluded to ghost anomalies, as a relatively transient acceleration of the oscillation of relatively reverse-holomorphic norm-states upon relatively forward-holomorphic norm-states, happens at a singularized locus at a metrical gauge that here works to produce a change in an additive derivative of the given arbitrary projection of the directly corresponding orbifold.  Such an alteration of the physical projection of the said orbifold works to form an integrative singularity that would here bear a Chern-Simmons singularity that bears -- in and of itself -- a kinematic locus as to where the limit of the mapped-out tracing of the said orbifold is not discrete, when going from one side of the eluded to locus of singularity to the other side of the eluded to locus of singularity.  This would make this latter example of a path of an orbifold, over time, to be able to be described of as a partially Chern-Simmons field trajectory.  This is because, although the orbifold would here change in more Ward-Caucy-based derivatives than the dimensionality of its trajectory, the said orbifold is at least not spurious in terms of the pulsation of its vibratorial oscillation over time here.  Any field trajectory that bears any genus of Chern-Simmons singularity-founded-basis -- whether such a genus of perturbation were to bear a whole basis of singularity that is not discrete OR even if there is a partial condition of a singularity that is not discrete, even though such a singularity may be offset by a countering bases that works to unitize the Jacobian eigencondition, then, the otherwise considered Chern-Simmons genus is here considered to be a given arbitrary example of a Cevita interaction.  I will continue with the suspense later.
Wess Zumino and Cevita Interactions will be discussed further in course 26!  Sam Roach.

More As to the Formation of Schwinger-Indices

Gauge-Bosons pull upon second-ordered light-cone-gauge eigenstates as these "pluck" the said eigenstates in such a manner in so that the said gauge-bosons are Gliossi to the eluded to second-ordered eigenstates, as the directly corresponding given arbitrary superstrings are initially swayed during BRST in the relatively forward-holomorphic direction, while, the said gauge-bosons are not Gliossi to the directly corresponding second-ordered light-cone-gauge eigenstates as the directly associated superstrings are swayed during BRST in the relatively reverse-holomorphic direction.  The moment of the eluded to release from the format of Gliossi-based Yakawa Coupling that was eluded to is during the completion of the eluded to relatively forward-holomorphic topological sway of superstrings -- right before the directly corresponding superstrings are swayed in a subtle manner in the respective relatively reverse-holomorphic directoral-based pull.  As the so-stated Gliossi-based tug that is operated by gauge-bosons is released, the corresponding vibrations that are Poincaire to the corelative second-ordered light-cone-gauge eigenstates are put into kinetic motion in the form of second-ordered Schwinger-Indices.  The integral effect of the interaction of the second-ordered Schwinger-Indices that stem from a whole first-ordered light-cone-gauge eigestate is what may be termed of as a first-ordered Schwinger-Index.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Holographic Relations To Construction of Space-Time Fabric

Let us say that a superstring is to move through a path in such a manner in so that it changes in four derivatives in a three-dimensional-based Minkowski plane, in such a manner that it jerks -- kinematically -- in what was initially a harmonic rhythm that is made anharmonically ellongated in a time-interdependant-based pulse of metric at the same general locus that the said superstring undergoes the said change in four derivatives -- this ellongation of kinematically-based pulse of which is conimetrically and coniaxial-based in format, at the relative conicenter of the just mentioned spot where the Ward-Caucy-based tensoric concavity is temporarily jerked out of what started out as a harmonically flowing superstring.  This happens in such a manner that the eluded to motion of the said superstring here becomes temporarily anharmonic at the said relatively discrete general said locus of the given eluded to perturbation.  The genus of Chern-Simmons-based singularity would here then be described by infinity times infinity, or, in other words, infinity squared.  (The directly associated singularity at the said locus of perturbation over the eluded to eigenmetric of the directly associated activity would be of a higher genus of singularity than may be described of as just infinity.  This is because one here has a singularity of a Lagrangian-based perturbation that is coupled by a singularity of a spurious-based perturbation.)  If, at a position of the trajectory of the Lagrangian-based path of the said superstring, that is, in this case, further down the time-interdependant-based mapping of the projection of that stated superstring -- at an ensuing metrically bracketed time eigenlocus of metrical delineation -- the said superstring will then here change in three derivatives.  This is while the motion of the said given arbitrary superstring jerks at this locus in an anharmonically-metrical-based manner.  This happens in such a manner in so that the thus formed pulse of the just mentioned superstring is sped-up at the conicenter of the coniaxial at where the said superstring was at, when it here changed in three derivatives as a plane of a one-dimensional superstring of holonomic substrate -- that is moving through a multiplicit spatial range over time.  The just mentioned one-dimensional superstring will then move as an entity in a manner that exhibits a directly corresponding two-dimensional field that bears a Lagrangian that is multiplicit in directoral covariance over time.  I will continue with the suspense later!  To Be Continued.  Sincerely, Sam Roach.

The Next Set of Test Solutions To The Last Test of Course 14 About Group Action

5)  Protons and neutrons are nucleons.  Nucleons are comrprised of more closed-strings over time than electrons do.  Closed strings in nucleons work to form the mass of phenomena -- in this case, particularly in the said nucleons.

6)  Real-Based cohomology is substringular Yakawa interconnection that is both Gliossi during group instanton, and also here involving a topological interconnection that is focused on the relative Real Reimmanian plane.

7)  Imaginary or Njenhuis cohomology is substringular Yakawa interaction that is Gliossi outside of group instanton, and/or Njenhuis cohomology may also often involve a cohomological bonding that is off of the relative Real Reimmanian plane.

8)  When two-dimensional world-sheets interact in a cohomological manner with three-dimensional world-sheets that bear even Ward-Neumman boundaries, the respective cylindrical ghost anomalies that are directly associated with the two-dimensional world-sheets are twisted or torqued by the respective three-dimensional shaft-like ghost anomalies in so as to form a Chern-Simmons effect upon the eluded to Yakawa Coupling that thus forms a resulting Doubolt cohomology.

9)  Njenhuis ghost anomalies are the residue of ghost anomalies that exist outside of the iterations of group instanton, and/or these may also be ghost anomalies that are situated off of the relative Real Reimmanian plane.

10)  When a cohomology that is Rham is connected into a Doubolt cohomology -- or vice-versa -- this is a cohomology shift.  A Rham-based cohomology is hermitian, while a Doubolt-based cohomology is Chern-Simmons.

11)  Cohomologies shift when a hermitian ghost-anomaly-based pattern is to shift from being  harmonic to being anharmonic -- and vice-versa.  This is to happen in order for there to be both essential entropy, reassorted entropy, and also for there to be a shift of anharmonic ghost-based patterns back into harmonic ghost-based patterns.

The First Set Of The Test Solutions To The Last Test To Course 14 About Group Action

1)  The fractal of an electric field in the substringular is the angular momentum of superstrings.  The angular momentum of superstrings is the Hamiltonian-based leveraged wave-tug/wave-pull that is exerted in a transversal manner upon a substringular phenomenon.  Amperage itself is charge per time.

2)  The fractal of a magnetic field in the substringular is the Hamiltonian-based spin-orbital-momentum that exists among substringular phenomena.  This is the Hamiltonian-based leveraging of the wave-tug/wave-pull that is exerted in a radial manner upon a substringular phenomenon.  Voltage is energy per charge.

3)  Planck phenomena flow as the discrete units of energy impedance in the substringular.  Wavelength of electromagnetic energy pulsates in a manner in so that the electric field that directly corresponds to this fluctuates over time, in accordance to the extrapolation-based measurments of their respective directly corresponding eluded to wavelengths.

4)  Electrons are comprised of more plain kinetic energy than neucleons, over time.  Plain kinetic energy bears discrete energy permittivity in the form of open-superstrings.  The just eluded to open strings close when such kinetic energy is released from a dropping electron, in the form of a photon.  A photon is a discrete unit of electromagnetic energy.

The Test Questions Of The Last Test Of Course 14 About Group Action

1)  How is the fractal of the electric field -- in the substringular -- associated with the differentiation of a superstrings?  What is amperage?

2)  How is the fractal of the magnetic field -- in the substringular -- associated with the differentiation of a superstring?  What is voltage?

3)  How do Planck phenomena flow as light?  Describe the wavelength of light in general.

4)  Describe the open-string relation of electrons.

5)  Describe the closed-string relation of protons and of neutrons.

6)  Describe Real Reimmanian-based cohomology.

7)  Describe Imaginary-based cohomology.

8)  Describe what happens when two-dimensional world-sheets meet three-dimensional world-sheets with even Ward-Neumman boundaries.

9)  Describe ghost anomalies that are relatively Njenhuis.

10)  Describe cohomology shifts.

11) Explain why both Njenhuis and Real Reimmanian-based cohomologies exist.