Indistinguishably Different Cohomological Indices

Although the cohomological eigenindices, that are here to apparentenly be "stuck" to any one given arbitrary GSO on-shell-related Ward-Cauchy-based kinematic structure, may "appear" to be stationed permanently there, in so as to being here in a tense of a general genus of an abelian group --  these specific indices are here to be constantly replaced and amended, in an indistinguishably different manner over time.  These cohomological indices may here apparently be spontaneously "stuck" to the external shell of the proximal locus -- that is of the topological stratum of the here directly pertinent superstrings, yet, these specific indices, that are here to appear as being kept as being Gliosis to the topological surface of the so-eluded-to discrete energy at the Poincare level, -- are, in reality, to constantly be in a flux, in which cohomolgical eigenindices are constantly leaving and being brought into the proximal locus of the topological stratum of such said superstrings, -- in so as to work to allow for the "appearance" of there to here be Ward-Cauchy-related phenomenology, that seems from an observer to be "stuck" to this earlier mentioned proximal local region -- that is of these said superstrings of discrete energy permittivity.
This is part of as to why I have equated cohomological eigenindices to ghost anomalies -- since the specific eigenindices that work to form a cohomological structure,  are constantly being brought in and taken away, -- in a manner that is here to appear as being "indistinguishably different."  Ghost anomalies refer here, in part, in my string theory model, to the relatively transient nature of the vast array of specific homological and cohomological eigenindices.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Terms Cohomologies Versus Ghost Anomalies

That description of the physical memories, as to the where, the when, and the how, that the multiplicit substringular eigenstates have differentiated over time -- as may be described by the term that I call ghost anomalies, -- works to imply the temporal nature of the existence of the so-eluded-to  individually taken cohomological entities.  This is since the presence of an anomaly -- works to imply the existence of something that may rarely be both significantly detected and apprehended as both real and observable, at any specific given arbitrary locus.  Whereas -- the eigenstate of a given arbitrary respective cohomology, may simply refer to the existence of the physical memories as to the where, the when, and the how, that the multiplicit substringular eigenstates have differentiated in the arena of space-time-fabric in general.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

A Little Bit About Certain GSO Ghosts

As I was starting to discuss in my last post -- the general genus as to the shape or the morphological texture, that is most directly appertaining to the Ward-Neumman and/or the Ward-Caucy contour of a mass-bearing superstring of discrete energy permittivity -- that is of an electron, versus the shape or the morphological texture that is most directly appertaining to the Ward-Neumman and/or the Ward-Caucy contour of a mass-bearing superstring of discrete energy permittivity -- that is here of a proton, is, in effect, two different individual classes of shape-based structural formats.  I have earlier worked to describe some hinting, as to the general shape-based texture of the cohomologial-based topological contour of the said mass-bearing strings of an electron, yet, here are some extrapolation-based hints as to the comparison of the just-mentioned case that is to be contrasted with the general condition of the mass-bearing strings of what would here be a respective given arbitrary proton -- that may be hypothetically of the same pairing of an atom (in this given case).  Here:  Take a postulative filled circle that is centered just above the central region of a given arbitrary xyz plane.  Next, center another filled circle that is centered just below the same central region of a given arbitrary xyz plane, as before.  Next, form a postualtive-based filled homeomorphic concavity for both the front and the back of each of the said so-stated circles, that is of a tightly-knit Laplacian-based restriction as to the scalar amplitude of the size of its relative field, on all four total sides -- each of which belongs as the respective front-side and the respective back-side of the two said individually taken filled circles at hand.  Next, consider the flow of the relative norm-to-holomorphic (relative top) so-eluded-to disc-like phenomenology to be moving radially, yet in a manner that tends to bear a wave-tug/wave-pull that is into the page.  Simultaneously (via the vantage-point of a central conipoint), consider the flow of the respective reverse-norm-to-holomorphic (relative bottom) so-eluded-to disc-like phenomenology to be moving radially, yet in a manner that tends to bear a wave-tug/wave-pull that is out of the page.  Now, what one is to do here -- is to integrate the last two just mentioned Laplacian-based topological flows, that I have just described.  Integrate this torus-like phenomenon into one more elongated spatial dimension -- arbitrarily say, axial l, with a directoral basis that would here be directly associated with an "l hat."  This torus-like structure, will, as well, bear an annulus that is positioned relatively proximal to the horizontal axis -- to where the holomorphic-based cohomological mapping of the said annulus would be from the positive horizontal direction to the negative horizontal direction.  This cohomological-based venue for a respective given ghost-based mappable tracing -- would tend to not bear any deciduous conical embellishments at the Ward-Neumman extrapolation, that may be Gliosis to the outer contour at the Poincaire level of any respective given arbitrary GSO ghost -- that is of this just-stated given arbitrary case.  Next, integrate the Laplacian-based mer of the just-stated general genus of a GSO ghost-based mappable tracing -- into the direction of the proscribed Lagrangian-based path, that corresponds to its correlative Hamiltonian operand, that is of such a unique and special case.  This is similar but different to the actual case of the mass-bearing superstrings of the f-field of a proton.  I will continue with the suspense later!  To Be Continued!  Sam Roach.

Static Charges

When one d-field that is directly associated with the immediate field of one given arbitrary electron, rubs against another d-field that is directly associated with the immediate field of another given arbitrary electron, there is -- to one extent or another -- an electrostatic charge that would here involve a certain degree of the scattering of the two so-eluded-to Calabi-Yau manifolds, that are here directly related to the scattering of the two general respective d-fields -- that would here work to form the two electric fields that are directly correlative to the two said electrons of this case scenario.  When two electric fields that are directly affiliated with the respective presence of two respective individual electrons, each, scatter amongst each other -- via the interchange of their correlative Yakawa-based indices, then, not only are the directly affiliated respective given arbitrary Calabi-Yau manifolds scattered to one extent or another, yet also, the directly affiliated Gliossi-Sherk-Olive ghost anomalies that are directly associated with each of such individually taken electrons, are also each scattered -- to one extent or another.  As the so-stated respective Gliossi-Sherk-Olive ghosts of the two given arbitrary electrons are scattered, the dual states of the Reimman-based cohomological indices -- that had initially here worked to form the physical memory of both the existence and the activity of the initial eigenbase of the two said respective given arbitrary electrons -- are scattered annharmonically, via  a Rayleigh-based scattering -- from the initial chiral-based and Reimman-based integrative cohomological-based ordering, into an entropic antichiral-based disorganization of the directly affiliated cohomological-based indices, that had initially worked to form the individual respective Gliossi-Sherk-Olive ghosts, that had been the mappable tracings of the two said respective given arbitrary  initially superconformally invariant electrons that will have here diverged from such a Majorana-Weyl Invariant mode by scattering amongst each other here.  To Be Continued!  Sincerely,
Sam Roach.

About the Recycling Of Ghost Anomalies

As I have stated before in certain past blog posts, ghost anomalies are formed by the harmonic scattering of relatively forward-holomorphic norm-state projections -- via a certain format or genus of a Reimman scattering, while, ghost anomalies are vanquished by the annharmonic scattering of relatively reverse-holomorphic norm-state projections -- via a certain format or genus of a Rayleigh scattering.  When Gliossi-Sherk-Olive cohomological indices are annharmonically scattered, the initial residue of such a format of a Rayleigh scattering is subsequently brought out of the relative Real Reimmanian Plane -- into the relative Njenhuis Plane, in so as to work to form the basis of the point commutative template for the ensuing formation of Neilson-Kollosh ghosts.  Once the said residue of the annharmonically scattered Gliossi-Sherk-Olive ghosts is brought into the so-stated relatively Njenhuis Plane, the dilatons and dilatinos thus formed work to form gravitons and gravitinos, respectively.  The relatively forward-holomorphic norm-state projections that are then harmonically scattered by the said gravitons and gravitinos -- via the just eluded-to Reimman-based scattering, works to then form what may be termed of as Neilson-Kollosh ghosts.  Once that the so-stated Neilson-Kollosh ghosts are formed, there will eventually be the activity of certain relatively reverse-holomorphic norm-state projections in the said Njenhuis Plane, that work to annharmonically scatter the initial said Neilson-Kollosh ghosts via another genus of a Rayleigh scattering -- that causes the residue thus formed to be transferred into the prior mentioned initial relatively Real Reimmanian Plane.  The resultant initial existence of that residue of annihilated cohomological indices, that are here initiated from the Njenhuis Plane into the initially stated Real Reimmanian Plane, is of the nature of norm-state projections.  The holonomic substrate-based spatial entities that work to pull the residue of broken-down ghost anomalies into either the respective relative Njenhuis Plane or the respective Real Reimmanian Plane, are a genus of group attractor-based matrices.   The holonomic substrate-based spatial entities that work to pull the residue of broken-down ghost anomalies away from either the respective relative Real Reimmanian-based Plane or the respective relative Njenhuis Plane may be termed of as ghost inhibitor-based matrices.  I will continue with the suspense later!  Sam Roach.

Part Two of What may be my Third Session of Course 18

The condition of each individual layer of reality of each set of parallel universes, as existing in a completely diversified manner of delineatory index -- in a granular-based flow of homotopically-based indices, in such a manner in so that each of the so-stated layers of reality of each set of parallel universes -- may be termed of as an extremely staggered tori-sector-range, to where this is related to what is termed of as the Gliossi-Sherk-Olive-Theorem.  Under the just mentioned multiplicit Ward-Caucy conditions, each layer of of reality, or, in other words, each tori-sector-range of each individual set of parallel universes, is intricately woven into the general fabric-based boundary conditions of all of the other parallel universes of a given arbitrary set of parallel universes, in so as to work at forming an inter-relationship of all of the layers of reality of one given arbitrary set of parallel universes, in retrospect to one another -- in an interdependently respective eminent manner.  The general condition of those directly applicable ghost anomalies -- as well as their directly associated cohomological-based projections -- as being formed as the multiplicit mappable tracing of the physical memory of the correlative superstrings of discrete energy permittivity -- is the basis of  what is formed of as a result of this genus of activity,  to where this works to form what are known of as Gliossi-Sherk-Olive ghosts.  The integration of such just-eluded-to ghost-based indices works to form those cohomologica-based entities that are directly related to the extrapolation as to the what, where, and how, those so-stated superstrings of discrete energy permittivity had kinematically differentiated, over a sequential series of group instantons.

The First Set of Test Questions For The Last Test Of Course 16

1)  What is a Doubolt cohomology?

2)  What is a Rham cohomology?

3)  Explain how ghost anomalies are annhilated.

4) What are the Donaldson-Ulenbach-Yau conditions?

5)  What is the Bette Action?

6)  What is the Polyakov Action?

7)  What is the Regge Slope?

8)  What makes superstrings oriented?

9)  What makes superstrings unoriented?

10) What is a Klein Bottle eigenstate?

11)  Describe the mobiaty of superstrings.

12)  Describe the mobiaty of world-sheets.

13)  What are Ward conditions?

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.

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.

Part Six of the 14th Session of Course 14 About Group Action

Often, two-dimensional superstrings, of which are closed-loops that act as bosonic superstrings of discrete energy permittivity -- may open simultaneously as a semigroup through the vantage-point of a centralized conipoint, in such a manner in so that the initial hoop-like topological phenomena that are here becoming strand-like topological phenomena act as superstrings that are here converting as a group from one genus of topological substrate to another genus of topological substrate, and, are also altering in their transversal, radial, and/or orbital kinematic differentiation -- over the course of the same group metric-based duration.  Such a manner of Fujikawa-based Coupling may happen in the process of a perturbation of both the spatially-based and the metrical-based locus of the formation of the ensuing world-sheets, to where the format of the consequential ghost anomalies that are formed will alter as a direct result of the directly prior mentioned general condition of such a genus of the eluded to multiplicit Fujikawa Coupling.  Thus, the cohomological alterations of the ghost anomalies that are formed as an integrable whole by the group alteration of the genus of the said superstrings -- that work together here simultaneously through the vantage-point of a centralized conipoint -- may often involve a relatively smooth interconnection of the mentioned ghost anomalies, that would thence act as a Hamiltonian operator. This activity would then involve an eluded to given arbitrary perturbative orbifold that translocates from functioning as an operation of superstrings that initially behaved as units of discrete kinetic energy permittivity, that act as a group in an orbifold -- that functions as an operation of superstrings that behave as units of discrete electromagnetic energy permittivity, that act as a group in an orbifold.  As such a cohomology of ghost anomalies work to denote a physical memory of the directly prior activity of the just mentioned group functional basis of certain codifferentiable, covariant, codeterminable, superstrings that work together to perform a specific function, the eluded to ghost anomaly-based structures of such said orbifolds are able to then be extrapolated over a sequential series of iterations of group instanton. Such a cohomology is then said to have a Real Reimmanian basis of mappable tracing.  When the said format of Fujikawa Coupling works to instead involve the jointal interconnection of the any given arbitrary said ghost anomaly-based indices during the generally unnoticed portion of Ultimon Flow, then, the flow of such ghost anomalies will, at such a metrical vantage-point, involve a genus of Imaginary or Njenhuis cohomology.

A Start As To Rham Cohomologies

When a superstring travels through a projection via any given arbitrary trajectory, it produces a physical memory in the form of ghost anomaly-based indices.  When a given arbitrary superstring travels straight through a unitary Lagrangian, it may often bear a hermitian delineation of physical memory in the form of a ghost anomaly-based formation of traceable mapping, that here bears no Chern-Simmons singularites.
This is considering the said given arbitrary superstring, when in terms the supplemental distribution of the corresponding ghost-based indices that, here, form an integrable linear trace as to where and how the said given superstring had moved in the relatively transient past sequential series of iterations of group instanton.  Such a path -- more than likely -- will not trace a Wilson linearity through the non-time-oriented Lagrangiann of the multiplicit coniaxial of the traceable mapping of the strings previous motion.  This is because, even at the Poincaire level that is adjacent to and/or Gliossi to any actual superstrings, space-time-fabric bends to an extent.  Yet, the supplemental basis of a physical memory of the mapable trace, as to where and how such said superstrings had kinematically differentiated over time, is said to be hermitian if the activity of the directly corresponding superstrings bears only as many changes in the derivative of its motion as the number of spatial dimensions that it is traveling in over time.  And, if the said superstrings pulse harmonically, then, the given superstrings are said to be kinematically differentiating in the just mentioned hermitian manner that bears no spurious-based conditions  -- as can be related to the eluded to group of superstrings that are being considered here.  The just mentioned general format of substringular motion is said to then bear no Chern-Simmons singularities.  Any ghost anomaly that bears such a genus of a traceable mapped-out holonomic path is said to bear a Rham cohomology, of which exists here between the individual ghost anomaly-based indices that come together in so as to form the eluded to extrapolation of what tends to be a relatively straight, or jointal, format of a smoothly curved physical memory of the described general format of superstring -- if the directly corresponding format of mapped-out tracing is not perturbated by its exterial-based surroundings.  Again, as a reminder, ghost anomalies include the immediate field of their multiplicit directly corresponding field -- that is Gliossi to the Poincaire level of such given arbitrary superstrings. This is why a world-sheet and the ghost anomalies that it forms always exists in one more spatial dimension than than the dimensionality of its directly corresponding superstring that works to form it.   I will continue with the suspense later!  Sincerely, Samuel Roach.

A Little Bit of Preparation, Other Part

I wish to finish course 14 by early November.   I wish to complete courses 16, 17, 18, 19, 20, 21, 24, 25, and 26 by the time that I turn 45 (11-6-2015).  As a heads-up, course 16 is about topology, cohomologies, and iterations -- both the spurious and the Yau-Exact kind.  Course 17 is about the Ricci Scalar.  Course 18 is about the Ricci Scalar and the Klein Bottle.  Course 19 is about orbifolds and Kaeler-differentiation.  Course 20 is about Calabi-Interactions.  Course 21 is about supersymmetry and supergravity.  Course 24 is about Superconformal and Conformal Invariance.  Course 25 is about Poincaire interactions.  And, Course 26 is about Wess-Zumino and Cevita Interactions.  This should give the reader some input as to how to learn as to what's next by reading in-between the lines in the posts that I have already written  (and will right soon).  Always remember:  Whenever a superstringular region of many superstrings reverses in its general holomophicity, a  Gaussian Transformation is about to happen.  Also, whenever electromagnetic energy strikes anything, there is about to be a certain general type of Gaussian Transformation happening known of as a gauge-transformation.  To sum-up what I am going to show you in relatively new future posts, if a cohomology of ghosts anomalies is completely hermitian in its kinematic translation over time, then it is of a Rham-based genus.  Yet, if a cohomology of ghost anomalies is Chern-Simmons in its kinematic translation over time, then, it is of a Doubolt-based genus over time.  That is all for now.  Let this knowledge incubate in your mind, and, I will get the ball rolling soon.  I will right to you soon!  Sam Roach.

A Little Bit of Preparation

I have recently discussed gluons and ghost anomalies.  My next six posts involve the four parts to session 13 of Course 14 about Group Action.  In the posts that appertain to the four parts of session 13 about Group Action, I thoroughly discuss the activity of ghosts -- as various formats of delineated displacements of the physical memories of world sheets.  World-Sheets are the physical trajectories of superstrings.  Such physical memories are mappable traces that are comprised of mildly bumped into forward-holomorphic norm-states, whose delineations work to show the directly prior motion as to what, how, and where various superstringular phenomena had been kinematically placed over a sequential series of iterations of group instanton.  The reverse-holomorphic norm-states that act as counterparts to the forward-holomorphic norm-states work to scatter ghost anomalies, so that the residual indices of the eluded to physical memories of superstrings may be extrapolated into fractals of Hamiltonian operators that subsequently work to form those gravitational particles that act in so as to interact along the Rarita Structure in order to operate the function of gravity -- when in conjunction with superstrings that act as discrete units of energy permittivity.  In later sessions, I will explain as to how the ghost anomalies of gravitational-based particles, which are known of as Neilson-Kollosh ghosts -- work to exchange indices with the ghosts of discrete units of energy permittivity, which are known of as Gliossi-Sherk-Olive ghosts -- in so as to balance the various loci as to where there needs to be room for both gravitational particles and the eluded to Gliossi-Sherk-Olive ghosts, so that there may be adequate space for energy to move kinematically over time in so as to remain as energy.  You will then soon learn about both the hermitian-based ghost anomalic formats, as well as the Chern-Simmons-based ghost anomalic formats, so that there may be a viable dialogue as to the harmonic nature of both the permittivity, impedance, and the mappable tracing of the integrable delineations of such ghosts in both a time-wise and in a time-less extrapolatory genus of parity.  Knowing how to trace and determine any given arbitrary past motions of superstirngs works to help one to understand the activity of the substringular. By the way, forward-moving time associated ghost anomalies are formed by positive-norm-states and scattered by negative-norm-states, yet, with backward-moving time associated ghost anomalies, ghosts are formed by negative-norm-states and are scattered by positive-norm-states.  This is because the holomorphic direction of reverse-time-based substringular action is in the reverse genus of general parity of the holomorphic direction of forward-time-based substringular action.  I will continue with the suspense later!  Sincerely, Sam Roach.

Session 12 Of Course 14 About Group Action, Part One

The integrated trajectory that is mapped-out of the projection as to where a superstring had recently been is known of as a world-sheet.  The mapped-out trajectory of a substringular encoder -- as to where any given substingular encoder had recently been, is another example of a world-sheet.  The theoretical "world-sheets" that are comprised of substringular mapped-out projections that work to trace one or more superstrings during the generally unnoticed duration of Ultimon Flow do not function or exist as such -- since the forward-holomorphic-norm-states and the reverse-holomorphic-norm-states that tend to respectively form ghosts and dissimilate ghosts (ghost anomalies) move at an analogous rate as is the motion of superstrings, over the said generally unnoticed duration of Ultimon Flow.  During the generally unnoticed duration of Ultimon Fow, the residue of mini-string segments go into the activity of the recycling of substringular states from norm-to-ground and from ground-to-norm -- in so that there may be a balance between the tendency of smooth-curved trajectory with the tendency of jointal-based-curved trajectory over a sequential series of instantons.  As such residue is released -- via a homotopical cascading of the retying of those related mini-string segments that alter, in so as to allow for the eluded to indistinguishably different conditions that allow for a balance of norm and ground states -- the directoral basis of such a format of the recycling of the multiplicit topological genus of various substringular states bears a general tendancy of approaching what I terms of as the Royal Arc, of which happens in a relatively holomorphic manner.  The integrated iterations of superstrings during a sequential series of group instantons works to form ghost anomalies in the direction of their trajectory -- as such a trajectory is redelineated either progressively in a Noether-based flow or perturbatively in a tachyonic-based flow.  As like before, the mapped-out traces of the projection of such trajectoral delineations and redilineations works to form a physical memory of the path that any given arbitrary superstring had traversed through -- either through a discrete Lagrangian and/or through a spin-orbital sequence of integratible motions.  I will continue with the suspense later!
Sincerely, Sam Roach.

Part Three of the 11th Session of Course 14 About Group Action

Ghost anomalies are inevitably annhilated by negative-norm-states, via a Yakawa-based Gliossi interaction of the said negative-norm-states upon the said positive-norm-states -- the latter of which are formerly arranged in so as to form map-based traces that act as  physical memories of the prior motion of the directly associated superstrings, in this given arbitrary type of case.  Such ghost anomalies, that are here being broken down, are known of as Gliossi-Sherk-Olive ghosts.  The given action of the said negative-norm-states, upon the just mentioned genus of anomalous phenomenology, works to elliminate the lack of room that would otherwise work to impede the motion of superstrings. The motion of both gravitons and gravitinos works to form what are known of as Neilson-Kollosh ghosts.  The motion of reverse-norm-states in the relatively Njenhuis fields of gravitons and gravitinos works to scatter the said norm and ground-based states in such a manner in so that these just mentioned states inevitably resurface back into the Real Reimmanian Plane -- in which superstrings of discrete energy permitivity kinematically differentiate in.  Such motion of both format-bases of reverse-holomorphic norm-states, that work to perpetually keep the overall volume of ghost anomalies in check, works to prevent the eventual formation of black-holes.

About The Ghost Anomalies Of Certain Heterotic Superstrings

The ghost anomalies of E(6)XE(6) superstrings in forward-time-moving-associated space are the residue of redelineated positive-norm-states that are redelineated by the motion of the said type of hetorotic strings per iteration of group instanton.  As positive-norm-states are "bumped", the just mentioned physical memory of the motion and existence of the said E(6)XE(6) strings is formed. This redelineation of the said format of norm-states works to form ghost anomalies that work to show the directly related pattern of both the motion and the condition of the said heterotic strings as these move through their respective Lagrangians over a given arbitrary duration of Real-based time.  Over a transient period of time after the said ghost anomalies of the said heterotic strings is formed, there are negative-norm-states that scatter the ghost anomalies just discussed in so that the arrangement of the distribution of the directly related positive-norm-states is scrambled into a real-based residue per iteration of group instanton.  Such scattered ghost anomaly-based indices that are here scattered will then tend to be pulled toward the relative interior of the directly related orbifold and/or the directly related orbifold eigenset that is arbitrarily being considered here.  The ghost anomalies of E(8)XE(8) superstrings tend to be "shuffled" toward the relative exterior of its directly associated orbifold and/or orbifold eigenset, or, sometimes toward the immediate exterial field that works here to be adjacent to the directly related orbifold and/or orbifold eigenset.  Just as with E(6)XE(6) superstrings, the directly related ghost anomalies that the said E(8)XE(8) superstrings form is created by the said Yakawa-based interaction of forward-moving norm-states with the said E(8)XE(8) superstrings right before the directly associated iterations of group BRST.  Again it is the eluded to backward-moving norm-states that work to scatter the eluded to ghost anomalies that are then formed here.  The scattered ghosts of E(8)XE(8) superstrings that are not directly impending to fray and the scattered ghosts of E(6)XE(6) superstrings that are not impending to fray always tend to bear no Gliossi-based Yakawa interaction with the ghosts of superstrings of discrete energy permittivity UNLESS there is a definitive cohomoligical index that is here used to pull these into their direct ghost-based field by the holonomic substrate of a directly related group attractor.  Again, with forward-moving-time-based substringular activity, it is the positive-norm-states that form ghost anomalies and it is the negative-norm-states that scatter ghost anomalies.  With backward-moving-time-based substringular activity, it is then the negative-norm-states that form ghost anomalies and it is the positive-norm-states that scatter ghost anomalies.  I will continue with the suspense later!  Sincerely, Sam Roach.

Ghosts

Substringular phenomena tends to move in such a manner in so that it leaves physical traces as to where it just was before it reached a different spot. Such physical traces are known of as ghost anomalies. Such ghosts may move in either form a euclidean-based mapping or a euler-based tracing. The tracing may be either proportional to its immediate surroundings, or, the expansion of the mapping as may be derived by a Laplacian-based tracing of the ghost-like delineations that here may be Clifford in nature. These just mentioned ghosts form a Laplacian-basis as to how one may work to determine where certain substringular phenomena were, and, from such knowledge, such a mapping may work to help determine -- through non-euclidean math -- where such substringular phenomena will be in the future. So, the activity that forms such traces happens over Fourier-based Transformations, yet, the actual mapping of such traces often involves a timeless determination that involves relative "snapshots" of what would here exist in such a manner in so as to work to determine the physical evidence as to where, what, and how certain substringular phenomena had moved over the directly prior period in which it had moved in so as to form such relatively stagnant traces. Such ghosts may be Rham or Doubolt in terms of their covariant cohomology. Often, though, the topological-based framework of certain ghost anomalies may be kinematic -- causing the basis of such a framework to instead bear the need to be mapped over a tracing that here involves a Fourier-based Transformation through an onset of redistributional extrapolation. Sincerely, Sam Roach

As To The General Nature Of Ghost Anomalies

The substrate of the mapping of the trajectory of substringular phenomena is known of as ghost anomalies. Over a sequential series of iterations of instanton, a substringular phenomenon exists in a given arbitrary display of distributions that integrate in such a manner in so as to form a path that may be mapped out via the existence of those positive-norm-states that indicate the directly prior delineatioins as to where the said substirngular phenomenon had existed in in the just mentioned metric. The physical trajectoral path of which may be mapped out -- in a Laplacian manner -- is known of as a ghost anomaly. Ghost anomalies may be Rham-based (supplementally based) or Doubolt (complementary based). Ghost anomalies often bear a certain degree of symmetry -- whether such a symmetry is trivially isomorphic, non-trivially isomorphic, trivailly assymetric, or non-trivially assymetric. The physical entities of ghost anomalies are gradually scattered by negative-norm-states so, via there counter-motion in codeterminable covariance with their corresponding positive-norm-states,such activity may work to allow for that substringular room that is necessary for room to be made in the substringular so that superstrings and their corelatively-related phenomena may continue to spontaneously move over time. Often, Gliossi-Sherk-Olive ghosts interchange with Kollosh ghosts so that there may be a recycling genus that can exist between superstrings of discrete energy and gravitational-based superstrings. The flow of ghost anomalies forms a basis of an allocation of residue of substringular phenomena that allows for certain indistinguashable replacement to exist from all three sets of universes that here exist within a few millimeters or so of everywhere one may go from within the confines of our universe --- even though all of the universes of our set of universes literally exist within every millimeter or so of anywhere where one may go witihin our universe. The norm-conditions of ghost anomallies work to complement the norm-conditions and the changes in norm-conditions of kinematically differentiating substrinular phenomena over time, while such mentioned ghosts work to recycle over time into various regions in so as to also allow for the appropriate redelinetion of first-ordered point particles that is necessary so that the proper point commutators may be localized where these may be needed so that the needed norm-based projections may be physically coherent enough to allow for those activities that are necessary for both changes in norm-conditions of superstrings, and, so that superstrings may go through those motions that allow for these to do their essential closing and opening over time (so that light may be formed from plain kinetic energy, and, vice versa).

A Tad-Bit More About Ghosts

A two-dimensional superstrings is resting in this case to all relatively Laplacian-based "appearances" in a differentiably integrable region in which it has iterated may times over a relatively tightly-knit Fourier-Transform.  The corresponding positive-norm-states here work to form a ghost anomalic region at the locus of the eigenbasis of the toroidal Jacobi that here work to define the related field of the angular momentum of the said two-dimensional superstring.  A set of zero-norm-states, acting as a projection, after a certain number of instantons, works to open the related toroidal eigenbasis so as to open the corresponding elluded to region up as a cylindrical shaft that is relatively thick.  After the said zero-norm-state projection do their work, the corresponding negative-norm-states work to orphoganate the related positive-norm-conditions that were previously existant in the described locus so as to elliminate the ghost anomalic eigenindices that had been mapped prior to the occurance of the mentioned scattering of ghost anomalies.  This ellimination works to scatter the related point commutators that had integrated to form the mentioned ghost anomalic eigenlocus so as to allowl a path for the operation of the incoming world-sheets, as well as to allow for a path for the other substringular fields that are also incoming.  Mobius-based ghosts are elliminated in the same general fashion, yet, such ellimination here involves more overall norm-states, and, thus, such ellimination involves a more prolonged Fourier Transform.  (It takes a duration of more instantons to elliminate these.) Such ghosts are elliminated at the critical cusps of the fold of the corresponding Mobius-based ghosts.  Two-Dimensional stringular world-sheets have ghost anomalic residue that is elliminated at multiple spots by both zero-norm-states and positive-norm-states.  Zero-Norm-States work to open the associated ghost anomalic eigenbasis at four general loci per codifferentiable pulse in which such a general activity occurs.  The said positive-norm-states work to alter the Gaussian conditions of the said corresponding negative-norm-states in order to supplement the field that was previously operated on by the succession of the kinematic activity of the two-dimensional field that we are discussing in this case.  This said supplementation works to clear what had just been a ghost anomalic field by scattering the said two-dimensional field's eigenbasis.  This kinematic activity works to open the described general overall locus in order for such a locus to remain as an operand for further substringular Fourier codifferentiation.  Sincerely, Sam.

A Little More About Ghost Anomalies

Let us consider a substringular condition in which a set of one or more superstrings moves around in a general locus that is undergoing a tense of conformal invariance -- if not superconformal invariance -- in which the said superstrings that are involved iterate and reiterate within a common general locus that is kinematically invariant over a repeated pattern that involves a sequential series of instantons that form a pattern of static equilibrium over a relatively tightly-knit Fourier-Transformation that works to form a tight-knit mapping as to the location and operation of the related given arbitrary superstrings that we are forming a scenario as to their behavior in this case.  The ghost anomalic residue that works to form the general pattern that works to indicate the topological history as to the activity and operation of the corresponding superstrings that I am describing here, may be exrapolated as a general type of ghost anomalic substrate that is transient in the given case until the holonomic phenomenology that works to describe the general entity that comprises the said ghost anomalic field that acts as the denoted discharge of physical memory that is the field-mapping of where the related superstrings whose Fourier-based kinematic activity that formed the said ghost anomalies is scattered by negative-norm states that work to redistribute the indices of the said ghosts so that the room that was initially filled in part by the related initial ghosts may be utilized by other phenomena that need to occur in the prior implied general locus so that the motion of holonomic discrete energy may have a place to happen and interact so that that motion that is necessary for the continued existence of reality may occur so that reality may continue to exist.  Such ghosts that I have just described -- that inter-play in a relatively tightly-knit locus in a repeated manner so that the condtition of the corresponding kinematic operation that I thus related is here either a conformal if not a superconformal invariance of Fourier differentiating superstrings -- whose ghost-like membranes that here involve a higher genus of discrete energy phenomena that is known as kinematically inter-active orbifolds and kinematically inter-active orbifold eigensets that form a pattern of a relatively compactified static equilibrium are what are known of as Gliossi-Sherk-Olive ghosts.  I will continue with the suspence later!  Sincerely, Samuel David Roach.