Orbifold Ghost Cohomologies

Often, sets of ghost anomalies that are comprised of the physical memories of the trajectories of sets of superstrings are inter-bound into a cohomology that is Gliossi in nature.  When the just eluded to ghost-like pattern is anharmonically scattered by relatively reverse-holomorphic norm-state projections, the eluded to Yakawa Coupling that had just bound the Ward-Neumman limits as to the locus of the said ghost-like physical memory, when in terms of what had been a mappable tracing as to the trajectory of  two sets of superstrings, is then brought out of the prior stated condition of a Gliossi-based Yakawa Coupling.  Often, a relatively minor anharmonic scattering of two or more cohomolically bound sets of ghost anomalies may only work to scatter the region of Ward-Neumman inter-connection that had just existed in so as to form a binding between two physical memories of the respective memories of the trajectories of two or more different sets of superstrings that had performed two or more respective operations.  Again, an orbifold is a set of one or more superstrings that functions to perform a specific operation.  As the Ward-Neumman boundaries that had once inter-connected two or more ghost anomalies is broken, the genus of the Gaussian inter-relationship that had just existed in so as to correspond the spatial inter-relationship of what had just been of a Real Reimmanian inter-relation will alter, in so as to decrease the isosymmetric parity that had existed just beforehand between the said sets of ghost anomalies.  Over time, the just eluded to physical memories are recycled into other phenomena, in so as to allow for the recycling of the field modulae of substringular differential geometry.  I will continue with the suspense later! Sincerely, Samuel David Roach.

Certain Activity Of Ghost Anomalies

At times, the ghost anomalies that are formed by different orbifolds and/or orbifold eigensets that are of different universes bind -- over time -- into a cohomology.  Often when this happens, the genus of the eluded to cohomology is Rham in basis, due to a cohomoligical Yakawa Coupling that is hermitian.  Often, when there is an interconnection that exists between two sets of ghost anomalies that are from two different universes, these may bear a cohomology that is Doubolt in basis, due to a cohomological Yakawa Coupling that is Chern-Simmons.  As such an inter-binding of sets of ghost anomalies forms the eluded to Yakawa Coupling that would here be Gliossi in nature, the ghost-like physical memories that are here formed will be Real Reimmanian relative to one another -- even though the eluded to sets of superstrings that would here bear a trajectory or world-sheet that forms the said ghost-like patterns would here be Njenhuis relative to the one set of superstrings comprising one physical space corresponding to the other.  As ghost anomalies of sets of superstrings -- in the form of the physical memory of the motion of superstrings -- interbind in a cohomoligical manner that is Gliossi, the memory of the superstrings will bear a space-based tracing that forms a unitary Gaussian format of each of the given arbitrary sets that I eluded to relative to one another, respectively.  This means that sets of superstrings, in the form of orbifolds, that may be only related in a Njenhuis manner via Li Algebra, may bear physical memories that are Real instead of Njenhuis when relating each of such spaces towards each other individual respective physical spaces.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Ghosts Of Orbifold-Based Phenomena

When  physical spaces -- in the form of  orbifolds and/or orbifold eigensets -- are pulled through dual discrete Lagrangians, whether or not the just mentioned general format of the respective singular Lagrangians are unitary, binary, or overtly multiplicit in directoral-based permittivity, the so-stated orbifolds and/or orbifold eigensets will form ghost anomalies as these move through the corresponding Hamiltonian-based operands of physical space in which the said orbifolds and/or orbifold eigensets move through here.  Such individual respective Hamiltonian-based operations will here involve the multiplicit formation of potentially many ghost anomalies that come together in a group-based cohomology that will here form, in so as to map-out a tracing as to the relatively recent physically-extrapolatable memory of where, how, and when an orbifold and/or an orbifold eigenset had been kinematically displaced and delineated over a sequential series of group instantons -- the physical memory of an orbifold and/or an orbifold eigenset when relative to one or more other orbifolds and/or orbifold eigensets.  Given the substringular environment that exists after an arbitrary discrete physical space has moved in so as to form a trajectory of its kinematic projection over time, the ghost anomalies that are thus formed may be anharmonically scattered at any time, once the corresponding mapping of the correlative group-based world-sheets have been traced-out by the harmonic scattering of the here given arbitrary relatively forward-holomorphic moving norm-states that get in the path of the motion of the corresponding superstrings that work to comprise the eluded to orbifolds and/or orbifold eigensets.  If such ghost anomalies are formed between two or more orbifolds and/or two or more orbifold eigensets that are Njenhuis in terms of their kinematic-based covariance towards each other over the same group metric, then, the ghosts that these form will tend to be Njenhuis relative to one another. Yet, if such ghost anomalies are formed between two or more orbifolds and/or two or more orbifold eigensets that are Real Reimmanian in terms of their kinematic-based covariance towards each other over the same group metric, then, the ghosts that these form will tend to be Real Reimmanian relative to one another.  Often, though, the residue that is formed by the anharmonic scattering of different sets of ghost anomalies that are initially of different universes may be brought into a closer Reimmanian inter-relationship towards each other after the corresponding recycling of their respective mini-string segmental partials have been recycled through enough times.  I will continue with the suspense later!  Sincerely, Sam Roach.

The Fifth Part of the Fifteenth Session of Course 14

When two-dimensional superstrings map out a trajectory, with only the existence of relatively transient ghosts, one may still call this format of mapping-out of the so-stated two-dimensional string -- whose mapping works to form a twisted shaft in the form of three-dimensional world-sheets, the said detection of the ghost anomalies -- as  formed by what is here the forward-holomorphic norm-states -- is Imaginary in this given scenario.  The two-dimensional world-sheets that work to form from the kinematic differentiation of one-dimensional superstrings often forms a twisted cylinder, because space not only displays jointal conditions, yet also, space also displays smooth curvedness.  The three-dimensional world-sheets that form from the kinematic differentiation of two-dimensional strings forms a twisted shaft, because space not only displays jointal conditions, yet also, space also displays smooth curvedness.  World-Sheets that are relatively Real Reimmanian are relatively limited in trajectory, because ghost anomalies are annhilated periodically in so as to balance gravitational force.  This causes the condition that both Real and Imaginary (Njenhuis here) cohomologies must always simultaneously exist.  Loci that display Imaginary cohomology are often shifted to display Real cohomology in other neighboring loci that involve multiple superstrings.  Homology that is between two and three-dimensional world-sheets is Imaginary, even when the directly corresponding Ward-Neumman conditions that exist here  in-between these given world-sheets is even.  The reason for this is because the Ward-Derichlet conditions of these world-sheets is centrally variant.  Central variance does not tend to allow for smooth interconnection.  As world-sheets codifferentiate, when involving Real-based ghost anomalies, the loci of the directly corresponding Real and Imaginary (Njenhuis) cohomology shifts in so as to allow the corelative superstrings and orbifolds to display differential tangencies in the multiple spatial dimensions that these said superstrings kinematically differentiate in.  I will continue with the suspense later, in the form of the test questions for this corresponding course!  Sincerely, Sam Roach.

About The Pheonmenology of Substringular Recycling

Let us say that a first-ordered point particle bears core field density -- in the form of mini-string holonomic substrate -- that is being recycled in an indistinguishably different manner. So, just as mini-string segments are homotopically fed out of the given arbitrary eluded to point particle that I have mentioned here, an equal amount of mini-string holonomic substrate is fed back into the said first-ordered point particle.  Even though the directly corresponding superstring that I have eluded here will, at this point, be only extrapolated as being in the same general condition as before the specific metrical index that I have eluded to had happened, the literal mini-string segmental holonomic substrate that one would have started out with, here, under the said arbitrary instant under consideration, is not the identically same mini-string segmental-based holonomic substrate as what one would have after the group metric in which the substringular recycling that I have mentioned in this post had proceeded any further. Substringular recycling is constant.  Every mini-string segmental-based holonomic substrate is constantly being shuffled and re-shuffled in an indistinguishably different manner, in so that the wear and tear that is imbued upon the eluded to core field density of superstrings will not have as much of a possibility of damaging the directly related superstrings. Also, substringular reycling works to interchange norm-based states with ground-based states -- so that relatively smooth-oriented curvature that is kinematically-based may be re-oriented with jointal-oriented curvature that is kinematically-based.  Not only does such activity work to allow for the possibility of Gaussian transformation, yet, this activity works to form a continual change in the genus of abelian-based interaction that the various operands in the substringular may be able to imbue upon the literal phenomenology of the said indices of the said mini-string segmental-based holonomic substrate eigenstates.  For instance, as an analogy, if one works different muscle groups each day of the week, one is less likely to injure your muscles.  So, on a much fractal-based scale, the interchange of the usage of mini-string segments over time -- in a recycling-based manner -- works to allow for the perpetual existence of the substringular.
I will continue with the suspense later!  Sincerely, Samuel David Roach.

Multiple Universe-Based Orbifolds

Let us say that there were a high number of orbifolds that each were initially of several different respective individual universes -- these of which decellerated as these said multiple orbifolds approached each other's Ward-Neumman physical bounds, over a discrete sequential series of iterations of group instanton.  Here, these orbifolds will -- in this given arbitrary instance under consideration -- become of the same universe.  This is once these orbifolds settle into a metrical consideration of superconformal invariance.  That orbifold, in this given arbitrary case, that worked to bear the greatest Hodge Index basis of Hamiltonian operation -- in the process of the eluded to approach of the said given arbitrary orbifolds towards each other, after a covariant, codeterminable, codifferentiable group metric -- when in terms of the directly associated multiplicit parity and chirality associated that would here be corresponding to the overall tensoric wave-tug/wave-pull that is here related to the fractals of both the directly affiliated angular momentum and spin-orbital momentum of the said orbifolds, in the kinematic projection of the diretoral path of the Lagrangian topological sway that the said orbifolds have here been traveling through over the group metric that here involves the multiplicit approach of these said kinematic physical spaces towards each other, will then here be the orbifold that will here act as the group attractor semi-group that all of the eluded to orbifolds that will have here approached towards each other over time, that will be taken as the template as to what all of the mentioned orbifolds of this given arbitray scenario will then here synchrounize their substringular vibrations to (into the intrinsic vibration of that semi-group mentioned that will here act as the predominant substringular-based template) in so that all of these said eluded to orbifolds will then alter in so as to then be of the same universe in a consideration of a condition of superconformal invariance.   At this point, all of these orbifolds will alter from each of these initially being of different Gaussian formats, into being of the same Gaussian format.  (These will alter from being each from Njenhuis subspaces into being of a common Real Reimmanian subspace.)  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Orbifold Couplings, A Little Start

When two orbifolds that are initially from two different universes are brought -- via an initial dual symmetrical Lagrangian of approach -- into a virtually Gliossi contact, then, these adjacent orbifolds that were initially from two different universes will often synchrounize their vibrations in so that these will then be of the same universe as each other.  This will, to an extent, depend upon both the binary dual directoral paths that are here to interact & the covariance of both the parity and chirality genus formats of the Hamiltonian operations of both orbifolds -- as these approach each other in a Yakawa manner that is here not Gliossi.  So, as such orbifolds come into an "apprehension" of each other, these slow down in a Reverse-Dirac-based manner as these become relatively near each other.  This given arbitrary tendency to slow is based, in part, upon the covariant, codeterminable, codifferentiable genus and amplitude of the respective Hamiltonian operation that works to describe the substringular momentum of the two approaching orbifolds & the Hodge Index of such an operation. The Njenhuis-based tensors of such  transversal and spin-orbital Hamiltonian dual operators that have just moved through the eluded to Hamiltonian dual operands will then, upon the synchrounization of their Gaussian Formats, become Real Reimmanian-based tensors.  Often, once such determined orbifolds have here become of Real-based spaces relative to one another, these will then enter a state of conformal invariance that tends to at least transiently be activated into a Noether-based mode.  To be continued.  Sam.

Overall Directoral Topological Sway

When two orbifolds that are of two different universes are brought into a spurious-based Gliossi-based Yakwawa Coupling -- which is the initially given arbitrary orbifold striking into the second given arbitrary orbifold -- there is a certain covariant kinematic-based symmetry as to the motion of one of the orbifolds relative to the other one that is struck, as I have mentioned.  So, although there is a dual activity of two different Hodge-Index-based Hamiltonian operations -- that work to describe the substringular momentum of the initial eluded to orbifold relative to the other given orbifold, there is, also to be considered, the dual genus of the Lagrangian that works to inter-bind the interaction of the two orbifolds, that, here, come into direct contact with each other.  There is also the dual symmetrical directoral-based path that, here, works to trace both the fractals of the angular momentum-based Hamiltonian index and the fractal of the spin-orbital momentum-based Hamiltonian index as to the format and parity of the here eluded to collision.  So, when one considers the traceable mapping of the Ward-Caucy-based path directoral of the Lagrangian of the intially considered orbifold with the traceable mapping of the Ward-Caucy-based path directoral of the Lagrangian of the second given arbitrary considered orbifold -- that the first so-mentioned substringular group attractor works to describe as then here directly touching the second so-mentioned substringular group attractor in this scenario, the overall parity and chirality genus of the first eluded to semi-group as here interacting with the overall parity and chirality genus of the second eluded to semi-group, at contact -- along with the angling of the directoral topological sway of the two inter-reacting orbifolds during the self-same interaction -- works to help describe the here resultant conditions that are to then bear a Majorana-Weyl covariant mode upon both the metrical and phenomenal-based activity that happens, once the two so-stated orbifolds come into a direct contact here.  I will continue with the suspense later!
Sincerely, Samuel David Roach.

Changes in Universe

When two orbifolds that are initially of two different universes work to synchrounize their intrisnsic vibrations while in the process of their covariant codeterminable codifferentiable approach relative to one another are brought into being of the same universe, the predominant orbifold that works to bring the other given arbitrary orbifold into its universe is the orbifold that bears what is at this point the greatest Hodge Index of Hamiltonian operation -- over the duration in which what were two orbifolds that are of two different universes into being of the same universe.  To Be Continued!  Sincerely, Samuel David Roach

Changes in Layers of Reality

When a Major Reality Change happens, -- when one-ten-thousandth of history changes -- multiplicity pairs of two orbifold eigensets that are respectively of different universes each strike each other in a prominently Gliossi maner.  This condition of multiple pairs of relatively Njenhuis orbifolds striking is, in effect, a condition of many orbifolds striking each other as different physically kinematic spaces that are Njenhuis to one another, while yet bearing a tightly bound Yakawa Coupling with and upon each other.  This direct physical contact of core substringular field density of two different universe-based spatial indices hitting each other head-on will here happen in a spurious manner -- to where there is not enough time for these spaces that are intrinsically Njenhuis to each other in their covariance to synchrounize their instrinsice vibrations as these are inflected by the resultant perturbation in their Ward-Caucy bounds.  This works to deactivate what was the predominant layer of reality -- while yet activating another layer of reality as then being predominant.  Enough said here for now.  I will continue the suspense later!  Sincerely, Sam Roach.

Membrane-Format of Various Orbifolds

The structure of orbifold eigensets that are not singularly are not 100 percent filled with the topological substrate of orbifolds. The structure of orbifolds is not 100 percent filled with the topological substrate of superstrings.  The exterial range of the core field density of superstrings is not 100 percent filled with the topological substrate of mini-string.  The interial core field density of superstrings is, though, comprised of relatively compactified mini-string segments.  Mini-Strings segments that are Gliossi in kinematic contact are homotopic in terms of their respective Majorana-Weyl Invariant mode.  As long as a substringular field is homotopic, the directly related mini-string segments are not frayed.  Yet, an orbifold eigenset and/or an orbifold is not pure mini-string that is compactified.  So, an orbifold may often be semipermeable with another orbifold and/or orbifold eigenset over the course of its kinematic translocation through a discrete Lagrangian.  Likewise, an orbifold eigenset may then be able to often be semipermeable with another orbiofld and/or an orbifold eigenset over the course of its kinematic translocation through a discrete Lagrangian.  Often, such membranes that occupy the same general substringular neighborhood at the same time are not of the same universe.  Orbifolds and/or orbifold eigensets that are not of the same universe are not of a Real-based spatial comparison when corresponding to one another.  Such a co-relation may be extrapolated when in terms of Li Algebra.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

A Comparison Of Certain Ghosts

When Gliossi-Sherk-Olive ghosts are exchanged from one general relative Real-based plane to another general relative Real-based plane -- the initially mentioned plane, of which, is Njenhuis to the second one -- there are, in this given arbitrary example, Neilson-Kollosh ghosts that are inversely exchanged from what was initially their Real-based plane to another general relative Real-based plane -- this initially mentioned plane, of which, is Njenhuis to the second so-stated plane.  The Real-based plane in which a Gliossi-Sherk-Olive ghost anomaly is formed is Njenhuis to the relatively Real-based plane in which a Neilson-Kollosh ghost anomaly is formed.  So, as this eluded to exchange of ghost anomalies interacts, in so as to form an exchange -- in the form of scattered ghost indices from one basis of Real-based plane being exchanged with scattered ghost indices from another basis of Real-based plane -- this works to involve a format of ghost indices that bears a condition of one of each set of scattered indices having a topological contour that may be viable in trace as orphoganal and inverse in mappable curvature to the respective other eluded to format of ghost indices.  Such a complementary set of conditions is one that is here comprised of a complementary pairing of individual sets of scattered indices that operate physically in so as to bear such an orphoganal and inverse contour -- due to both the individual non-time oriented condition that may be compared via a Hodge-based extrapolation, as well as the time-wise kinematic covariant codifferentiation that may be compared via the geometrical affiliation that such residue of ghosts works to respectively bear over a sequential series of iterations of group instanton.  As such residue is re-inactivated as norm-based topological stratum, in what was initially a Njenhuis genus of planar domain, the interaction of the norm-based phenomena upon such a basis of holonomic substrate works to activate the residue as a basis for the formation of ghosts and/or ghost scattering for the here indistinguishably different planar activity.  As this is going on, there is a relatively small discrete topological substrate that is pulled into codifferentiation with the Royal Arc -- in an indistinguishably different manner -- in so that such activity may fascillitate the recycling of norm-states, through the redelineation of mini-string segments, in so that substringular fields may be able to recycle from norm to ground and back.  This condition that involves Cassimer Invariance works to indirectly cause the basis of all phenomenology being relative to the motion and existence of light to bear a condition as to being viable.

An Informative View As To the Interaction of Certain Ghosts

As the Ricci Scalar is operative per the successive series of iterations of group instanton, the Rarita Structure operates in so as to enable the capacity for the Ricci Scalar to take a viable effect.  Over time, the Rarita Structure ebbs from a condition of pulling into a condition of tugging -- in a manner that works to take into consideration the flow of kinematic directoral indices that operate in so as to work in the direction of a relatively relaxed codifferentiable state of covariant norm-conditions.  As the codeteminable drive of the multiplicit activity of Rarita Structure eigenstates is swayed in so as to work in the eluded to operational capacity of the most viable inter-relationship of norm-conditonal stability, the ghost anomaly-based indices that have just been anharmonically scattered in a given arbitrary situation in which a given set of Gliossi-Sherk-Olive ghosts are broken-down into dilatons and dilatinos by relatively reverse-holomorphic-based norm-states, the kinematic-based directoral sway of the Rarita Structure works to pull the said Gliossi-Sherk-Olive ghosts -- and the ghosts that comingle with these -- into the direction of least resistance, while, the Neilson-Kollosh ghosts that are formed by gravitational-based particles are pulled in the direction of least resistance.  The codeterminable activity of the swaying of the Rarita Structure eigenstates works to make the said direction of least resistance of the mentioned ghost anomalies to be in the Njenhuis directoral pull of the relative Real-based plane for both respective codifferentiable, codeterminable, covariant binary-based settings.  This Njenhuis pull works to form an exchange of Gliossi-Sherk-Olive ghosts with Nieilson-Kollosh ghosts over a successive series of instantons.  The eluded to ghost anomaly-based residue that is tugged in the eluded to Njenhuis genus of manner at all during the generally noticed durations of group instanton is a Real-based Residue.  While, the eluded to ghost anomaly-based residue that is tugged in the eluded to Njenhuis genus of manner during the generally unnoticed durations of group instanton is an Imaginary-based Residue.  This recycling works to form permutations in the topological norm-state conditions as to the physical memory of superstrings, of which works to gradually alter the ghost-based cohomological structure of the interbinding of certain substringular structures. When such a permutation-based setting causes a relatively hermitian format of cohomological change or perturbation, then, the directly related genus of recycling mode is discrete relative to the relatively Real-based plane.  Yet, when such a permutation-based setting causes a relatively Chern-Simmons format of cohomological change or permutation, then, the directly related genus of reycling mode is of a Njenhuis tense of singularity.  -- The Rham-based cohomology becomes a Doubolt-based cohomology (in the latter case).  I will continue with the suspense later!  Sinerely, Sam Roach.

Still Some More Ghost Anomaly Stuff

The ghost anomalies of both light-cone-gauge eigenstates, Fadeev-Popov-Trace eigenstates, and counterstrings, comingle with the ghosts of superstrings of discrete units of energy permittivity (Gliossi-Sherk-Olive ghosts) during each succeeding iteration of instanton in which the ghost-based indices -- as to the physical memory of the substringular -- works to bear a Real Reimmanian-based residue that is effectual to the sequential series of Real-based substringular iterations of group instanton.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Some Added Stuff To Say About Ghost Anomalies

Just as the Gliossi-Sherk-Olive ghosts are being formed as the physical memory of the trajectory of superstrings of discrete energy permittivity, the physical memory of the directly corresponding counterstrings, light-cone-gauge eigenstates, and the directly corresponding Planck-like phenomena are being formed by the Gliossi interaction of these said additive phenomena with the relatively forward-holomorphic-based norm-states that come into contact with the projection of the said formats of phenomena -- that are directly related to the initially mentioned discrete units of energy permittivity.  The counterstrings act as a direct differential supplement to the directly corresponding discrete units of energy permittivity.  The light-cone-gauge eigenstates that directly co-relate to superstrings work to spring the said superstrings into the continual activity of Ultimon Flow (aside from other functions of the light-cone-gague), and, the Fadeev-Popov-Trace eigenstates (Planck-like phenomena that work to form the Fadeev-Popov-Ghosts as their physical memories) act as discrete units of energy impedance.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Part Four of the 15th Session of Course 14 About Group Action

The activity of negative-norm-states -- when with a forward-time-moving condition -- interacting in a Gliossi manner with ghost anomalies in so as to anharmonically scatter the indices of the respective ghost anomalies, in such a manner that the said indices are able to intially reform into dilatons and dilatinos, is due to the projected motion or the trajectory of the eluded to reverse-holomorphic states that are angled from an underlying subtentive condition by a 22.5 degree angle from off of a relatively straight subtension.  (The so-called "straight" linear basis of the plane that works to form this subtension curves to the same format of manner as the general curvature of space-time-fabric that exists in which the given arbitrary spatial region in which the directly corresponding reverse-holomorphic norm-states approaches the eluded to ghost anomalies.) As those reverse-holomorphic norm-states -- that angle from off of a reverse-holomorphically delineated subtension by 22.5 degrees -- come into contact with a relatively static and relatively forward-holomorphic norm-states that have been harmonically redistributed and "calmed" by the Gliossi interaction of superstrings upon the topology of the holonomic substrate of the relatively forward-holomorphic norm-states, the mini-string that inter-binds the first-ordered point particles is mildly compactified and also pulled into a closer-knit distribution -- when relative to the alterior first-ordered point particles that work to form the mentioned relatively static norm-states that had initially been moving in the relative forward-holomorphic direction.  This activity works to draw a more perturbative kinematic interaction of the different loci around the perimeter of the topological substrates of the eluded to norm-states that were said to have been relatively static once these became indices of ghost anomalies.  This perturbative contraction and spurious state of what were relatively calmed forward-holomorphic norm-states works to reassemble the differential geometry of both the ghost anomaly-based indices as individual phenomena -- as well as the interaction of such indices toward each other, in an entropic-based covariant manner.  This alteration in the genus of norm-state topological substrate pulls the prior ghost anomaly-based indices off of the relative Real Reimmanian plane.  As the eluded to entropic condition of the eluded to dilatons and dilatinos become a relatively rearranged static convergence of an inter-play of what were initially forward-holomorphic norm-states that had "calmed" into either Campbell, Hausendorf, and/or Campbell/Hausendorf states that were disrupted into a process of translocation and topological redelineation, the net effect of the redelineation of the eluded to reassembling of the said holonomic stratum works to form gravitons and gravitinos. I will continue with the suspense later!
Sincerely,
Samuel David Roach.

Isomorphisms Among Adjacent Orbifolds

If a given arbitrary orbifold is shaped in a manner that is neither Minkowski (flat) shaped nor parabollic shaped nor elliptical shaped, then an adjacent orbifold that is of the same universe is not necessarily trivially isomorphic to the initially eluded to orbifold that is shaped in a respectively unique manner.  Depending upon the shape that an orbifold has, an adjacent orbifold that is of the same universe as the initially eluded to orbifold may be shaped in one of many different manners of potential permutation -- depending upon the respective shape of the initially said given arbitrary orbifold.  The more permutations from an orbifold as being either flat, parabollic or elliptical in shape, the more of a chance that a given arbitrary adjacent orbifold that is of the same universe is not necessarily trivially isomormphic to the first given arbitrary said orbifold -- in terms of the corresponding differential geometry.  This is when one is comparing a relationship of the initially eluded to remapping of the topological contour of the first respective orbifold with the topological contour of the second respective orbifold. Again, two adjacent orbifolds that are of the same universe are comprised of Planck-like phenomena that bear an orphoganal differential arrangement -- when relative to one or more of the Planck-like phenomena of the other said orbifold that is here to be of the same universe.  Also, two orbifolds that are of the same universe bear Planck-like phenomena, to where each of the said phenomena bear an intrinsic vibration that is norm to one or more of the Planck-like phenomena that work to comprise the other orbifold that is here of the same universe  -- with a codeterminable wobble that is at a differential sway of ~1.104735878*10^(-81)I degrees.  This angle is equal to the span of arc that 96 spatial dimensions is capable of -- 96piI degrees-- divided by 273*10^(81)I degrees.  This angle is also equal to the span of arc that 32 spatial dimensions is capable of -- 32piI degrees -- divided by 91*^(81)I degrees.  As I have mentioned before, between superstrings that are adjacent -- there is a capability of up to 10^(81) formats of angling.  I will not say what the rest of the derivation as to the number of parallel universes that there are both in overall spatiality and also are just in our set of universes, since this is a touchy subject.  Sometimes, I would rather have people underestimate me than to overestimate me.  Yet, this is no fudging of anything at all.  I will continue with the suspense later!  Sincerely, Sam Roach.

Part Three of the Fifteenth Session of Course 14 About Group Action

When it comes to open, or fermionic, superstrings, one may be able to describe the mapping of a one-dimensional superstring of discrete plain kinetic energy permittivity -- whose mapping forms a twisted cylinder, when one considers the added spatial dimensionality of the added cyclic permutative unitary field networking that stems from the kinematic directoralization of the directly corresponding genus of superstring being redelineated through a discrete Hamiltonian-based Lagrangian, as a strand-based phenomenon that works to exhibit a sequential series of redistributed mini-string segments that would have here circulated around a conformally exactified radial Ward-Caucy hoop-like spatial trejectory.  This trajectory of which is here redelineated in a circular manner around the bounds of the Poincaire region that is exhibited by a sequential series of placements that the said one-dimensional superstring occupies per iteration of group instanton.  So, as the said one-dimensional superstring is projected as a trajectory of holonomic substrate over a given arbitrary metical-based set of instantons, the said unitary-based inter-bound radial arcing  that works to comprise the exterial field of the just mentioned superstring is reiterated and redistributed as such a closed field-based loop, that is exhibited as the outer Poincaire boundary of the Hamiltonian-based field density of the said superstring.  This happens as the string is covariant in kinematic eigenindex per instanton.  So, as the said superstring of discrete plain kinetic energy permittivity bears the activity of wave-tug, in so as to perturbate in its parity after the genus of its directoral parity is pulled spontaneously into a different tense of holonomic directoral index, the cylindical mode of the given arbitrary Hamiltonian-based field density of the eigenstructure of the holonomic substrate of the world-sheet -- that directly relates to the directly corresponding one-dimensional superstring -- forms an anharmonic spur in both its vibratorial-based directoral propagation and its metrical-based Lagrangian of its directoral propagation. This spurious and non-hermitian fluctuation is the sequential series of the redelineation of the said field density, that is of the genus of the said given arbitrary one-dimensional superstring of this scenario -- which is the case of which I have been describing here.  Such an eluded to activity works to form a kinematic extrapolation of a twisting cylinder.  As the Hamiltonian operation of the said kinematic extrapolation of the structure that here behaves as a twisting cylinder in space is projected through the eluded to trajectory, this works to form ghost anomalies that work to indicate the here described and eluded to motion of and the existence of the mentioned Hamiltonian field density of the said one-dimensional superstring of discrete plain kinetic energy permittivity.  Again, it is the Gliossi interaction of certain given arbitrary relatively forward-holomorphic moving norm-states with the corresponding superstrings, that interact in a harmonic-based scattering that works to form the mentioned ghost anomalies.  The interaction and bonding of ghost anomaly-based indices works to form either a Rham and/or a Doubolt ghost-based cohomology.  I will continue with the suspense later!  Sincerely, Sam Roach.

Orbifolds that Alter in their Gaussian-Basis of Format

When two different orbifolds that are flat-based, or, Minkowski-based -- that are initially of two different universes -- come into a close proximity the one toward the other, their intrinsic vibrations tend to syncrounize -- to where these two different orbifolds that were initially of two different universes become two different orbifolds that are of the same universe.  This same concept may happen, yet, in a slightly different manner, when in terms of the genus of orbifolds that are, instead, Hilbert in nature instead.  With a Hilbert-based set of two different orbifolds that are initially of two different universes, the same concept applies as to how the norm-based conditions of adjacent Planck phenomena are to both angle and vibrate if these are of to be from the same universe, yet, in the case of the just mentioned Hilbert-based orbifolds (volume-based), the manner as to what is actually adjacent Planck phenomena is altered in terms of the directly related differential geometry. Yet, as in the first mentioned case, any individual  orbifold consists of superstrings that are of the same universe.  -- To where if two different orbifolds that are initially of two different universes are adjacent in a manner that works to syncrounize their intrinsic vibrations, this activity will, in the different manner of which I have here recently eluded to, work to cause both of these said orbifolds to then be of the same universe.  Two different orbifolds that are each from two different respective universes bear relatively different Gaussian-based formats -- since these two given arbitrary orbifolds are initially not Real Reimmanian the one towards the other.  Yet, once two initially different relatively Real-based orbifolds are to become of the same universe, then, these said given arbitrary orbifolds are no longer Njenhuis the one toward the other.  This causes these two said orbifolds to then share the same Gaussian-based format of spatiality, since these will then be of the same basis of Real Reimmanian spatiality to each other.  I will continue with the suspense later!  To Be Continued!  Sincererly, Sam Roach.

Part Two of the 15th Session of Course 14 About Group Action

When one-dimensional superstrings of discrete energy permittivity map out a physical memory of the projection of the trajectory of the said one-dimensional string, without the contined existence of what here would have been those ghost anomaly-based indices that existed initially in the path of the kinematic-based differentiable Lagrangian -- that would here appertain to the tracing of the prior motion of the multiplicit eluded to one-dimensional superstrings of the eluded to directly prior extistent physical memory of the said superstrings.  This would then here mean that the ghost anomalies that had been formed by the inter-relative Gliossi contact, that would here exist between the said one-dimensional superstrings of discrete energy permittivity with the directly associated relatively forward-holomorphic-based norm-states that had been immediately scattered out of their initial basis of physical memory -- in a manner that is of an anharmonic manner, by the activity of relatively respective reverse-holomorphic-based norm-states.  So, if a superstring of both a relatively forward-time-based forward-holomorphic-based Hamiltonian operation moves through a given arbitrary Lagrangian -- in so as to harmonically scatter those positive-norm-states that were in its path, there would here, in this case, be negative-norm-states that had moved upon the initial said harmonically scattered arrangement of ghost anomalies that I had eluded to, in such a manner in so that the said ghost indices that had initially formed as a physical memory as to the directly prior motion and existence of the directly associated superstrings -- of which may here, in this given case scenario, be tentatively considered as appertaining to one-dimensional superstrings of discrete energy permittivity, in this given arbitrary case, form a Gliossi interaction with the Ward-Caucy bounds of the said ghost anomalies in an anharmonic genus of scatteriing.  This is to where the resultant Hamiltonian perturbative reaction would bear both a non-linear-based Clifford-based covariant basis of Yakawa -based topological sway -- that would form interactive Njenhuis singularities that work to pull and tug the initial arrangement of positive-norm-states from the Poincaire setting of the said ghost anomaly-based traceable mapping into a covariant-based codetermiable Njenhuis sway, this of which works to take the said perturbative scrambling of the indices of the said ghosts to be redistibuted and redelineated off of the relative local Real Reimmanian plane, with enough of an amplitude to where the resultant holonomic substrate of anharmaonically scattered norm-states may be pulled into dilatons and dilatinos that convert into gravitons and gravitinos.  This is due to a dual tense of both relatively infinite and relatively infinitessimal kinematic-based singularities that are interactive, yet, without canceling -- due to the dual  multiplicit binary directoral-based Lagrangian partials that are here involved with each other in an unborne tangency over time.

Part One of the Fifteenth Session of Course 14 About Group Action

The mapped-out path of one-dimensional superstrings -- as the traceable mapping that acts as the physical memory as to the relatively given arbitrary recent trajectory of the projection of the just mentioned delineated and redelineated one-dimensional superstrings of discrete energy permittivity -- as the directly associated ghost anomalies that act as the actual physical memory of the mentioned world-sheets, of which correspond to the extrapolated history of the kinematic differentiation of the said one-dimensional superstrings -- form a commutation that acts as an inter-relationship of the mentioned physical memory -- with its local gauge-action-based surroundings, forms a cohomological-based field of the said directly corresponding ghost anomalies.  This activity works to cause the overall actual spatial field density of the corresponding respective world-sheets to have a dimensionality that is conformally two-dimensional -- at the Poincaire level of the relatively holomorphic end of the Lagrangian eigenlocus, as to where the eluded to world-sheet may be generally extrapolated at as last iterating in -- in so as to form a relative group instanton (as an instant under consideration).  Likewise, the mapped-out path of a two-dimensional superstring of discrete energy permittivity forms a ghost anomaly-based field that is three-dimensional at a relatively considered Poincaire level of vantage-point -- at an endpoint of a Lagrangian locus that may be extrapolated at a given arbitrary iteration of a group instanton metrical vantage-point, that acts as an instant under consideration.  Such a field also forms a covariant isometric commutation with its local codifferetiable, codeterminable surroundings.

Some Stuff As To Minkowski-Based Orbifolds

If  two orbifolds that are adjacent are flat -- or, Minkowski-based -- then, the two orbifolds have, in this given arbitrary scenario, a composition that consists of two sets of superstrings that perform two different specific functions each, respectively, that would here involve two sets of superstrings that bear a unitary-based adjacency the one toward the other.   This would mean, here, that each superstring of one of the two given arbitrary orbifolds are then here adjacent to one of the superstrings of the other given arbitrary orbifold.  So, if the Planck phenomenon of one of the superstrings of discrete energy permitivity that works to comprise one of the orbifolds that I have here mentioned is adjacent to the Planck phenomenon of one of the superstrings of discrete energy permittivity that works to comprise the other given arbitrary orbifold that I have eluded to in this case, then, the two orbifolds of this case scenario are of the same universe.  This is because all of the superstrings of any given arbitrary orbifold are of the same universe -- since an orbifold is a set of superstrings that work to operate in so as to perform one specific function.  So, if one superstring of one given arbitrary orbifold is of the same universe as another superstring of another given arbitary orbifold, then, the two just mentioned orbifolds will be of the same universe.  I will continue with the first part of the fifteenth session of course 14 later!  To Be Continued!  Sincerely, Samuel David Roach.

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.

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

The cohomologies of the various orbifolds that consist of many different individual superstrings that work together over the course of a sequential series' of iterations of group instanton -- that are inter-related during codifferentiable eigenmetrics of the activity of the multiplicit Fujikawa Coupling -- bear many different potential individual substringular settings that are covariant, throughout not only the said eigenmetrics of group instanton that correspond to the so named Fujikawa Coupling, yet, this also involves the group metrics that simultaneously happen in the Royal Arc -- through the vantage point of a central conipoint.  The activities that happen in the Ward-Caucy bounds of the Royal Arc work to involve a pajority of the eigenmetrics that act upon substringular residue -- in so as to help recycle that residue, so that norm-state residue may be able to recycle back into ground-state residue elsewhere.  This just mentioned residue is in the form of mini-string segments that are re-manufactured from one tense of substringular genus to another, at another codifferentiable locus of substringular activity.  So, one-dimensional superstrings of discrete energy permittivity may close as one given arbitrary semigroup at one spot, while, such open strands of discrete kinetic energy may often -- in the process of closing into a bosonic superstring -- vastly alter or perturbate when in terms of their genus, on account of the effects that may be able to happen to the parity and format of their transversal, radial, and orbital kinematic differentiation -- over the relatively brief time in which such superstrings go from a static condition of being open strands of a fermionic substringular format into a static condition of being closed strands of a bosonic substringular format.  This is because the Ward-Caucy conditions that work to involve a spontaneous change in the genus of a superstring, in so as to alter from a fermionc superstring into a bosonic superstring, form an initial entropic perturbative condition that is local to the given arbitrary superstring that is to close, to where such an entropic perturbative condition is continued until a relatively brief number of iterations of group instanton after the open superstring that I have just here eluded to has then become shut.  Likewise, the Ward-Caucy conditions that work to involve a spontaneous change in the genus of a superstring, in so as to alter the superstring from being a bosonic superstring into being a fermionic superstring -- forms the said opening of the relatively local topology in this given arbitary case, to where such an entropic perturbative condition is continued until a relatively brief number of iterations of group instanton, after the said closed superstring that I have just here eluded to has then become open.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

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

So, Fujikawa Couplings tend to involve the group differentiation of multiple superstrings that work to define a region of mapped-out space where world-sheets act, in so as to form certain Gliossi-Sherk-Olive ghost anomalies -- these said ghosts of which work to form some of the indices of the topological tracing that becomes scattered, in so as to form those partial eigenstates that are brought into order off of the relative multiplicit Real Reimmanian plane over time  This happens in such a manner to where gravitational particles may be formed and/or reformed so that gravity may perpetually exist spontaneously.  This means that superstrings that undergo Fujikawa Couplings often involve the condition of group cohomology, that here involves the orbifolds and electrostatics of many individual substringular settings -- that are metrically gauged in a proximal manner through the vantage-point of a central conipoint.  This happens in such a manner to where these just stated substringular phenomenology may be able to codifferentiate in a covariant manner that will here involve an inter-relationship, due to certain activities that happen -- both during the generally unnoticed portion of Ultimon Flow & during the inter-connectivity of homotopic stratum that happens during the generally noticed portion of Ultimon Flow as well.  Homotopy is the topological inter-binding of the chords of beaded second-ordered point pariticles in the form of twined substringular field density (mini-string segments that are tied together).  During the Bases of Light and the simultaneous "space-hole," homotopy of substringular phenomena, that is then not to be frayed, just begins to unbind.  The wave-tug/wave-pull of the multiplicit pressurized vacuum eigenstates that are proximal to the eluded to eigen-indices of the virtual topological separation will, at this point, pull the eluded to strands of virtual topological breakage into a slightly different venue of a basis -- as to how the eluded to mini-string segments are tied.  This is the basis as to how homotopy is maintained, in spite of the constant rearrangement of physical norm-based conditions.  The opening and the closing of superstrings -- particularly as photons are formed and/or dissimilated -- works to initiate a pajority of the Wick Action eigenstates that iwork to cause the existence of Gaussian Transformations.  Gaussian Transformations operate in so as to allow for the continued physical alterations in norm-conditions.  Such alterations in norm-conditions are necessary so that superstrings may be able to perpetually inter-relate, while yet also have enough room to move freely enough so that space-time may be able to avoid any spontaneous blockage.  I will continue with the suspense later! Sincerely, Sam Roach.

A Little Addendum

What I termed of yesterday as a Clifford Expansion is a consideration of a genus of the kinematic-based flow that is directed away from the directly corresponding format of superstring that was to be extapolated over the given arbitrary situation that I had been stating at the time.  At the more specific locus of the superstring of the just mentioned genus of inter-relation that I had so stated, the genus of kinematic-based flow would more appropriately be described of as an inverse Clifford Expansion.  Likewise, when a superstring is undergoing an inverse Fujikawa Coujpling, the genus of the kinematic-based flow that is directed away from the directly corresponding format of superstring may be described of as an inverse Clifford Expansion, yet, when one considers the genus of kinematic-based flow that is proximal to the Poincaire field of the superstring would then here more appropriately be described of as a Clifford Expansion.  I appologize for the confusion yesterday, and, I will continue with the suspense later!  Sincerely, Sam Roach.

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

Superstrings that are translocated from one spot to a totally different covariant setting kinematically differentiate spatially in a directoral set per iteration of a given arbitrary group metric -- from one relative format of setting to the next relative format of setting, over the duration of the initially mentioned group metric that I had mentioned.  This said group metric involves the said given arbitrary set of superstrings.  Superstrings often open or close in a relatively static covariant-based setting that operates in so as to work to define a tense of both a radial, orbital, and/or a transversal kinematic function of differentiation -- that is initiated at an initial locus, where the superstrings that are to either open or close may here begin to vibrate in such a manner that works to begin a projection of metrical gauge that operates in so as to bring in local zero-norm projections that function as a genus of holonomic substrate.  Such a substrate here works to pull in those corresponding topological sways that do the actual activity of respectively either opening or closing the given arbitrary superstrings, that will here either convert from a bosonic form of a superstring to a fermionic form of a superstring, or, will convert from a fermionic form of a superstring to a bosonic form of a superstring -- when in terms of the tracing of the corresponding loop amplitudes of such eluded to superstrings.  With Inverse-Fujikawa Couplings, the activity of the reversal of a relative condition of an initial given arbitary forward holomorphic basis of activity functions to form a Wick Action eigenstate, in an indirect manner, in so as to operate an inverse of a unitary Clifford Expansion that acts upon a relatively local zero-norm-state projection in so as to form a net inverse of a binary Clifford Expansion -- in so as to act upon the holonomic substrate of the binding-cite of a given arbitrary closed string, in such a manner to where the binding cite that initially worked here to keep the eluded to bosonic string as a closed-loop of integrated first-ordered point particles, may be opened at the apex point of where the said binary inverse expansion of the inverse Fujikawa Coupling is Gliossi to the point of contact -- as to where the said zero-norm-state projection integrates with the binding cite of the said closed-loop of substringular phenomenology at the Poincaire field density of the eluded to locus of inter-binding of that so stated closed-loop.  At the general region that is localized at the opposite holomorphic substringular local neighborhood from where the apex of the said binary structure eluded to, of the said inverse Fujikawa Coupling, works to loosen the binding cite of the said closed-loop phenomenology in a Gliossi manner at the Poincaire level of the exterialized twining that had initially bound the closed-loop together in the first place, there is an exterialized obtuse basis of a binary structure that here involves an inverse Clifford Expansion that acts as a "V-shape" strutural operator that is projection-wise open at both ends at in the process of opening the closed-loop of this scenario -- while yet being an apex at a further reverse-holomorphic delineation of norm-state distribution, as the said closed-loop (superstring that is here bosonic) in to be opened.  As the "V-shape" of binary inverse Clifford projection tugs in its relative holomorphic Hamiltonian gauge-metric delineatory topological sway -- over the course of the then current group instanton -- while yet compensating for the then inter-active Polyakov Action eigenmetric and the simultaneous inter-active Bette Action eigenmetric, -- the closed-loop is opened in so as to then operate as a discrete unit of plain kinetic energy.  I will continue with the suspense later!  Sincerely, Sam Roach.

The Second Part of the 14th Session of Course 14

Substringular residue that is in the process of being recycled while iterating during a successive series of iterations in the Royal Arc are constantly vibrating per each said iteration, that the eluded to eigenindices are in the process of gradually altering -- as these said eigenindices are occupying the premises of the general region of the Royal Arc over the said successive series of group instanton that such eigenstates of redelineated segments of mini-string are being redistributed progressively in the general vacinity of the so-stated premises of the just mentioned Royal Arc Ward-Neumman boundaries.  Superstrings, per iteration of group instanton, bear a residue of mini-string segments that are homotopically redistributed in an indistinguishablly different manner from the multiplicit loci -- as to the regions that the corresponding superstrings are iterating at -- toward the corresponding eigenloci that are here affiliated with the general sustringular structure that I name of as the Royal Arc.  The eluded to indistinguishably different redistribution of the said substringular residue is redelineated per group instanton, in a manner that is neither based on a Noether Flow nor a tachyonic-based flow.  This is due to the condition that substringular residue that is in the form of mini-string segments that are specifically redelineated from any given locus from where superstrings that are of discrete energy permittivity are iterating at -- toward the general multiplicit loci where the Royal Arc is structurally located -- are not in and of themselves discrete units of energy.  These eigenindices of substringular residue are a homotopic release that is released from the Poincaire field density of discrete units of energy permittivity, toward a format of locality that re-manufactures those eigenindices that work to comprise the homotopic topology of superstrings, into norm-based indices -- in an indistinguishably different manner, in an operation that bears a flow that is a fractal of this conditionality of Ultimon Flow.  So, as eigenindices  that are indistinguishably released homotopically from the general multiplicit loci of superstrings is undergoing the process of such a group metric throughout the Continuum, there is a balance that is imperceivable to any time-wise extrapolation, that, in effect, shares the conditions of ground-state kinematic differentiation with the conditions of norm-state kinematic differentiation -- over the directly corresponding successive series of inter-relations of group instanton -- in which the fabric of the substringular eigenstates that are not frayed are being recycled.  This process works to strike a balance between the general format or genus of jointal static differentiation that is made kinematic over time with the general format or genus of smooth-curved static differentiation that is made kinematic over time.  This balance that is struck here is based on the multiplicit genus of norm-relationships of first-ordered point particles -- relative to one another -- that are to bear both a local and a non-proximal time-wise interdependence.  This recycling is a fractal of Gaussian Transformations. To Be Continued.  Sam Roach.

Part One of the 14th Session of Course 14

For every one-dimensional superstring of discrete energy permittivity that closes into a two-dimensional superstring of discrete energy permittivity, there is a two-dimensional superstring of discrete energy permittivity that opens into a one-dimensional superstring of discrete energy permittivity.  The directly prior eluded to Fujikawa Couplings and inverse Fujikawa Couplings are examples of Yakawa Couplings.  What a Fujikawa Coupling is is the bonding of the alterior ends of a one-dimensional superstring that initially functions as an operator of plain kinetic energy -- in so as to form a two-dimensional superstring that functions as an operational index of electromagnetic energy.  This is the case, when a discrete unit of plain kinetic energy that stems from the operational locus of an electron is pulled in a hermitian manner in so as to form a closed loop of integrated first-ordered point particles that is known of as a photon.  Whenever a photon is formed, there tends to be an equal and opposite reaction of a phontonic potential that loosens an initially closed-loop of a given arbitary locus that functions as a discrete unit of electromagnetic energy into an open strand that instead functions as a discrete unit of plain kinetic energy operational index.  So, whenever there is a Fujikawa Coupling, there tends to be an inverse Fujikawa Coupling.  The entity of the closing of one-dimensional superstrings into bosonic two-dimensional superstrings -- as well as the opening of two-dimensional superstrings that are closed loops into open strands that are here one-dimensional superstrings -- are zero-norm-state projections.  A zero-norm-state is a differentially isolated homotopic point commutator that acts as a first-ordered point particles that is not of a Campbell, Hausendorf, nor a Campbell/Hausendorf nature.  As such a first-ordered point particle is interconnected to other first-ordered point particles in a manner that is both of a somewhat abelian wave-tug/wave-pull Hamiltonian operation over a relatively transient duration, and, also here bearing no Campbell, Hausendorf, nor Campbell/Hausendorf homotopic differentiation -- in the directoral sway of its here considered holomorphic Hamiltonian gauge, such a tracing of the eluded to projection over the eluded to transient duration is said to function as what may be here termed of as a zero-norm-state projection.  The Clifford Expansion of the indirect leveraging of a Wick Action eigenstate upon the Poincaire field of a zero-norm-state projection -- that is proximal to the Poincaire field of an open strand of the directly corresponding first-ordered point particles -- that forms a given arbitary one-dimensional superstring of discrete plain kinetic energy that is here released from an electron, which is happening as the said electron is dropping an energy level, forms a cascading of Clifford Expansion in the eluded to locus of the mentioned substringular neighborhood of the said one-dimensional superstring that was released in so as to work to form a hermitian wave-tug/wave-pull that closes the eluded to open string in so as to form a bosonic closed string known of as a photon.  Such a hermitian closing of an open string acts as according to the Green Function.  The eluded to Poincaire field of such a Fujikawa Coupling acts as the euclidean-based holonomic substrate of the resultant binary Clifford Expansion that I have recently implied in this post.  I will continue with the suspense later!  Sincerely, Sam Roach.

Some Stuff You Might Like To Know About Minkowski Space

When you have a Minkowski space that is uni-layered, yet planar, the gauge-actions and/or the superstrings that are within the directly associated planar region -- in a timeless manner -- are settled at the given locus of metric within a structure that is two-dimensional, if this involves a field of a truncated set of one-dimensional superstrings and their directly associated gauge-actions -- or is three-dimensional, if involving a field of a truncated set of two-dimensional superstrings and their directly associated gauge-actions.  If a super-space involves a timeless-based Minkowski F-field that is planar with no depth, the truncated field, that is operationally four dimensional in spatiality here, will bear a resultant Minkowski field that will bear a certain basis of five spatial dimensions.  This is since a flat F-field space that is not time-oriented will involve a linear stationality of four spatial dimensional -- with a planar dimensionality that would here involve one added Njenhuis spatial dimension.  Or, in other words, here, we are considering a five-dimensional field that only considers the existence of that field, in that many spatial dimensions.  This is because a substringular field will always tend to consider an integrated Njenhuis dimension that is not inclusive to the eluded to given arbitrary phenomenon that the said field is in.  So, whatever the dimensionality of the stratum of an actual phenomenon itself has, its given arbitrary field will always tend to bear the partial derivative dimensionality of the majorizaton of the given said phenomenon's stratum per substringular stratum,that is to be considered during the iteration of a given group instanton.  This condition may be extrapolated under any given scenario in which this is pertainent. This means that a substringular field will always tend to bear at least one Njenhuis spatial dimension that is additive to the dimensionality of the actual operators of any given arbitrary substringular function that is Yakawa to a given arbitrary region in a respective scenario that may be perceived.