Part Three of the Fourth Session of Course 17 About the Ricci Scalar

Both the topology and the cohomology of an orbifold is affected by gravity.  An orbifold eigenset is combined and interconnected to each orbifold, that works to comprise the so-stated orbifold eigenset.  The topology of a harmonic flowing orbifold -- that is not Chern-Simmons in its Lagrangian-based path trajectory, as the said orbifold is delineated from one given arbitrary location to the ensuing given arbitrary location -- is said to bear a natural tendency of hermicity, over the mappable tracing of the motion of the said given arbitrary orbifold, as it moves over time.  And if the given arbitrary orbifold has a magnetic response -- that is directly proportional to the Hodge-Index of that said orbifold, as it exists in its correlative orbifold eigenset, then, the connections that would exist in-between the said directly corresponding orbifolds will then have a unique type of a basis of singularity -- that does not necessarily belong to the same eigenbasis as all of the other individual orbifolds, that work to comprise the directly corresponding orbifold eigenset.  This is in so that the said given arbitrary orbifold in which we are primarily discussing here is acting within the Ward-Caucy bounds of a specific electrodynamic-based orbifold eigenset, that is, in this case, over the correlative given arbitrary group metric that I have eluded-to here.  This acts in so as to form a specific genus of some sort of Chern-Simmons effect upon the just eluded-to type of orbifold eigenset in question.  Yet, any given hermitian and/or paritially Chern-Simmons eigenbase of singularities that exists amongst the orbifolds that work to comprise any given arbitrary orbifold eigenset, is said to bear a certain degree of hermicity -- if the gravitational effect that exists upon the so-stated orbifold eigenset is steady, as this is in terms of both the Lagrangian-based wave-tug/wave-pull that is exerted upon it, and, also in terms of the group metrical harmonics that is also exerted upon the so-stated orbifold eigenset, over time.  This will be of a completely hermitian case, if there is no jerk in either the Lagrangian-based topological sway of the directly corresponding Rarita Structure eigenstates, that are directly applicable to the correspondence of the interactivity of gravitons and gravitinos upon the given arbitrary orbifold, as is also the case if there is no annharmonic-based spur in the group metrical-based activity, that would here be involved in the so-eluded-to interactivity of gravitons and gravitinos upon the given arbitrary orbifold, over any directly corresponding period of time in which the said orbifold exists as the Gaussian-based physically spatial-based Hamiltonian operator that it began as, over the said given arbitrary eluded-to time frame.  If there are none of  the just eluded-to Lagrangian-based singularities, and, if there are also none of the the just eluded-to metrical-based singularities, acting upon the here discussed orbifold eigenset -- over a specific directly corresponding period of time that is here pertainent, then, the so-stated orbifold eigenset is said to be both completely hermitian -- as well as Yau-Exact in its eigenbase of kinematic vibratorial oscillation, as it differentiates as a manifold of a specific set of superstrings that operate to perform a specific substringular function over time.
I will continue with the fifth session of this course later!  To Be Continued!  Sam Roach.

Part Two of the Fourth Session of Course 17 About the Ricci Scalar

Orbifolds work to form many of the basic cohomological settings. World-Sheets always form a type of cohomological setting which depends upon the given contour that the given arbitrary world-sheet propagates in, over time.  An orbifold has a topology as well -- this being the Gliossi-based contour of the core-field-density of the so-stated orbifolds, at the Poincaire level.  Orbifolds often exists as D-Branes.  D-Branes are manifolds of superstrings that work here to comprise electrons (mainly), in so as to act as operators, that work to perform a specific function in the substringular.  D-Branes are substringular manifolds that exist in a minimum of six spatial dimensions plus time, over any given arbitrary duration -- in which one is able to extrapolate any given arbitrary corresponding Fourier Transformation.  Such a manifold often exists as a Calabi-Yau manifold, since electrons bear mass, and, any mass that is struck by a photon acts -- over that group metric in which such a mass is struck at its core-field density in a Gliossi manner by a discrete unit of electromagnetic energy -- as a manifold, that would then be described of as a Calabi-Yau manifold.  Orbifolds, if these are basically of a Majorana-Weyl nature, bear at least one Njenhuis tensor -- in order to allow its magnetism to actually exist.  This is because substringular phenomena, that are of the general size of the nucleus or smaller, exist in a minimum of four spatial dimensions plus time, in any directly corresponding Fourier Transformation -- in which such phenomena exist in, and, when one includes the existence of more than three general formats of spatial dimensions plus time, then, one is dealing -- in one manner or another -- with at least some Njenhuis tensors, that are then here inter-mingling with the correlative Real Reimmanian tensors that would be pertainent here over any given arbitrary discrete time period that could be applicable here.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part One of the Fourth Session of Course 17 About the Ricci Scalar

The many varied topological-based settings that exist throughout the substringular each have a given arbitrary shape or morphology.  Often, those world-sheets -- that act as the trajectoral projections of superstrings, act as a significant portion of the just eluded-to topological settings -- in so as to behave as the ghost-based indical mappable tracings, as to the physical memories that may work to extrapolate both the existence and the motion of the directly corresponding superstrings.  World-Sheets often combine -- in a Yakawa-based manner -- in so as to form cohomoligical-based settings.  World-Sheets may either be of a Rham-based manner, or, of a Doubolt-based manner.  A Rham-based cohomology is a cohomology that is completely hermitian -- in terms of its Lagrangian-based singularities -- and this being on the relative Real Reimmanian Plane.  A Doubolt-based cohomology is a cohomology that either works to bear respective correlative Chern-Simmons singullarities of a Lagrangian nature, and/or works to bear its activity within a Njenhuis-based plane, that is thus off of the relative Real Reimmanian Plane.  Superstrings that work to operate as one -- in so as to perform a specific function -- are known of as working to comprise an orbifold eigenset.  An orbifold eigenset often works in so as to interact to form one cohomoligical-based setting, at one general tense of a specific locus -- that works to act as one discrete Hamiltonian operator -- that moves kinematically through a discrete Hamiltonian operand, in so as to perform one discrete Hamiltonian operation.
 To Be Continued!  I will continue with the suspense later! Sincerely, Sam Roach.

Part Two of the Second Interim In-Between Sessions Three and Four of Course 17

Conforming to the eluded-to redistribution function of the set of first-ordered point particles -- whose homotopic encodement bears an indical basis with the group-based trajectoral index of the so-stated partially integrated genus of superstring of discrete energy permittivity, that I had been discussing during the first part of this interim, if the said superstring bears a translational transformation matrix of converging proximity with its directly corresponding local alterior Hamiltonian operators -- that are here performing the same general function at the same format of group metric, the key superstring that I am here discussing will reiterate at the given arbitrary locus that involves optimum rest, yet at a slightly different specific spot.  The so-stated superstring will then relocalize within its given arbitrary delineation, that is of its specific layer of reality -- since that is what the translation of the interacting group code called for, by means of the directly corroborating substringular encodement.  The directly corresponding resultant partially differentiated group repulsion wave-tug permittivity of the given region will re-delineate the locus of the so-stated superstring, relative to the resultant partially integrated group attractor matrix -- that would here converge at the relative local tori-sector-range.  Each locally kinematically interactive tensoric permittivity-based index -- which would here act multiplicitly as redistributed group attractor eigenstates -- will here re-associate the holonomy of the homotopic wave-functionability, as a local morphological-based phenomenon. The just eluded-to convergence of the redistribution of the directorals -- as a harmonic/annharmonic function-based operator, because of the correlative ebbing of group attractor/group repulsion pointal-based phenomena -- works to define, through a succeeding series of instantons, the field holonomy of the substringular neighborhood of the localization of the said key superstring that I am here discussing.  This so-eluded-to activity happens, relative to the sanctity of the general operation of the Ultimon.  The correlative field covariance and kinematic differentiation, through the process of the directly corresponding relatively indistinguishable re-assortment of superstrings, that happens as superstrings are delineated and redelineated -- over a gradual and/or spurious perturbation in the Majorana-Weyl covariance, in a relatively tightly-knit substringular neighborhood over time -- works to define the process of the re-addition of each of such sets of altered Ward-Caucy boundary conditions.
 To Be Continued!  I will continue with Session Four Next!  Sincerely, Sam Roach.

The First Part of the Next Interim In-Between Sessions 3 and 4 of Course 17

Here. Let us look at the directoral fluctuations that transpire when a superstring of discrete energy permittivity -- in context of the substringular -- is reiterated within a substringular neighborhood, whose Ward-Caucy boundaries are defined in part by the determination of coefficient-based repulsive wave-tug delineations, that are of the kerneled group attractor semi-groups that are directly pertainent here.  The given arbitrary directly corresponding superstring that we are here discussing is iterated initially as a transition kernel of discrete physical phenomenology -- in the general locus that may be extrpolatable as being the center-state of the ebbing of ghost-anomalic/point commutator-based interconnection. The so-eluded-to first-ordered point particles, or, at least those "partitions" that both are comprised of certain first-ordered point particles, and are also part of what works to comprise superstrings of discrete energy permittivity -- act in such a manner in so as to dissociate, to some extent or another, after the activity of the directly corresponding group instanton.  Both the existence and the physical condition of both those first-ordered point particles that work to comprise superstrings of discrete energy permttivity, and, those "partitions" that work to form a slightly higher degree of the composition of the same so-stated superstrings, alter in the manner that these act -- as a fractaled tense of the said superstrings, from the onset of that duration that I term of as the space-hole, until the end of the directly ensuing instanton-quaternionic-field-impulse.  Right after the just mentioned instanton-quaternionic-field-impulse, the multiplicit existence in the substringular is moved into the condition of group instanton.  The majority of group instanton is known of as the metrical-bearing state or condition of BRST.  BRST acts metrically as ((the Planck time)-(2pi hbar-~.283hbar)), when in terms of the generally noticed activity of what we know of as time.  After BRST, the ending of the generally noticed portion of the duration of each group associated instanton moves either directly into the Regge Action, or, if the directly associated superstring is then in the mode of the Kaeler-Metric, the so-eluded-to superstring will spend half of the remaining duration of group instanton in the general locus of the correlative multiplicitly-based Klein Bottle eigenstates, and, the other half of the remaining duration of group instanton in the Ward-Caucy bounds of the activity of the Regge Action. (The mappable tracing of superstrings going into the so-stated activity of the Regge Action is known of as the phenomena of the Regge Slope).  Again, what we tend to notice is only that activity of group instanton -- mainly, the activity of that multiplicit sequential series of group metrics known of as a sequential series of instantons, that we tend to term of as "time."  Group instanton is the multiplicit existence of superstrings, as these are basically at a standstill.  Superstrings are delineated as being redistributed the Planck Length, and/or, the Planck Radii, as individually taken phenomena from the gauge-metrical activity of one instanton to the next, if such said superstrings are of a Noether-based flow and not of a tachyonic-based flow.  The sequential series of such so-stated instantons is known of as the flow of time.  Time that is existent under the multiplicit-based conditions of tachyonic-based flow is of a different nature than time that is of a Noether-based flow.  Certain forms or tenses of tachyonic-based flow makes certain forms of time-travel possible.  I will not explain more of that here.  The logic behind that, is that phenomena are not able to rationally jump from one spot to the next without anything existing in-between such Hamiltonian-based delineations -- there has to be an orchestration that works to allow for each ensuing iteration of superstrings -- from going from the multiplicit distribution that these exist in at one conimetric of positioning, at one group instanton, toward going to the next multiplicit distribution that these exist in at the ensuing conimetric of group instanton. The general idea of Ultimon Flow that I present in this blog works to rationally describe the logic as to how such multiplicit-based re-delineation is able to happen as such.  This is also the case when in taking into consideration the factual condition that a vast majority of the speed in a worm-hole is a state of the contoursioning of space-time-fabric.  This just mentioned contoursioning also works to act upon the directly corresponding respective given arbitrary gravitational particles -- via the activity and the existence of the locally acting Rarita Structure eigenstates, in so as to effect the Ricci Scalar eigenbases that these appertain to.
I will continue with the suspense later!  To Be Continued!!! Sincerely, Sam Roach.

The Second Part of the Interim Between The Third and the Fourth Sessions of Course 17

So, although a substring may work to vary within closely knit neighborhood in the substringular, the directly associated Lorentz-Four-Contracted-tensors will here bear a permittivity that will bear a topological sway -- that will here have a Yakawa-based effect upon the corroberative superstring, because of the given normalization factors that are caused by the kinematic-based conditions of the strings time-wise differentiation, relative to the correlative Basis of Light.  This happens in a manner which is involved with the recycling of core differential geometries -- that works to allow for an indistinguishably different superstring of discrete energy permittivity in the globally distinguishable, to be able to reiterate in a manner that may or may not bear a flush contour of mappable tracing in the correlative regional substringular neighborhood --which happens as the eigenbase of such a relatively regional substringular neighborhood is centered upon a general locus that is Gliossi at the so-eluded-to elliptical Hamiltonian operand.  This happens in so that the so-eluded-to substringular phenomena may be able to localize at the general conicenter of that state of location, in which the so-stated superstring of discrete energy permittivy is kinematically determined.  This general format of activity will then cause a correlative centering of both the directly associated couterstring, its correlative light-cone-gauge eigenstate, and, its correlative Fadeev-Popov-Trace egienstate -- based upon the same general format of the convergence of that Jacobian eigenbasis, that works to act in so as to delineate the general  so-eluded-to eigenstate of discrete energy -- as being a re-distributed Hamiltonian operator, that is sequentially reiterated over time.  Again, the counterstring acts as the holonomic substrate of the wave-function of discrete energy permittivity, and, the light-cone-gauge acts as the holonomic substrate of the wave-function of discrete energy impedance.  So, superstrings act as the holonomic substrate of the template of the wave-function of discrete energy permittivity, and, the Fadeev-Popov-Trace eigenstates act as the holonomic substrate of the template of the wave-function of discrete energy impedance.

An Interim Between the Third and the Fourth Session of Course 17 About the Ricci Scalar

How about if we consider the parallax between the substringular neighorhood that a given arbitrary superstring of discrete energy permittivity reiterates in, and, the correlative region that the same so-stated superstring of discrete energy permittivity reiterates in -- in the globally distinguishable.  Consider the given arbitrary substring that we are here discussing, to converge upon a set locus.  The eigenbasis may not discretely integrate upon the specific eluded-to locant, yet, the directly associated convergent series of wave iteration will certainly devolve the said given arbitrary locant -- after the said convergence of the eluded-to sequence of pointal iteration is normalized via the particular delineatory solution here implied, which may be valued at the said substrings defined location in the Ultimon - in so long as that said superstring exists in a state of conformal invariance.  Each iteration of the string adds a wave-tug delineation that works toward the integrating factors that had acted as the group attractor, and, which had worked to allow for the said superstring to "shadow-box" at the general solution of locant, that that string reforms and dissociates at. The wave-tugs that I have just eluded-to here take into account the condition that the so-stated substring will here act as a holonomic substrate of phenomenology,  that may be viewed of as "three-dimensional" at the Poincaire level -- no matter how many physical dimensions that the eluded-to substring exists in and/or is moving in from a generally conceived of level.  The topological mappable tracing of the contour of such a substringular situation would here curve away at a level that is close to the Poincaire level, in a very small increment per iteration -- the iterations of which vary in their parameters, in order to define that strings substringular neighborhood.  Now.  Each 3-dimensional re-orientation of the string that may be conceived of as right up the Poincaire level will bear a certain degree of orientation with the Basis of Light of the directly associated layer of reality, or, with the
Basis of Light of the directly associated tori-sector-range, as the so-stated tori-sector-range has here majorized, over the course of the instanton-quaternionic-field-impulse (that happens right after the activity of what I term of as the "space-hole."  Each string, treated as having its own world-sheet bearing, and thence, having a determinism that is directly associated with a unique particular solution of "polarization atrophy," must work to normalize its Majorana-Weyl eigenbasis of determinism -- in order that the necessary wave-based funcionability may be shared among the other correlative superstrings of discrete energy permittivity over time.  This happens, on account of the direct basis of interaction of substringular counterstrings with their directly associated superstringss -- in the process of their correlative light-cone-gauge eigenstates with their directly associated Fadeev-Popov-Trace eigenstates -- in so that the discrete energy permittivity, of which bears wave-functionability by the nature of its correlative counterstring -- may be able to interact with the discrete energy impedance, of which bears wave-functionability by the nature of its  correlative light-cone-gauge eigenstate, so that the general wave-pull of energy may be held back just enough so that the so-eluded-to discrete energy will not resonate to the point of shattering.
I will continue with the rest of this Interim later!  To Be Continued!!! Sincerely, Sam Roach.

Part Five of the Third Session of Course 17 About the Ricci Scalar

So, topological interconnection is via the existence and the activity of mini-string segments.  Orbifolds bear a topology -- on account of the condition that such manifolds of superstrings that operate in so as to perform a specific function bear a definite surface that works to bear a specific contour, this contour of which may often be permutated and/or otherwise perturbated over time.  This is on account of the condition that the activity and the Laplacian-based structural conditions of both superstrings and their multiplicit respective manifolds -- of which these work, in so as to bear changes in their fractal of "topographical" state quite often and all over the place -- are changing in both their eigenbase of mappable tracing, and in the quantum of their Hodge-based delineation, all of the time and all over the place.  On account of this, stringular response to gravity only tends to happen when the directly corresponding superstrings of discrete energy permittivity work to interact with each other via a topological Jacobian eigenbasis that works to bear either a Real Reimmanian Gaussian base of inter-relation, when in terms of a Real-based tensoric displacement of delineaetion, and/or a Li-Algebra Gaussian base of inter-relation, when in terms of a Njenhuis-based tensoric displacement of delineation.  The topological eigenbase of an orbifold works to effect the correlative gravitational affect that the directly given arbitrary corresponding phenomena has -- in its given arbitrary medium, when in terms of the so-eluded-to Hamiltonian operator that acts as a kinematic activity that may be described of as a Hamiltonian operation that works through a Hamiltonian operand over a discrete period of time. So, if a topological eigenset of discrete Hamiltonian operators -- that take form as a cohesive unit of a quantum of discrete energy permitttivity that is coupled with a quantum of discrete energy impedance -- works to bear a minimum response to its directly corresponding gravitational pull, via the activity of the correlative Rarita Structure eigenstates --through the basis of the mechanism of the local eigenbase of the Ricci Scalar -- then, the directly corresponding topological eigenset has one multiplicit unit of minimal Ricci Scalar delineation that is then influencing the gravitational effect of the directly corresponding local superstrings, upon each other, during such an eluded-to duration of time.  If a discrete quantum of such eluded-to topological eigensets is existent in such a manner in so that the directly correlative singularities of a Chern-Simmons nature will here work to increase the gravitational response -- in terms of a quantum increase of local gravitational force, in either a euclidean manner that is relatively non-perturbative,or, in a euler manner that will here operate via a Clifford Expansion  -- then, the so-stated increase in gravitational force may be extrapolated to some extent by multiplying like-quantum-based Hodge-indices by their physical quantity, while then putting together the basis of the eluded-to proportionality by "divying" the corroborative coefficients of scalar magnitude, in so as to be able to get an idea of the scalar magnitude of the correlative implement of the here local Ricci Scalar eigenbase.
I will continue with the suspense of the next session later! To Be Continued! Sam Roach.

The Fourth Part of the Third Session of Course 17 About the Ricci Scalar

Any given arbitrary superstring has a topology.  A superstring of discrete energy permittivity has either an abelian light-cone-gauge topology or a non-abelian light-cone-gauge topology.  An abelian light-cone-gauge topology is known of as a Kaluza-Klein topology, while, a non-abelian light-cone-gauge topology is known of as a Yang-Mills topology.  Phenomena of mass is considered to tend to have both a Kaluza-Klein topology, with Yau-exact singularities in-between those superstrings that work to comprise any given of such phenomena of mass.  Any given phenomenon that has both a Kaluza-Klein topology and Yau-exact singularities can not -- as such -- travel at the speed of light or faster, or else it will have all of the mass in the universe.  Yet, if one is able to temporarily alter the light-cone-gauge topology of a mass into having a Yang-Mills topology -- over a relatively brief terestrial-based duration of time (over a relatively limited sequential series of group instantons), then, the just-eluded-to mass may then be translated as being able to then go at the speed of light or faster over the just-eluded-to relatively brief period of time.  As the said general condition of such a mass is being translated as going at the speed of light or faster, the so-stated mass is --- over the so-stated general given arbitrary duration of time in which it is going at such a general eluded-to rate -- technically not a mass.  This is even though such a mass both begins and ends up as a mass from the respective moment before it is translated as such, and also after such a so-stated mass is translated back into bearing a Kaluza-Klein light-cone-gauge topology after such a so-eluded-to translation.  This is also in consideration of the condition that a vast majority of the speed of a worm-hole is simply the contorsioning of space-time-fabric.  A world-sheet has a topology -- since such a traceable mapping is comprised of cohomologically-based mini-string segments, that are organized into a physical memory as to the prior motion and existence of the directly corresponding superstrings that had moved upon the directly corresponding Hamiltonian-based operands over a previous extrapolated period of time.  What I mean by a topology is the surface along both the contour of any given arbitrary superstring and the surface along the contour of any given arbitrary ghost-based index that works to be traced by the mapping of the directly corresponding world-sheet.  This works to consider the condition that all superstrings and all ghost anomalies are interconnected, in one manner or another, by the inter-connectivity of both the activity and the existence of mini-string segments -- that work to form the basis of both core-field-density and also the basis of the existence of homotopy (through Cassimer Invariance). This also works to consider the condition that all superstrings are interconnected -- one manner or another -- to all world-sheets as well, via the said general condition of the same basic pretext, -- the existence and the activity of mini-string segments, as these branch out to allow for the tying together of all substringular fabric to one another over the course of the unfrayed portion of all physical phenomena that are iterated over the course of each succeeding group instanton.  This also works to consider the condition that all first-ordered point particles are constantly being recycled in an indistinguishable different manner over each succeeding iteration of group instanton.  The general interconnection of superstrings of discrete energy permittivity  to gravitational particles is via the Rarita Structure.  This works to cause the existence of the Ricci Scalar. To Be Continued!  Sam Roach.

Part Three of the Third Session of the 17th Course About The Ricci Scalar

When an orbifold, or, in other words, when a set of adjacent superstrings that operate in so as to perform a specific function, work to perform a specific tense of mangnetism in a specific respective multidimensional setting over time, then, this so-stated orbifold will act as an eigenset of Hamiltonian-based indices that operate in so as to perform a specific sub-atomic function, over a sequential series of group instantons -- these just-eluded-to eigenmemebers of such a Hamiltonian operation of which would then happen as a holonomic substrate that is both codifferentiable, codeterminable, and, covariant over that so-eluded-to group metric, that would here involve the "cooperation" of a certain given arbitrary set of superstrings -- in such a manner in so that the eigenbasis of the activity of such an orbifold eigenset would bear a basis of a fractal of momentum that would then here bear an even tense of a Jacobian-based eigenbase.  So, as the so-stated set of superstrings -- that would here work to perform a specicfic function, in so as to act as a specific substringular group operator -- works in so as to bear a specific index of Hodge-based codetermination over time, then, the activity of such an orbifold eigenset will bear a Real Reimmanian basis that is both covariant, codeterminable, and codifferentiable with other orbifold eigensets, that operate in so as to be of the same universal-based setting.  This here would work to designate each of such relatively Real-based orbifold eigensets as viabely inter-relateable with each other in a manner that is not only Yakawa to one another in a respective manner, yet, would work to form a common Gaussian-based format that is both trivially Li-Algebra-based, in terms of the relationship of the covariance of the inter-relationships of the activity of their respective codetermination, when such a codetermination is applied from one of such orbifold eigensets toward each of the other so-eluded-to orbifold eigensets, yet, this would also work to form a potential setting of such so-stated geni of eigensets as being able to bear a viable Gliossi-based inter-relationship of any given arbitrary individual orbifold eigensets with each of the other of such eluded-to orbifold eigensets, that I have here eluded-to as being of the same universal setting -- over the eluded-to duration of such a so-stated sequential series of group instantons.  The chief characteristic of an orbifold eigenset is a basis of a set of orbifolds that work to function as a Hamiltonian-based operator.  When such a Hamiltonian-based operator is of a unique relatively Real-based space -- in so as to not spontaneously perturbate out of such a respective format of codeterminable eigenbase, then, the tense of that fractal of magnetism -- that would be displayed as a group attractor that is operational over a discrete Hamiltonian operand -- would bear an inter-relationship with electromagnetic energy that would then, over a spontaneous inter-relationship with its environment, work to form a manifold of vibratorial oscillation that would then here work to form a manifold that is Calabi-based in nature.  Such a manifold will either be Calabi-Yau, Calabi-Wilson-Gordan, or, it will be Calabi-Calabi. The activity of Calabi-based manifolds works to involve Gaussian Transformations that may be termed of as gauge-transformations.  I will discuss this more in course 20.  In the meanwhile, the manner of the activity of such a just-eluded-to manifold will always bear at least some format of interaction with both the local indices of gravity, which will also bear at least some format of interaction with the local indices that are needed in order for any relatively neighboring Wick Action eigenstate to occur.  Such a format of interaction will always involve the activity of the Rarita Structure -- the Rarita Structure of which is the general physical mechanism by which the bearings of the Ricci Scalar is able to take into effect.
I will continue with the suspense later!  To Be Continued!!! Sincerely, Sam Roach.

Part Two of the Third Session of Course 17 About the Ricci Scalar

Planck-Like phenomena, or, in other words, Fadeev-Popov-Trace eigenstates, that are both of the same parallel universe, while yet being placed in an adjacent manner -- during any given arbitrary iteration of group instanton -- are normal to one another, with a wobble that may be subtended by a directly corresponding angle of 1.104735878*10^(-81)I degrees, when the so-stated subtension is made codeterminable in a relation of one of the so-stated Fadeev-Popov-Trace eigenstates relative to the other so-eluded-to Fadeev-Popov-Trace eigenstates.  What I mean by an Imaginary-based angling is a wobble that sways in one given arbitrary directoral-based tensoric sway, to the directly opposite given arbitrary directoral-based tensoric sway -- from a subtension that is pulled through a scalar angular Hamiltonian operand that is equivalent to the initially so-stated directoral topological-based sway, that is from a central conipoint of delineaetion, to a wave-pull that works to pull through a scalar angular Hamiltonian operand that is equivalent but opposite in holomorphism to the initially so-stated directoral topological-based sway, that is from a central conipoint of delineation. ( The second so-eluded-to portion of topological sway is here being an equal and opposite Hamiltonian-based operation that occurs in the opposite basic directoral genus of wave-tug/wave-pull.)  This is true, in one manner or another, for all adjacent Planck-Like phenomena, or, in other words, this is true, in one manner or another, for all adjacent Fadeev-Popov-Trace eigenstates, in the following general manner.  One initially considers that coniaxion of each of two different respective Fadeev-Popov-Trace eigenstates that would here work to elude to the directoral-based subtension -- as to the topological-based sway of each of the two implied covariant so-stated Fadeev-Popov-Trace eigenstates, that is operational over the course of any directly corresponding iteration of group instanton, in which these two adjacent so-stated Planck-Like phenomena, that are here of the same universe, are oscillating in so as to act as eigenstates of discrete energy impedance.  One then needs to consider the subtension of the central coniaxion that may be extrapolated -- in so as to work to determine the directly corresponding angle of correlative topological relation, at the so-eluded-to directoral inter-relationship that I have stated here.  The angle of subtension that may be here used to determine the correlative vibratorial oscillation, that would then here be both codeterminable and codifferentiable in-between these two so-stated Planck-Like phenomena would here be the so-stated angle of 1.104735878*10(-81)I degrees.  So, the tensoric-based motion of those vibratorial oscillations -- that would then be subtended between two different Planck-Like phenomena that are both adjacent, and, are of the same universe, would then bear a smooth-based curvature, that would work to complete the operational-index of the functionability of the Hamiltonian-based activity of that format of topological sway, that would here work to directly associate one adjacent Fadeev-Popov-Trace eigenstate of any given universe to the initially so-eludud-to Fadeev-Popov-Trace eigenstate.  Such a Fadeev-Popov-Trace eigenstate is one that may then here be extrapolated of as an operator of an initial basis of case scenario.  Such a subtended curvature of vibratorial oscillation tends to work in the direction of bearing a hermitian eigenbase of topological-based sway. I will continue with the suspense later!
To Be Continued!  Sincerely, Sam Roach.

The First Part of the Third Session of Course 17 About the Ricci Scalar

For a set of superstrings that are in a relative state of superconformal invariance -- in an indisinguishably different manner of motion-based superconformal invariance, both superstrings, their respective correlative substringular counterstrings, their respective correlative Fadeev-Popov-Trace eigenstates, and their respective correlative light-cone-gauge eigenstates -- that are of the same general substringular neighborhood, work to differentiate kinematically per iteration of instanton, in a state of normalization, that works to appease the given arbitrary condition of Gaussian-based relationships -- that work to allow for these respective correlative substringular phenomena to be of the same universal-based setting.  This is in consideration of those orbifolds and/or orbifold eigensets of substringular phenomena that are both adjacent -- while yet also being of the same tense of Real-based Gaussian-related spaces -- to where the so-stated respective correlative substringular phenomena, that have here been eluded-to, are each of a certain degree of a Real Reimmanian nature  This is when these said orbifolds and/or orbifold eigensets are inter-related to one another over the directly corresponding sequential series of group insantons -- that operate in so as to function as having an eigenbasis of a Hamiltonian operation, that is akin to the same basis of group-based attraction. This works to then consider a relatively non-perturbative state of covariance that is both codeterminable and codifferentiable over the just eluded-to framework of time -- to where the directly corresponding Gaussian Transformations that would then thence bear a certain degree of Majorana-Weyl Invariance would bear a viabely Yakawa-based tense of Gaussian Translation, that is of each correlative alteration of norm-based conditions, in so as to allow for the then viabely considered activity of substringular phenomena both re-attaining their fractals of discrete impedance, re-attaining their fractals of discrete permittivity,  as well as re-attaining their fractals of the wave-functionablity of discrete impedance, and re-attaining their fractals of the wave-functionability of discrete permittivity, and, the active process of the freeing-up of substringular flow that is needed in order to have the necessary condition of optimum substringular flow per iteration of group instanotn -- so that the so-eluded-to activity of the just eluded-to condition of superconformal invariance of the so-stated substringular phenomena may be able to viabely happen over time.
I will continue with the next part of this session later!  To Be Continued!  Sincerely, Sam Roach.

Part Four of the Second Session of Course 17 About the Ricci Scalar

If a certain given arbitrary tense of energy works to form a condition of homeostasis --  that is in a static state, when this is taken relative to its immediate surroundings, then, the given arbitrary energy of this specific case works to form a state or condition of matter.  If any given arbitrary tense of energy that starts off as plain kinetic energy works to form a harmonic-based kinetic differentiation -- that acts in-between its electric field indices and its magnetic field indices, then, the so-stated given arbitrary energy, that has been discussed in this given case, will tend to form an electromagnetic or electrodynamic eigenbase of energy.  Any energy that is harmonic is relatively non-perturbative -- when this same given arbitrary general format of energy is compared to another state of such energy that is instead of an annharmonic nature.  This is due to the condition that an annharmonic tense of energy tends to bear more of a spurious state of alteration then a similar format of such a general given arbitrary genus of energy, that is instead of a harmonic tense of kinematic delineation over time.  Any energy that is of an eigenbase that would here directly appertain to a tense of matter has a condition or state of being of a genus of a mass.  Mass is that general form of energy, that is in a closely-bound format of static equilibrium -- that is most directly effected by the force of gravity.  I will continue with the suspense later!  Sincerely, Sam Roach.

The Third Part of the Second Session of Course 17 About The Ricci Scalar

What is termed of as the field of a substringular format of stratum often is in reference to the spatial delineation of the directly corresponding respective index-based physical eigenmembers of holonomic substrate -- that appertain to the Hamiltonian Hodge-based distribution of the region in which such a so-stated given arbitrary field is Gliossi to the directly corresponding respective substringular neighborhood --that appertains to the phenomena that are of any given arbitrary physical case that is to be discussed.  Often, the medium in which a field is actively inherent from within the correlative Ward-Neumman bounds of such a so-eluded-to basis of regional whereabouts, is in the form of what may be termed of as a vacuum.  A vacuum is a region in which there are no molecules, or, in other words, in which there is no mass from within the directly corresponding Ward-Neumman bounds -- of the so-eluded-to region, that is respective to the so-stated vacuum.  Once energy is created in a region, the so-stated energy may become either harmonic or anharmonic -- when taken relative to the field arrangement that the given arbitrary so-stated energy is propagated through, over the directly correlative given arbitrary sequential series of instantons, in which the directly corresponding Hamiltonian operatives are kinematically differentiating from within the Ward-Caucy bounds of the so-eluded-to group metrical time-based delineation.   This so-stated format of a creation of energy, from within the realm of a medium in which a field is altered -- eludes to a perturbation in the substringular delineation of those field indices, that work to form the substringular distribution as to what has been happening in the directly corresponding medium in which the correlative field has been changing from within. This may inter-relate to a change that may be implemented as either a harmonic-based delineatory alteration, or, as a change that may be implemented as an annharmonic-based delineatory alteration.   I will continue with the suspense later!  Sincerely, Sam.

The Next Part of the Second Session of Course 17, On, the Ricci Scalar

There are many different formats and geni of field -- of which work to inter-relate the covariant, codifferentiable, and codeterminable vector and tensoric basis of the conditions of the flow of any given arbitrary form of energy.  There are, as well, many different formats and geni of medium-based stratum -- that work to inter-play as the operand of that energy, that would here act in so as to allow for a region in which the so-stated given arbitrary form of energy may be able to happen from within this over time.  Another way of working to conceive of the concept of an alteration in the general flow of any given arbitrary format of energy, is  the concept of a perturbation.  A perturbation is a relative major change in the general venue of the process of the flow of any given arbitrary tense of energy.  This goes for any distinctive change in the general format of the basis of the activity of any electromagnetic energy, plain kinetic energy, mass, and/or entropic photon.  So, when the eigenbasis of any gauge-metrical format of any given arbitrary respective source of energy alters -- then, there is what may be termed of as a perturbation in the general course of the so-stated given arbitrary genus of energy, in any given arbitrary case scenario.  So, whenever there is the introduction of any relatively new tense of energy in any given arbitrary medium -- new, here, meaning that such an eluded-to tense of energy has then just started in the so-stated medium or region in which the so-stated energy is here starting to propagate through -- then, one may be able to say that this works to describe an alteration that is here happening from within the Ward-Caucy bounds of the so-stated medium, that works to act as the just eluded-to perturbation in the so-stated respective given arbitrary medium.  So, here, there is a given arbitrary perturbation that is then acting in a given arbitrary manner -- in so as to form a respective alteration in the eigenbasis of the general field of the so-stated given arbitrary medium, in which a source of energy is then here newly propagated in the general region that is within the given arbitrary Ward-Neumman and/or Ward-Caucy bounds of the so-stated general networking of field-based indices.  So, here, an exterial activity -- that is initially outside of a given arbitrary medium -- acts in so as to start a course of a given arbitrary disturbance in the so-stated medium -- in so as to activate the presence of a given arbitrary source of energy to then exist from within the Ward-Neumman bounds of the so-eluded-to region, or, operand, of any respective Hamiltonian or inverse-Hamiltonian-based eigenbasis of core-field-networking.
I will proceed with the next part of this session later!  Sincerely, Sam Roach.

Part One of the Second Session of Course 17 About the Ricci Scalar

To start, as I have said before, both matter, electromagnetic energy, plain kinetic energy, and entropic photons are forms of energy.  So, both matter, electromagnetic energy, plain kinetic energy, and entropic photons are different forms of the same thing -- that bear different conditions of interaction, that appertain to a tense of having a capacity of being able to be converted into being of the same general format of holonomic substrate.  Energy -- as a general concept of phenomenology -- is a disturbance that occurs in a medium.  A medium, here, being a given arbitrary operand in which a given arbitrary operator is acted upon within.  Also, what I mean by a disturbance is an activity that is to happen over a discrete period of time  -- in which the so-eluded-to medium is existent, in order for the so-stated disturbance to be able to occur.  So, when any given arbitrary activity happens in any given arbitrary region in any given arbitrary discrete period of time -- in what I term of as the globally distinguishable, then, one is then to have here a disturbance in a medium.  So -- in the substringular -- any given arbitrary Hamiltonian operator that is to function in any given arbitrary Hamiltonian operand over a discrete period of time, works to comply to the condition of an activity that happens in a region,that happens in a sequential series of iterations of instanton, or, in other  words, this works to comply to the condition of a disturbance that is then here occurring in a medium.  This is the case of all general phenomenology that would here work to describe any format or genus of energy -- when one is to here consider the kinematic display of any given arbitrary form of energy.  All of such so-stated disturbances are alterations in any given arbitrary directly corresponding respective field of the so-eluded to given arbitrary directly corresponding medium.  What I mean by an alteration here, is a perturbation in the delineations of those field indices -- that would here appertain to a kinematic change in the distribution-based indices -- that are here associated with a directly corresponding respective eigenset of delineation-based eigenmembers -- as such Hodge-based eigenmembers are "shuffled" in one respect or another, over a discrete period of time.  More specifically, such so-eluded-to eigenmemebers would here specifically mean discrete superstrings of any given directly appertaining eigenbasis  -- that are projected kinematically from one genus of delineation-based distribution to another, over a discrete period of time.  So, when one has any given arbitrary set of superstrings -- that are redelineatd over a successive series of group instanton -- then, such an eigenbasis of redistribution may be determinable as a tense of activity, that may be then termed of as one format or another of what we would call energy.  To keep it simple, the superstrings of any given arbitrary case in tact would be considered to be the given arbitrary Hamiltonian operators.  The activity of the so-stated superstrings would then be the given arbitrary Hamiltonian operation.  So, the regions in which such Hamiltonian operations are occurring would then be considered to be the directly corresponding given arbitrary Hamiltonian operands. The general tense of gauge-metric that would then be directly associated with such a general genus of operation, would then here be based upon any directly related sequential series of covariant, codeterminable, and codifferentiable instantons -- of which would here be described of as group instantons ( in terms of their iterations and reiterations, that would here be more directly appertaining to the interdependence of all unfrayed superstrings -- as such superstrings of discrete energy permittivty are displaced and redisplaced over what we term of as time.)  More speicifically, the superstrings -- of which I mentioned of as Hamiltonian operators -- are the phenomenology of discrete energy permittivty.  Their directly corresponding Fadeev-Popove-Trace eigenstates are the directly related respective units of discrete energy impedance.  The directly corresponding counterstrings are the eigenbase of phenomenology that directly appertains to the basis of the wave-function of discrete energy permittivity.  And, the directly corresponding first-ordered light-cone-gauge eigenstates would here work to act as the basis of the wave-function of discrete energy impedance.  Let us just absorb that for now!  On to the second part of this session later!  To Be Continued!!  Sincerely, Sam Roach.

Part Four of the First Session of Course 17, the Ricci Scalar

The holonomic substrate of the second-ordered light-cone-gauge eigenstates of a one-dimensional superstring bear 120 mini-string segments that work to form a chord of core-field-density -- that is bundled together in a linear-based manner, that is compactified to the extent that these are relatively de-compactified from a tense of mamimum compactification by a factor of two.  On a similar note, the holonomic substrate of the second-ordered light-cone-gauge eigenstates of a two-dimensional superstring bear 60 mini-string segments that work to form a chord of core-field-density -- that is bundled together in a linear-based manner, that is compactified to the extent that these are relatively de-compactified from a tense of maximum compactification by a factor of two.  This way, each second-ordered light-cone-gauge eigenstate of any given arbitrary one-dimensional superstring -- of discrete energy permittivity -- bears a condition of having 120 gauge-bosons -- that work to pluck each of these said second-ordered eigenstates like a harp over each succeeding iteration of BRST, in which the so-eluded-to stringular topological stratum is of the said dimensionality of one..  Likewise, each second-ordered light-cone-gauge eigenstate of any given arbitrary two-dimensional superstring of discrete energy permittivity bears a condition of having 60 gauge-bosons -- that work to pluck each of these said second-ordered eigenstates like a harp over each succeeding iteration of BRST, in which the so-eluded-to stringular topological strutum is of the said dimensionality of two.  The so-stated condition of the chord-like phenomenology of each given arbitrary second-ordered light-cone-gauge eigenstate (5 of such chords for one-dimensional superstrings, and 10 of such chords for two-dimensional superstrings of discrete energy permittivity), being de-compactified from maximum compactification by a factor of two, works to allow for the condition to where the "plucking" of these so-stated chords may be able to happen without any fraying of homotopic-based invariance.  This general format that I have just discussed is true for light-cone-gauge topological-based chords that are either of a Kaluza-Klein-based abelian topology, and also for light-cone-gauge topological-based chords that are of a Yang-Mills-based non-abelian topology.  The main difference, being here, that an abelian light-cone-gauge topology is plucked at the extrapolatable even-based distributions -- in a symmetrical-based delineation, that is along the contour of the relatively supplemental contour of each so-eluded-to second-ordered light-cone-gauge eigenstates, whereas, a non-abelian light-cone-gauge topology is plucked at the loci where the so-eluded-to chord-based phenomena is perturbated, distribution wise, into its Laplacian-based sinusoidal-based cusps (that is as well in a symmetrical-based delineation).  This added description is, as an ansantz, true for both the core-field density of light-cone-gauge eigenstates of either one-dimensional strings of discrete energy permittivity -- as well as for the core-field-density of those light-cone-gauge eigenstates of two-dimensional strings of discrete energy permittivity.  The core-field-density of first-ordered light-cone-gauge eigenstates act as the counterpart of the correlative respective Fadeev-Popov-Trace eigenstates.
I will start the second session of Course 17 later!  To Be Continued!  Sincerely, Samuel Roach.

Part Three of the First Session of Course 17, the Ricci Scalar

Electromagnetic force is energy that fluctuates in both its electric and its magnetic fields.  The magnetic field indices of a quantum of electromagnetic energy act in so as to wrap around the directly corresponding electric field indices in an orthogonal manner -- as is according to the right-hand-rule.  So, electrodynamic energy has magnetic field-based indices that are orphogonal to its directly associated electric field-based indices -- as is according to the right-hand-rule.  As is in going in the relative forward-holomorphic-based direction, both Fadeev-Popov-Trace eigenstates, their respective superstrings, and their respective counterstrings work to form a unit of discrete energy -- as this may be extrapolated in one discrete basis, over the course of one iteration of instanton.  This is during each discrete period of time in which each discrete unit of energy iterates, over the course of  each successive increment of the series of motion -- in which energy happens over time.  A Fadeev-Popov-Trace eigenstate is a discrete unit of energy impedance.  A superstring is a discrete unit of energy permittivity.  A counterstring is the Fock Space increment of a discrete unit of energy permittivity -- that most exhibits the wave characteristics of the so-stated discrete energy permittivity per instanton.  Energy impedance holds back discrete energy wave-tug/wave-pull enough -- so that the so-eluded-to energy will not shatter.  Discrete energy permittivity is the energy characteristic of discrete wave-tug/wave pull in and of itself.  The counterpart of any given arbitrary superstring is the Fock-Space exhibition of the directly affiliated given arbitrary unit of discrete energy permittivity -- that acts as the basis of the wave characteristics of the drive of energy itself.  The light-cone-gauge is that phenomenology that is "plucked" like a harp, in so as to form those discrete vibrations -- that indirectly inter-relate superstrings of discrete energy to their directly corresponding gravity-based superstrings --  so that phenomenology may be held together enough, in so as to allow for enough spontaneous and continuous proximal interactions, so that energy may exist at all.  The so-stated "plucking" of the light-cone-gauge also often works to stimulate those changes in Gaussian-based format that are needed, so that both norm-conditions may change, and, so that the essential fractals of energy may be re-implemented into the Gliossi-based topological contour of the directly affiliated superstrings.  The general core-field-density of the Gliossi-based compactified twining of mini-string segments, that works as a whole -- in-between one given arbitrary Fadeev-Popov-Trace eigenstate and its correlative superstring -- to be plucked like a harp -- in so as to form Schwinger Inidces, is a first-ordered light-cone-gauge eigenstate.  The individual strands of twined compactified mini-string, that form one stratum of holonomic substrate -- that is acted upon by one relative column of gauge-bosons, in so as to form either one of sixty (for two-dimensional superstrings), or, one of 120 (for one-dimensional superstrings) second-ordered Schwinger Indices -- along the topological stratum of the either sinusoidal (for a Yang-Mills topology) or, the supplemental (for a Kaluza-Klein topology) shaft-like twining -- are second-ordered-light-cone-gauge eigenstates.
Enough to absorb for now.  I will continue with the suspense later!  Sincerely, Sam Roach.