Hermitian World-Sheet -- Smooth Homotopy

 When the mappable-tracing, as taken along the topological surface of a given arbitrary world-sheet, is hermitian, then it may be said, that the directly associated cohomology, is here to tend to bear a smooth homotopy. I WILL CONTINUE WITH THE SUSPENSE LATER! TO BE CONTINUED! SAM.

The Homotopy Duality Paradox

 Here is a paradox that I have thought about, that I would like to share with my readers here:

Let us initially consider two different world-sheets of cohomology-related holonomy. Let us now say, that these two different respectively considered world-sheets, are, in at least some manner or another, to inter-bind, in a cohomology-related manner, at some Laplacian-Related particular region, in time and space. Let us next say, that one of these two stated world-sheets, is primordially of five physical spatial dimensions, whereas, the other of the two stated world-sheets, is instead, primordially of six physical spatial dimensions. Let us next say, that there is some sort of a tense of homotopic convergence, of which is here to help work to facilitate, at least some sort of a connection, between these two different and distinct inferred of, cohomology-path-based topological manifolds, of potentially traceable propagated holonomic curvature-related structure. Next; Let us say that there were here to be, two different sets of two propagational Ricci-Based flows of cohomology-related deformation, that are here to be distributed in delineation, both along and through, the general proximal local region, at which these two different individually taken sets of inferred homotopic curvatures are to inter-bind, in so as to work to bear a potential case scenario of homotopy, when this is in terms of the desirable continuous flow of space-time curvature, from the propagational Transform of Fourier-Related-Progression of one of these two said world-sheets, to the other. Let us now consider, when each of the individually taken sets of cohomology-related flow, are to become eminently Gliosis to one another, at the Poincare level to their core-field-density, that the inferred consequential collision of vibrational oscillation, will thereupon tend to result, in a net generative flow of cohomology-related deformation, of which is here to be tugged into the "arena," of only one of the two individually taken earlier mentioned world-sheets. Let us say, that one of these two net gauged flows of cohomology-related deformation, is to be tugged into the respective world-sheet eluded-to earlier, that is of five spatial dimensions plus time. Whereas; The other of these two net gauged flows of cohomology-related deformation, is to be tugged into the respective world-sheet eluded-to earlier, that is of six spatial dimensions plus time. Let us next say, now, that the mentioned net flow, that is to be tugged into the field of cotangent bundle R5, at the point of crossing the inferred boundary, that is here to be indistinguishably interconnecting the two stated world-sheets, is to be changing in its sixth  spatial-related derivative. Also; The mentioned net flow, that is to be tugged into the field of cotangent bundle R6, at the point of crossing the inferred boundary, that is here to be indistinguishably interconnecting the two stated world-sheets, is also to be changing in its sixth spatial-related derivative. The cohomology-related flow of the two, as such, that is to be net transferred into the world-sheet of R5, will tend to have a Chern-Simons-Related spur, at the regional locus of the general interconnection, that is here to be between the two earlier stated "meshing" world-sheets; Yet -- The cohomology-related flow of the two, as such, that is to be transferred into the world-sheet of R6, will tend to be hermitian, at the regional locus of the general interconnection, that is here to be between the two earlier stated "meshing" world-sheets. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. (PHS1989).

Analogy To The Fujikawa Coupling

 The smoothly hermitian folding of a flat cohomology-related world-sheet into a rounded cohomology-related world-sheet, is relatively analogous to the Fujikawa Coupling. SAMUEL ROACH.(1989).

Conical World-Sheets -- Permittivity

 The more conical of a world-sheet, that a superstring of discrete kinetic energy is to generate, the greater the scalar amount of permittivity, that such a superstring will thereby tend to exhibit. SAM.

Conversion Of Kinetic Energy Into Mass

 When a given arbitrary set of world-sheet-related superstrings, of discrete kinetic energy permittivity, are to convert into a respective given arbitrary set of world-sheet-related superstrings, of discrete mass-bearing energy permittivity, -- this works to function, in a similar but different manner, -- as to acting like a general respective particular genus, of a modified heuristic example, of a covariant gauged coupling, that may be mathematically expressed, via the workings of the Green Function. To Be Continued! Sincerely, SAM.

Alteration Of World-Sheets Involved -- Conversion Of Mass Into Pure Kinetic Energy

 When a Noether-Based mass-bearing cohesive set of discrete energy quanta, is to theoretically convert into pure kinetic energy -- the set of individually taken component superstrings of discrete energy permittivity, that are here to have initially worked to comprise the earlier mentioned set of discrete energy quanta, are to tend to convert, from initially working to bear the general nature, of appertaining to a set of toroidal cohomology-related world-sheets, Into consequentially resulting, in working to bear the general nature, of appertaining to a set of individually taken conical cohomology-related world-sheets. (1989). I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.

As To Conical World-Sheets

Let us say that we are to initially be considering a respective given arbitrary one-dimensional superstring of discrete energy permittivity, that works to bear a two-dimenisonal world-sheet -- that works to map-out the projection of the trajectory of the said respective string.  This so-stated world-sheet acts as the physical memory of the field density that is most Yukawa to the said superstring, in its proximal localization at the Poincare level.  Such a so-eluded-to field -- that would here appertain to the integration of the correlative eigenindices, that are to here act as that force that may be exhibited by the so-stated superstring, in a manner that is Gliosis to the immediate external surface of the topology of the said superstring -- that is here in this particular case, a given arbitrary open-loop of discrete energy permittivity, that is to then behave as the fermionic string of this case scenario.  Now if the superstring were to be projected into that tense of holomorphicity -- that would here be directed in such a manner, in so as to work to form a cross-product that would here be in the direction of its thickness, then, the correlative resultant cohomology that would thence be formed would tend to form a Rham-based integration of a washer-based pattern of shape -- that would here tend to bear a relatively small annulus, when this is taken in consideration of the scalar magnitude of one "mer" of each so-eluded-to ghost-based index, that is here to work to form the directly corresponding cohomological trace of the said one-dimensional superstring.  Yet, if instead, the said open-loop or fermionic superstring -- were to be projected into that tense of holomorphicity -- that would here be directed in such a manner, in so as to work to form a cross-product that would here be in the direction of its length, then, the correlative resultant cohomology that would here be formed, would tend to form a Rham-based integration of a set of conical-shaped ghost-based indices -- that, in so long as there is no spontaneous antiholomorphic Kahler condition immediately following -- will tend to point its coniaxial-like apex at least somewhere n the relative Minkowski-based direction that will tend to behave as more of a Hamiltonian operator that is moving as a relative cross-product, rather than tending to point its coniaxial-like apex in the relative Minkowski-based direction that would otherwise behave as more of a Hamiltonian operator that is to then be moving in the relative dot-product direction of the so-eluded-to Ward-based general substringular neighborhood of such an arbitrary scenario.  This has to do with the general tendency of superstringular inertia, in that it tends to be unthwarted -- until an external force is to act upon it.
To Be Continued!  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Part One of the 12th Session of Course 17 About the Ricci Scalar

Both superstrings, world-sheets, and orbifolds, exist with a topology.  A superstring may either be hermitian, a superstring may be topologically unsmooth in its Lagrangian-based mappable tracing,  a superstring may be annharmonic in its metrical-based pulsation -- while yet being topologically smooth over its directly corresponding  Lagrangian-based mappable tracing -- over its vibrational genus --  per iteration of group instanton, a superstring may be annharmonic in its metrical-based pulsation and unsmooth in its Lagrangian-based mappable tracing -- over its vibrational genus -- per iteration of group instanton, and/or a superstring may vibrate off of the relative Real Reimmanian plane -- over the course of a given arbitrary sequential series of the directly applicable iterations of group instanton.  The topological-based framework of a world-sheet may either be hermitian, it may be topologically unsmooth in its Lagrangian-based path -- while yet vibrating in a harmonic manner, it may be annharmonic in its metrical-based pulsation, while yet being smooth in its Lagrangian-based path, over the course of its vibration per iteration, it may be both annharmonic in its metrical-based pulsation and also unsmooth in its Lagrangian-based path -- over the course of its vibrations per iteration of group instanton, and/or, such a topological-based framework of a world-sheet may vibrate off of the relative Real Reimmanian Plane.  Likewise, the topology of an orbifold may be hermitian, it may be unsmooth in its Lagrangian-based mappable tracing, it may be annharmonic in its metrical-based pulsation -- over the course of its vibrational-based genus -- per sequential series of group instanton, it may be both unsmooth in its Lagrangian-based path while yet also being annharmonic in its metrical-based pulsation -- over the course of its vibration --  per sequential series of group instanton, and/or such an orbifold may vibrate off of the relative Real Reimmanian Plane.
This says allot.  I will continue with the suspense later!  To Be Continued!!! Sam Roach.

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

Superstrings and world-sheets kinematically differentiate both radially and/or transversally per iteration of group instanton.  So, each time that a superstring of discrete energy permittivity iterates per instanton, the so-stated superstring differentiates either radially and/or transversally -- depending upon both the format as to whether or not the given arbitrary superstring is undergoing a certain genus of conformal invariance, and/or if the said superstring is going through a condition of viable perturbation that is not conformally invariant in genus (but still of a Noether-based flow), or, if the so-eluded-to superstring is undergoing some type of format of a tachyonic-based flow.  Each time that a world-sheet iterates -- if the directly corresponding superstring that worked to form the said world-sheet is of a Noether-based flow, over the course of the extrapolatable mappable tracing of those given arbitrary ghost-based indices, that indicate both the existence and the activity of the so-stated given arbitrary world-sheet -- the mentioned world-sheet will be translated one Planck-Length and/or one Planck-Radii from the initially based eluded-to general condition of delineation to the next eluded-to general condition of delineation.  Yet, if a superstring of discrete energy permittivity is of a tachyonic-based manner, then, the distribution of the scalar magnitude as to the delineatory index of how far any given arbitrary superstring is delineated -- from one specific spot to the next -- will then here involve a kinematic-based extrapolation of more than one Planck-Length and/or more than one Planck-Radii per each respective succeeding iteration of instanton that would then be involved here.  This would then mean that the resultant directly corresponding world-sheets -- of which are the projection of the trajectory of the so-stated given arbitrary superstrings -- will be delineated in such a manner in so that each succeeding iteration of instanton will then here involve a distribution of scalar magnitude that would involve a translation of more than one Planck-Length and/or more than one Planck-Radii per each of such so-stated iterations.  Gravity is altered or perturbed to a certain extent, whenever there is tachyonic activity.  This is because tachyonic activity effects the Ricci Scalar -- via the effect that this has upon the respective given arbitrary Rarita Structure eigenstates.  I will continue with the suspense later!  To be Continued!
Sam Roach.

Part Two of the Last Interim

A world-sheet is the trajectory of the projection of a superstring.  A superstring bends, as is according to the general curvature of time and space.  The general curvature of space-time-fabric is as according to the general Mobiaty of physical phenomena -- as such an eluded to torsioning acts as according to the Ricci Scalar, via the multiplicit and multivarious eigenindices of the Rarita Structure over time.  So, as a superstring moves over time through any given arbitrary Lagrangian, its directly corresponding world-sheet forms a delineatory eigenbasis of the redistribution of the conicenter of the local coniaxions -- that appertain  to the local conditionality of those interchanges of Mobiaty that appertain to the functioning of the so-stated superstring.  Such a redelineation of Mobius-based coniaxions are more torroidal-based for the redistribution of two-dimensional superstrings, and, such a redelineation of Mobius-based coniaxions are more conical-based for the redistribution of one-dimensional superstrings.  I will continue with the suspense later.  To Be Continued!
Sam Roach.

A Start As To Rham Cohomologies

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

The Third Part of The 12th Session of Course 14 About Group Action

Let us say that there are -- in this arbitrary given case -- a group of superstrings that are being considered to be extrapolated at the same general multiplicit-based metric at a succeeding series of group instantons.  As the superstrings just mentioned continue to iterate and reiterate in slightly different spots over the eluded to sequential series of instantons, ghost anomalies form to provide an ability for the relatively local holonomic substrates of each of such cases to detect -- via the motion of the local substringular entities of such a related case -- the directly corresponding world-sheets that are formed, indirectly, by the trajectory of the projection of the said superstrings.  As the said ghost anomalies form via the basis of the relative positioning and delineation of the corresponding superstrings -- as the said superstrings bump into positive-norm-states per iteration of group instanton -- the eventual activity of the counter-basis that exists as the physical entity of negative-norm-states that strike the mentioned physical-basis of memory of the directly related superstrings, in so as to work to scatter the eluded to ghost anomalies.  As the directly previous is going on, the said superstrings continue to iterate and reiterate as holonomic substrates -- that are comprised of indistinguishably different compositions of integrated first-ordered point particles, whose inter-bound mini-string segments are constantly flushing out and pulling in exterial mini-string segments in the process of the recycling of ground-to-norm-to-ground states.  This happens, so that topology may work to remain homotopic.  This activity works to allow superstrings to continually form new paths that work to form various mutiplicit world-sheets that are thence multiplicitly formed over the course of the sequential series of iterations of group instanton.  So, every time that a superstring of discrete energy permttivitiy iterates in the process of redelineating its Ward-Neumman-based phenomenology, in so as to form those integrative pulses that work to form the flow of motion that forms the basis of energy, an index of the physical memory of those superstrings is multiplicitly formed in so as to form ghost anomalies that are here known of as Gliossi-Sherk-Olive ghosts.  So, a world-sheet is the actual trajectory of a superstring -- in this context --, while, a ghost anomaly is the physical entity that forms in so as to form a basis of being able to detect the path of any given arbitrary world-sheet.  This may be enough to "chew-on" for now!  I will continue with the suspense later!  Sincerely, Sam Roach.

Session 9 of Course 9

A dilaton is a quantum of phenomena that comprises gravity.  A graviton is a quantum of transversal gravity.  A gravitino is a quantum of radial  gravity.  Perturbations in the metrical directoralizaation of gravitons and gravitinos are examples of space-time-related spurious operations.  World-Sheet-related spurious operations are characterized by perturbations in the transversal and radial propagations of superstrings.  Anharmonic differentiation in the radial actions of strings during the general Ultimon metric, coupled with the anharmonic differentiation of norm-states that act upon these strings, are spurious -- and such a spurious operation acts to redelineate the spacial transfiguration of the surrounding gravitons and gravitinos.  When spurious states quantize and propagate in a differentiating Hilbert Fock Space -- after countless iterations of instanton -- in the threshold of a given tori-sector-range that is multiplicitly delineated in an arbitrary region, are initially made taut (the abelian geometry will here involve a more directly Gliossi tangency) relative to one another -- while the consequence of such an arbitrary Fourier Transformation is that the described superstrings are then sucked into a quantum of dilatons and dilitinos that are inactivated by the prior tadpole-related group action.  The pull of the mentioned dilatons and dilatinos, coupled by the described spurious operation of the mentioned tadpoles upon the either Yang-Mills or Kaluza-Klein topological surface (such a surface that the given activity acts upon may holonomically be, in and of itself, either abelian or non-abelian in terms of the topological geometry of its wave-tug through a given arbitrary Lagrangian over the course of an arbitrary Fourier Transformation that is occuring in the region, that may be arbitrarily perceived within a relatively limited locus) that may be metrically described as existing within a Majorana-Weyl tense of conformal invariance.  Such a metrically-based Majorana-Weyl-associated topological interaction of the described superstrings of the given tori-sector-range, when dangerous tadpoles increase in terms of the frequency of their summed Hodge-Indices, may fray the substrigular fabric of the given tori-sector-range in its multiplicitly delineated region to form a black-hole.  Meanwhile, the space-hole eigenstates of the other tori-sector-ranges of the Overall-Space-Time-Continuum reconnect their topologically-ordered eigenstates so that the operation of Cassimer Invariance may keep the here associated superstrings that are left into a more consolidated network that lets the existence of pre-existing black-holes to fray to some extent the phenomena of their regions.  This consolidation transfigures after each iteration of instanton in which phenomena is brought into the mentioned black-holes.  Such tranfigurations is allowed by the resettling mode of the space-hole via Cassimer Invariance before each instanton-quaternionic-field-impulse-mode.
Black-Holes may be elliminated in a fashion that alters these into a harmonic substance that is composed of homogeneous sets of kinematically covariant inter-relations of Campbell and Hausendorf Projections that still allow star and planetary cycling that does not eat up the mentioned stars and planets.  This mentioned operation also works to allow the assymetric radial and spin-orbital motion of galaxies in such a manner so that space-time-fabric will here no longer need to expand or contract.  The manner of such conversion I will not put on  the Internet no matter what!!!  Sincerely, Samuel David Roach.