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

1)  What is a Doubolt cohomology?

2)  What is a Rham cohomology?

3)  Explain how ghost anomalies are annhilated.

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

5)  What is the Bette Action?

6)  What is the Polyakov Action?

7)  What is the Regge Slope?

8)  What makes superstrings oriented?

9)  What makes superstrings unoriented?

10) What is a Klein Bottle eigenstate?

11)  Describe the mobiaty of superstrings.

12)  Describe the mobiaty of world-sheets.

13)  What are Ward conditions?

Some More Stuff About Electrons

Electrons that are a part of their respective atoms are constantly orbiting around the nucleus of the directly corresponding atoms in an elliptical manner.  Any phenomenon that is orbiting around some other phenomenon is constantly accellerating -- even if it is then maintaining a constant velocity, since a pheonomenon that is orbiting around another phenomenon is constantly changing in direction.  Such a basis in the directoral flow of an electron is a significant part as to why an electron that is part of an atom -- at any given arbitrary consideration that may be extrapolated -- will always be delineating at least some Chern-Simmons singularities, during the process in which such individually considered electrons are in the process of orbiting around the nucleus of an electron.  So, it is the orbital momentum of any given arbitrary electron that may be considered in any case, in which such an individually considered electron is under those specific Chan-Patton rules, to where such a given arbitrary electron will always be delineating one format or another of Chern-Simmons-based singularities upon its immediately surrounding environment -- over the so-stated course in which the said genus of electron is accellerating around the respective given arbitrary nucleus of its directly corresponding atom that it is in, in so long as such a said electron is moving in some manner or another around such an eluded-to nucleus of an atom.  Again, this is because any orbifold or any orbifold eigenset that is accellerating will, by its very nature, be delineating Chern-Simmons singularities -- at least of a metrical-based genus.  Furthermore, if an electron is initially released from an atom -- for any duration in which such a phenomenon of orbifold eigenset is pulled out of the Ward-Neumman constraints of any atom that may here be considered, over a directly affiliated extrapolation -- those mappable traces in which the motion of the so-stated electron of this case is moving in a perturbative manner that is not of a hermitian manner -- will bear at least some degree and format of Lagrangian-based Chern-Simmons singularities, for that duration in which the said given arbitrary electron is displaying a mappable tracing that may bear an extrapolation that is not fully hermitian.  The resultant of such an initially non-hermitian wave-tug/wave-pull that is imbued upon the kinematic activity of any given arbitrary electron is a discrete increment of electromagnetic energy that is known of as a photon.  This is what works to form, in part, the condition that discrete units of electromagnetic energy are partially hermitian -- photons tend to bear a high degree of metrical-based hermicity, of which bears Lagrangian-based hermicity that still affords Chern-Simmons singularities -- since the latter mentioned Lagrangian-based hermicity has a bearing that is off of the respective relative Real Reimmanian Plane. This works to describe the Chern-Simmons singularities of photons as lacking a foundation of spuriousness -- while, still affording a viable degree of hermicity.  The high degree of metrical-based hermicity of electromagnetic energy is what works to form the basis of Lorentz-Four-Contractions, while, the condition of discrete units of entropy being formed by any scattering of the respective photons is the Chern-Simmons resultant of the directly related lack of Lagrangian-based hermicity of electromagnetic energy -- in a propagatorial-based tense.  The main operation of entropy is the formation of infrared photons -- of which works to allow for the spontaneous and continuous existence of mass,as well as for the spontaneous and continuous changes of the physical states of the so-eluded-to quantums of mass.  I will continue with the suspense later!  Calabi Interactions -- coming to this blogcite in Course 20.  To Be Continued!  Sincerely, Sam Roach.

Lorentz-Four-Contractions and Oscillations

The Lorentz-Four-Contractions involved with a given arbitrary directly corresponding two-dimensional core-field-density of an affiliated given arbitrary one-dimensional superstring of discrete plain kinetic energy permittivity works to make the so-stated one-dimensional superstring appear as a vibrating ring, when such a superstring is moving within the Ward-Caucy bounds of a directly affiliated electron that is not here in the process of dropping an energy level -- at the Poincaire level that is Gliossi to the outer fringes of the so-eluded-to core-field-density of the said superstring. Over the course of a directly corresponding group metric in which the directly previous conditions of activity are happening to such a given arbitrary electron, those give arbitrary two-dimensional superstrings of discrete energy permittivity of that electron that work to form the discrete increments of its mass will work to bear a three-dimensional core-field-density that would then here appear as a vibrating cylinder, when such a superstring is moving within the Ward-Caucy bounds of the so-stated electron that, again, is not dropping an energy level during the so-eluded-to scenario -- at the Poincaire level that is Gliossi to the outer fringes of the so-eluded-to core-field-density of the said superstring of this second case.  This directly previous scenario will then work to form two and three-dimensional field pockets that will act as orbifolds -- that come together in so as to form that given arbitrary orbifold eigenset that is known of as an electron.  Such an integration of partial core-field-densities, that work to form an overall core-field-density of a common subatomic particle, work to perform those operations that are involved with the Chan-Patton functionablitiy of an electron -- in this given case -- in the course of a sequential series of iterations of group instanton, that works to bear a gauge-metrical basis that may here be considered as a fractal of a covalent operation that behaves as a reverse-fractal of a Hamiltonian nature.  The convergence of the operations of those orbifolds, that are within the so-eluded-to orbifold  eigenset of a non-perturbated electron, that come together in so as to perform a common function as one entity -- is fascilliated by the nature of the quaternionic-instanton-field-impulse-mode. -- The here eluded-to interdependance of the activity of the directly associated homotopic residue, that is involved with the said given arbitrary activity of any non-perturbated electron, is maintained as a topologically sound entity -- via the kinematic activity of the process of Cassimer Invariance.  For example, the superstrings of a non-perturbative electron may, at time, switch Laplacian-based relative neighborhoods -- when in terms of the mappable tracing of those orbifolds that are here inter-laced within the orbifold eigenset of such an electron.  Such a relative local rearrangement of the regions that may be mapped-out from within the Laplacian-based setting of an electron, would then be delineated as a convergent-divergent-convergent sequential series -- in which the directly affiliated wave interactions would bear a conformally invariant condition of hermicity that would have at least some sort of a flush Minkowski topological sway that would be distributed, as the Laplacian-based delineations of such a non-perturbated electron would here involve a local re-allocation of the internal orbifolds that work to comprise the said electron. This, though, does not rule out the condition that the added dimensionality of the electron would still involve tensors that would produce a certain degree of Chern-Simmons singularities that would be driven via both the permittivity and the impedance of such a non-perturbative electron -- whether such an electron is Noether-based or tachyonic-based.  Such a need for Chern-Simmons singularities is actual because of the nature of the angular momentum of the kinetic energy of even a non-perturbative electron.  For instance, the propagation of the directoral indices of the angular momentum of any electron will tend to follow the path operand of the norm-conditions of the initialized encoding of that electron -- per increment of the sequential series of the motion of such an electron -- as taken as a reverse-fractal of a Hamiltonian-based nature.  Such a Hamiltonian-based nature is most directly proscribed by the internal operational nature of the Hamiltonians of those superstrings that internally function as a group in so as to work to form the momentum-like conditions of the affiliated electron.  Such an encodement works to act as the quantifying operator of the eigenbasis of the wave characteristics of the said electron.

Substringular Reiterations

May we look at substringular reiterations as a convergent sequence of slices in the space-time fabric -- whose bases are exact and linear differential associations of physical point particles, the convergent series of wave reiteration being the summed wave interconnections which work to differentiate all neighboring semi-groups as a covariant platitude -- in which the superstrings that code for a given globally distinguishable homotopy remain unchanged, when relative to the directly corresponding parity attributions, these attributions of which are delineated by the overall eluded-to system of phenomenology?  Well, this mean that the so-stated superstrings may change, yet, does this mean that the directly associated particular supersymmetry will here work to cause the net apprehendable condition of the said superstrings to then remain unchanged?  Any given arbitrary superstring of discrete energy permittivity will iterate, during group instanton, at a slice locant.  It works to orientate with its directly covariant Fock Space counterpart.  Once that the first-ordered point particle neighborhoods of the affiliated superstring are working to exchange the output of their wave-based indices, a quaternion is formed among all of the superstrings of discrete energy permittivity of the directly corresponding tori-sector-range.  This leads to the reiteration of group instanton.  After group instanton, the given superstring that I have eluded to will bear a relative dissociation -- scattering as a mildly cohesive set of first-ordered point particles that are more annharmonically delineated than these are during the directly prior conditions that existed at instanton.  The mappable tracing of where and how the superstring had behaved during the directly previous iteration of instanton will then be imbued upon the "turf'" of the substringular as a set of ghost-based indices.  Once that the so-stated first-ordered point particles that appertain to an indistinguishably different superstring, that is here moving in a relatively conformally invariant setting, have moved along the Ultimon -- in so as to be brought to virtually the same spot at which these had iterated during the prior stage of group instanton, the so-stated first-ordered point particles that had worked to form the so-eluded to superstring of discrete energy permittivity will then work to form a superstring that will be distributed at the ensuing iteration of istanton, since such a superstring is here obeying Noether Flow.  This would here mean that the so-stated superstring that is reformated to reiterate at an adjacent delineation from where it had previously iterated, will be distributed at the ensuing instanton at the same general substringular neighborhood, and thus, at a very similar basis of slice locant.  This process will then continue, following a variation of parameters localization -- in which the coefficients that would here work to describe the specific delineation of the first-ordered point particles that comprised the formation of the directly corresponding superstring, will integrate in such a manner in so that the individual Poincaire-based cites -- as to the bringing together of the so-stated point particles -- will bear a Hamiltonian-based eigenset that will work to determine the basis of that group attribution that will most fascillitate the Gaussian eigenbasis of the wholeistic set of antiderivatives that would here work to form the foundation of the so-stated ensuing local substringular delineation of superstrings that are to come together at the said given arbitrary cite.

Some Stuff As To The Substringular Nature of Electrons In The Substringular

You may wonder about the vibrations of an electron from within the neighborhood as the said electron exists as a transposition of indical bases of which appertains to eigenstates of both mass and kinetic energy which quantify within the expected range of a double-majorized-plane-sector, which has a probablity that is minimized analogously to the elevation of tensorism as delineated by the covariance of the iteration and the reiteration of the superstrings and the quantific waves which work to form the eigenspace of the neighborhood of the said electron as it may be transiently measured within a range which is homogeneously proximal to its path operand.  Well, then, what is this vibration???  Such a vibration is the applied tensorism of the association of redistributed eigenstates of superstrings which swipe out a semigroup of heterogeneous potential morphology, whose field bears covariance with an inexact and nonlineaer differential association of reassorted factor groups -- which work to integrate the pulse of the said electron after each group convergent series of the directly corresponding magnetic dipole -- as the so-stated dipole delineates a morphological tense of permittivity -- which causes the constancy of the electrons tangency to abide by its directly associated orbital conditions.  So, what is a potential application to this eluded-to tensorism?  I will only give you a hint on my blog.  As the physical point particles (of the first-order) which work to comprise the relevant superstrings are minimized -- in terms of their repulsion factors -- the rate of the integrating factors, caused by the relative angular momentum of the orientation of that parity that is among the neighboring point commutators, increases -- in terms of the magnitude of reassortment transition.  This implied activity works to pull together first-ordered point particles to the given arbitrary regional distribution, which may be most "eigen" within the so-eluded-to tense of spontaneity.  If one were to be able to "pull" such a directoral topological sway -- on account of the added condition of all substringular wave that is unfrayed, being connected by the condition of Cassimer Invariance -- an equal and opposite "push" that would be inacted in the opposite general direction, will then be afforded by the directly corresponding activities that appertain to the presence of homotopy -- which would work to form a semi-permeable flow of wave-based delineation to be exacted, in terms of the wanted tenses of condensed wave oscillation, whose pushing-out of waves from the thence forming superstrings of discrete energy permttivity would work to help control the sub-atomic vibrations of the so-eluded-to given arbitrary electrons that appertain to such an activity.

As To The Configurations of World-Sheets

If a given arbitrary world-sheet is of a toroidal-shaped-nature, then, the physical ends of the Ward-Neumman boudaries of those ghost anomalies that work to trace the mapped-out extrapolation as to the trajectory of the projection of the directly corresponding superstrings -- that worked to form the so-stated ghost anomalies -- via the physical evidence of the directly corresponding world-sheets, bear cap-like permutations that act as critical cusps that are due to the just-eluded-to cyclic permutation of those cross-sections of the so-stated external format of first-ordered point particles that bear a chirality, which is relative to the other of such so-stated critical cusps, that may be either symmetrically fashioned or assymetrically fashioned -- in relation to the directly corresponding trivially isomorphic alterior end caps of that toroidal-based pointal-construction of the mentioned ghost-based configuration -- that bears a mappable tracing that is shaped like a "doughnut" that bears a central anuulus that contains a non-time-oriented Lagrangian that is Gliossi to the so-stated pointal configuration of the world-sheet, which is relatively hermitian in unitary flow, as one were to map the coniaxions that work to indicate the relative vacuum that would here be at the Poincaire level of the center of the so-stated world-sheet.  If the so-stated end caps in this case are symmetrically arranged, any given arbitrary superstring that may be potentially caught in the said anuulus -- during any given arbitrary group metric in which the said ghost anomaly configuration is not yet annharmonically scattered -- will propagate out of the Ward-Neumman bounds of the so-eluded-to ghost-based configuration, in a forward-holomorphic-based directoral flow of the given topological sway.  If one of the so-stated end caps is arranged symmetrically, with its so-eluded-to counterpart, yet, the other end Lagrangian-based mapping of end caps is arranged antisymmetrically with its counterpart, then, the chirality of the so-stated Lagrangian will bear Chern-Simmons singularities.  Also, with the past format of scenario, over time, such a situation will work to form metrical-based singularities -- with the kinematic flow of its external-based enviorenment.  This metrical dissonance would then work to pull any given arbitrary superstring that is within the region of the so-stated anuulus of the toroidal-based world-sheet configuration in the reverse-holomorpohic directoral flow of topological sway.  If two or more of such sets of end caps is annharmonic -- in terms of the non-time-oriented mapping of the chirality of their counterpart -- as taken via a trivially isomorphic extrapolation, then, any given superstring caught within this genus of construction will rebound between the end caps per iteration.  Yet, this is given the general space-time-curvature-based considerations. So, ironically yet logically enough, if the end caps of this general format of scenario are only harmonically chiral, via the extrapolation of a Wilson-based linearity, then, the so-stated rebounding of superstrings that would be caught-up in a configuration such as this would rebound in a manner that would work to reattain fractals of discrete energy permittivity in superstrings. Hint: the Schotky Construction and the Klein Bottle.  I will continue with the suspense later!  To Be Continued.  Sam Roach.

Some More Knowledge As To World-Sheets

There are many other superstrings that may be able to iterate and reiterate in the general locus as to where a given arbitrary world-sheet had acted upon -- as evidenced by the sequential set of permutations that may be imbued upon an initial given arbitrary ghost anomaly that had been formed, in a set locus that may be reformed and perturbated by the ensuing activity of the kinematic motion of alterior superstrings -- that will then have here moved upon the so-stated given arbitrary set of ghost-based indices, that had initially integrated at a previous discrete metrical instant.  This happens in such a manner  to where the so-eluded-to "initial" ghost anomaly had been formed here will then function in so as to act as the physical evidence of the given arbitrary superstring, that was implied to be the prior extrapolated Hamiltonian operator that had "first" moved upon the starting so-eluded-to Hamiltonian operand.  A world-sheet may be either cylindrical, a disc with an anuulus, a toroid, a mobius-shaped configuration, or, another general format of planar-based configuration, whose topology is hermitian -- if the torsioning of the Ward-Caucy bounds of the Sterling approximation, as to the kinematic "thrust" of that superstring, that would here work to form the so-eluded-to world-sheet and its corresponding ghost anomaly, bears both a harmonic Hamiltonian-based gauge-metric and a harmonic Hamiltonian-based local tracing of its directly corresponding Lagrangian.  If the superstring in question is perturbated into either an anharmonic singularization of gauge-metrics and/or if the superstring in question is perturbated from a local base of Lagrangian-based tracing -- that would here map a format of singularity in its delineatory eigenbase, then, the topological genus of the progression of the kinematic changes in the derivatives of the Ward-Caucy bounds, of the kinematic-based tracing of the motion of the said given arbitrary superstring, would bear a Chern-Simmons eigenbase.  This latter genus of implied torsioning would work to form an added eigenbase of Mobiaty to the extrapolatable tracing of either the pulse and/or the path of the so-stated given arbitrary superstring, which would here work to involve a Njenhuis set of tensors that  would work to alter the local "infrastructure" of the Rarita Structure eigenbase, -- that would then work to alter the local format as to how both the local gravity and the local space-time-curvature would be primed at the so-eluded-to cite.

More As to a Description of Topology in reference to Iterations

A zero-norm-state may often act as a benevalent "tadpole" -- by latching to the general cite of a world-sheet distributioin, by the Gliossi interaction of the directly corresponding zero-norm-state-projection with the general topological stratum of an operational stratum of cohesive ghost-based indices.  These so-stated indices of which work to function as a ghost-inhibitor-based group attractor that is to be facilitated as a counterpart Hamiltonian operation, in order to allow for the said operation of the so-eluded-to wholeistic ghost anomaly.  Here is a basic run-down as to how what I am implying works:  Positive-Norm-States form ghost anomalies at the cite of activity where a world-sheet had traversed -- the kinematic flow of the motion of superstrings works to displace those norm-states and norm-state-projections that are moving in the same general director eigenbase of Lagrangian flow as the so-stated superstrings.  Norm-States and norm-state-projections tend to iterate and reiterate in more of a tense of conformal invariance than whatever the local superstrings are bound to move in over a discret period of time in which the so-stated given arbitrary superstrings move in a sequential series of multiplicit instantons, in so that the resulting relatively mild collisions of the said superstring with the so-stated relatively forward-holomorphic norm-states and norm-state-projections works to form a physical memory as to the directly prior existence and activity of the said given arbitrary superstrings.  Although all superstrings and norm-state-projections move by either Noether Flow or tachyonic flow, the Noether-based flow of norm-state projections tends to be in more of a state of static equilibrium than the Noether-based flow of the immediately surrounding superstrings that cross their path, in the course of the eluded-to interaction of superstrings with norm-states.  This is why the world-sheets, which act as the trajectory of the projection of superstrings -- are the arena of the harmonic scattering of forward-holomorphic norm-states and norm-state-projections that work to form ghost anomalies.  With forward-moving-time-based motion, forward-holomorphic norm-states are positive-norm-states.  Norm-State-Projections are any given arbitrary group of operational physical indices of first-ordered-point-particles that operate to perform a specific function.  First-Ordered-Point-Particles are attached by mini-string.  The so-stated mini-string acts as the holonomic substrate of substringular core-field-density, and, mini-string works as that physical entity that forms homotopy by both directly and indirectly binding all unfrayed superstrings with each other over Ultimon Flow.   I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Some discussion as to Topology-based Interactions

The reiteration of superstrings may be extrapolated by the mapping of their correlative world-sheets via tthe successive series of both the physical placements, distributions, and the delineation of the directly corresponding ghost anomalies -- as such so-stated ghosts are traced through the multiplicit and multivarious Lagrangian-based settings where there are physical memories of the correlative superstrings that have kinematically moved  through over time.  A superstring iterates over a tightly-knit spot -- over the course of one given arbitrary eigenmertic of BRST.  Any given arbitrary eigenmetric of BRST involves a multiplicit set of  specific eigenmembers of discrete energy that coelesse into a given eigencondition of that flow of covariant energy delineation, as taken basically like a snapshot in which the said superstrings   are in their respective individual iterations of their encoded-for delineation, that works to form a discrete Hamiltonian pulse of all of the unfrlayed superstrings that still are viabel in a metric-based Gliossi manner.   This delineation is progressed by a sequential series of such distributions and redistributions of both that phenomena that form discrete energy permittivity and of that phenomena that forms discrete energy impedance, in a manner of which works to form that flow of discrete physical energy-based phemomena that is simply what works to allow enegyy and is energy.  The physical memories of superstrings act as a raw holonomic substrate for the recycling of Gliossi-Sherk-Olive ghosts with Neilson-Kollosh ghosts, as well as providing the physical basis of the formation of gravitational-based particles, that inter-play in a covariance that brings in freshly assorted norm-state-projections into each eigenstate of Real Remmanian-based  plane --- in the process of the said recycling of the just eluded-to physical memories.  Such a physical-based cooperation is managed, too, by the recycling of norm-states to ground-states and vice-versa.  -- so that there may be an indistinguishably different inter-play between the conditions of multiplicit singularized jointedness with the condition of multiplicit hermitian smooth-curvedness, as is fascillitated by the existence and the activity of the Royal Arc.  The just mentioned process of indistinguishable difference of the recycling of norm-states to ground-states and vice-versa is the general manner of what may be discerned of as the inter-change of homotopic residue.  Homotopic residue is the set of those segments of topoligical stratum of which are in the immediate locus where topological-based chords of mini-string are re-connected to alterior local substringular cites -- which is during that gauge-metric that happens right before instanton-quaternionic-field-impulse  in which those changes in the general delineation of substringular homotopy happen, in order for Gaussian Transformations may successively happen during the multiplicit interaction of the Kaeler-Metric.  Such an eluded-to transformation in homotopy works to establish a tense of topological-based setting that goes in the direction of optimum relaxation.

Up Close

Anything over time that is a thing going through a duration, that involves one or more instantons, will involve at least three spatial dimensions plus time At The Poincaire Level.  This includes phenomena that are most fundamentally zero, one, or two dimensional at their core field density.  This means that there is an eigenstatic manner of approaching any actual physical phenomena - at least up close -- when one works to consider the interaction of any given arbitrary physical phenomenon with its exterior surroundings.  An index is fundamentally of zero dimensionality -- when one considers a physical phenomenon that acts as an index of physical placement, whether or not such a physical placement is relatively kinematic over a given arbitrary considered time period or not.  In the real world, all physical indices are at least partially redistributed and redelineated over time -- whether such a so-stated redistribution or redelineation is viable to determine via a particular extrapolation or not.  The field-networking of physical indices over a kinematic-based Lagrangian is a norm-state-projection.  A norm-state-projection is sometimes linear, yet, it is generally multiplicitly displaced per spatial index of its stand-still distributions, taken idividually, since there is constant wave-pull and wave-tug that works to delineate and redelineate holonomic substrate from a Wilson-based topological sway -- even at the most fundamental scalar magnitude of physical spatial separation of one physical index from another, over the course of the motion of a norm-state-projection.  The pull of a norm-state-projection works to bear a Hamiltonian operation upon its immediate surroundings that is fractal to the Hamiltonian operation of superstrings.  The wave-pull/wave-tug of norm-state-projections works to move superstrings and their corresponding ghost anomalies into a covariance with one another that works to establish a Majorana-Weyl-Invariance.  This "invariance" works in the direction of a homostasis of what involves the substringular relaxation processes with the processes of entropy. Later!  Sincerely, Sam Roach.

About Eigenstates and Mobiaty

An eigenstate is a physical phenomenon and/or a physical condition that is based upon a squared space.  A squared space is a region that is comprised of a planar-based product that is either Gliossi to the Poincaire-based locus of a given arbitrary spot, is of a cross-product-based Lagrangian -- when relative to the kinematic delineation as to a set given arbitrary flow of motion, that is metrical-based over a topological sway that is either euclidean and/or euler in Clifford translation, or, is of a dot-product-based Lagrangian -- when relative to the kinematic delineation as to a set given arbitrary flow of motion, that is metrical-based over a topological sway that is either euclidean and/or euler in Clifford translation.  A planar-based product that is Gliossi to a Poincaire-based locus would be a physical phenomenon that is based upon a squared space.  A squared space is most fundamentally Minkowski in nature. A Minkowski space is flat, yet, it is not generally flush to a surface.  A Minkowski space may incorporate permuations -- of which may be either entropic in terms of Majorana ghost inhibition, and/or may be cyclic in terms of Majorana ghost inhibition.  Such permutations work to form a manifold-like general locus that is binary in its core basis, yet, may form a multiplicit integration of up to 26 spatial dimensions plus time.  An electron exists in a minimum of six spatial dimensions plus time, as it moves over a successive series of instantons.  When one adds the 26 maximum spatial dimensions of a Minkowski space, in one set of parallel universes, to the six spatial dimensions that work to complement it -- over the Mobiaty-based curvature of space and time, that would be over a Lagrangian that completes its second edge/second side, one gets a maximum Hilbert space of 32 spatial dimensions plus time in one set of parallel universes.  A planar-based product that is either of a cross-product-based Lagrangian or of a dot-product-based Lagrangian -- when relative to the kinematic delineation as to the set given arbitrary flow of motion that is metrical-based over a topological sway that is either euclidean and/or euler in Clifford translation, is a physical condition that is of a squared space.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Some More about Mobiaty

As a bosonic superstring of discrete energy permittivity that is swivel-shaped reiterates in a region, the vibration of the given bosonic superstring works to form a hermitian-based mobius pattern -- that forms a trajectory that also has a hermitian mobius pattern -- as one traces the so-eluded-to spatial delineation through the respective space-time-curvature that would be involved here.  The vibration of any given arbitrary superstring obeys the directly corresponding Chan-Patton set of functions, if the said given arbitrary superstring is acting in a Noether manner.  The Ward conditions of the Yang-Mills topology of any superstring that is of a non-abelian light-cone-gauge topology is either of a Ward-Caucy nature that is tachyonic, or, is of a Ward-Caucy nature that is Noether -- depending upon whether or not the said superstring is relatively perturbative or relatively conformally invariant.  The just-eluded-to relatively perturbative condition does not work to conform to Chan-Patton rules -- seeing that this so-stated condition is of a tachyonic nature.  The Mobiaty of a tachyonic set of superstrings is continually changing in its neighboring indices of those group inhibitors that work to define the gradient of the flow of the so-eluded-to space-time-curvature, that is involved with any given arbitrary tachyonic flow of superstrings.  The just eluded to general flow of such a gradient in Mobiaty-based indices will bear an indistinguishably different set of tensoric-based eigenstates of parametric hermicity-based flow -- that is of a tense of cyclic permutation that is encoded to each succeeding set of directly corresponding group attractors that work to constitute the respective succeeding stationing of the so-eluded-to tachyonic-based superstrings.  In this tense, the flow of such a gradient is hermitian, although, the adjacent homotopic residue will always bear both Chern-Simmons metrical-based indices and Chern-Simmons Lagrangian-based indices.  I will continue with the suspense later!  To be continued!  Sincerely, Sam Roach.

Part Three of the Last Interim

Bosonic superstrings of discrete energy permittivity that are swivel-shaped -- when in terms of their general contour, in comparison with other two-dimensional superstrings of discrete energy permittivity -- are more likely to become unorientable, and thus, these so-stated closed superstrings are more likely to be or are to become tachyonic.  The tendency of a tachyonic flow tends to be a relatively transient duration of flow -- relative to the tendency of Noether Flow, when in consideration of the lengths of comparative metrical duration.  Yet, the length of the parametric sway of the Lagrangian-basis of a tachyonic-based flow is often of a greater scalar magnitude than the length of the parametric sway of the Lagrangian-basis of a comparative Noether-based flow.  This is whether the kinematic basis of such a so-stated parametric flow is unitary, binary, tritiary, or of more multiplicity, respectively to another of such a comparative traceable substringular flow that is instead of a set Noether basis -- in terms of the respective consideration of the basis of directoral permtttivity that is over the directly corresponding given arbitrary group metric.  The more of a multivarious and/or multiplicit basis of a tachyonic-based flow is, the more likely that there will be a Chern-Simmons-based format of a Gaussian-based group attractor that will then here work to integrate within the general Lagrangian of Mobiaty that the holonomic substrate of substringular phenomena that is to become tachyonic will then, here, kinematically be able to be mobilized within -- over the ensuing duration in which the so-eluded-to substringular phenoemena is to be activated as being tachyonic, as a cross-product-based delineatory subgroup that is within what here may be considered any given arbitrary so-eluded-to Ward-Caucy bounds in which a tachyonic phenomena is thus formed.

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.

Part One of the Interim Between S11 and S12 of C16

The topological sway of  superstrings and of world-sheets, as these are kinematically differentiating through the interplay of the multivarious Lagrangians that these so-stated substringular phenomena go through over time, work to form a torsioning that behaves as to the general Mobiaty of space-time-fabric -- substringular phenomena act, via the interaction of the Ricci Scalar, in so as to work to form the multilateral and interactive space-time-based curvature in which the physical members of space and time act within, as these so-eluded-to superstrings and world-sheets are pulled and pushed into an ebbing that works in the direction of most potential relaxation in the eluded-to process of torsioning that is operated upon -- via the physical existence of and the activity of the eigenstates of the Rarita Structure.  This general eigenbase of topological sway-based torsioning that I have here just mentioned works to form an erixtricable foundation as to what may be termed of as a Mobius Twist.  Such a general eigenbase of the kinematic interplay of substringular phenomena, as acting through a topological-based foundation of Mobius-based twisting, bears a kinematic parity that bears a differential clause that is hermitian -- when one considers the looping of the so-eluded-to conditionality of the torsioning of the eigenbase of the so-stated Mobiaty.  Yet, when one considers that Mobiaty considers a "one-side, one edge" conditionality, the unitarity of the torsioining of the so-eluded-to Mobius Twisting of space-time-fabric will always work to consider at least one independent substringular factor, that will involve at least two dependent substringular factors.  Since there will always be at least one more dependent factor to interact with whatever the sum of the independent factors are, in any actual physical scenario -- in so as to form the so-stated existence of that topological swaying that works to form the general condition of substringular Mobiaty, the so-eluded-to unitariy-based parity of the flow of the substringular course of space-time-fabric works to form a condition that is undoubtably Chern-Simmons in nature.  That is the general reason as to why a Hamiltonian-based expression will always bear more rows than collumns -- there will always be more dependent factors than independent factors, as to the tracing of the topological flow of the parameteric idices of space-time-fabric -- in so as to work to form the reason as to that a Hamiltonian expression is to always be described as a Jacobian.  I will continue with the suspense later!  Sincerely, Sam Roach.

Part Six of the Eleventh Session of Course Sixteen

The Ward-Neumman boundaries of a world-sheet is defined by two parallel Wilson Lines that are flush to each dimensional endpoint of delineation -- as to the furthest linearly-based mappable tracing that may be extrapolated in, in so as to mark each directoral basis as to the mapping of the region of where the directly corresponding ghost anomaly-based index may be tractable in one set locus, in so as to extrapolate the trajectory of the projection of any directly associated given arbitrary superstring -- that works to bear such a physical memory as to where and how the so-stated superstring had kinematically differentiated over time.  As ghost anomalies form a basis as to where and how the world-sheets of superstrings had moved over time, there is a parallelapiped-based integration of world-sheets that are formed in general space-time fabric that may be multiplicitly utilized -- as to what may be termed of as a Klein Bottle.  A Klein Bottle is composed of three sets of parallel Wilson Line-based world-sheet-like phenomena that work, in so as to bear a spatial operation that is kinematic and multispatially distributed and multispatially delineated in so as to work to allow for Kaeler-Metric eigenstates over time.  The structural context of the Klein Bottle is known of as a Schotky Construction.  The condition of World-Sheet-like phenomena that are parallel to one another is known of as the existence of orientafolds.  The orientafolds that work to form the Schotky Construction are flush, as is according to the concept of Wilson-Lines.  Wilson Lines are projections in the substringular that are literally flush, and thus do not bend as is according to the general curvature of space-time-fabric.  The condition that the Schotky Construction bears orientafolds that are flush -- as is according to Wilson Lines -- is part of as to why the Klein Bottle is able to both shake superstrings into reattaining the fractal quantum indices of their discrete energy permittivity, as well as to shake Fadeev-Popov-Trace eigenstates into reattaining the fractal quantum indices of their discrete energy impedance.  The static equilibrium of the indices that work to form the Schotky Construction is a given arbitrary condition of a conformal invariance of integrable orientafolds.  Any given Klein Bottle eigenstate may be utilized, in so as to perform multiple eigenmetrics of Kaeler-Metric eigenstates, as long as the directly applicable Schotky Construction is not frayed.
I will continue with the suspense later!  To Be Continued!  Samuel Roach.