Symplectic Versus Khovanov Knotting Equations

When one is to work to determine the knotting equations for a system of cohomology, to where these so-eluded-to equations are here to work to be describing a symplectic geometry, -- the main difference that there is, between the formulation of this said cohomology and the formulation of a Legendre homology, is that, when determining a cohomology, one is here to be converting a Minkowski space into a Hilbert space; whereas, -- when one is to work to determine the knotting equations for a system of a Legendre homology,  to where these so-eluded-to equations are here to work to be describing a Khovanov geometry, -- the formulation of this said general genus of homology is as such, to where one is to instead, to be converting a Hilbert space into a Minkowski space.  To Be Continued!  Sincerely, Samuel David Roach.

Compleltion Of The Rarita Structure -- Forces

Do you remember me mentioning to you on this blog, something to the effect of (but not specifically this exactly, though) -- that the multiplicit light-cone-gauge eigenstate acts as the 'opening phenomenology' of the Rarita Structure, and that the multiplicit gauge-bosons act as the 'closing phenomenology' of the Rarita Structure?  Furthermore, it is those vibrational oscillations that are formed, by the plucking action of the multiplicit gauge-bosons upon the correlative multiplicit second-order light-cone-gauge eigenstates (which is here to form the here correlative Schwinger-Indices) -- that work to behave, in so as to work to form the exhibition of the four general forces of nature (these of which are -- the strong force, the electromotive force, the gravitational force, and the weak force).  This said plucking activity by the so-eluded-to E(6)XE(6) strings (these just mentioned strings of which act as the said gauge-bosons), works, as well, to help at making what would otherwise be a maxed-out Minkowski or holographic space (flat space), to instead, be a Hilbert or volume-based space.  (This would then work to help at making a 26 spatial dimensional world, instead, be a 32 spatial dimensional world -- for each of the three individually taken sets of parallel universes, that are here to exist in time and space.)  So -- it is the very nature, as to what helps to work to make a maxed-out flat-based space behave, instead, as a maxed-out volumed space, -- that works to form those vibrational oscillations, that are here to ripple along the Rarita Structure -- in so as to work to influence, as to what the correlative exhibitions are to be, as to the corresponding display of the four physical forces of space and time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Three As To Magnetic Flux Density

To recap from what was eluded-to before, each of the first-order point particles of any one given arbitrary Fadeev-Popov-Trace eigenstate -- will bear a viable reaction with that set of ghost-related Lagrangian-based traces, that are of the relatively proximal local light-cone-gauge eigenstate, as to the immediately prior interactions, in which the particle-related tense of discrete energy impedance had just interacted with the wave-related tense of discrete energy impedance -- when this is here to work to involve their Gliosis-based interactions that these work to bear, with the norm-state-projections that had surrounded these.  All ground-states, in general, work to bear a kinematic relationship with Fock Space, in such a continuously iterative manner, of which is here to be developed over a sequential series of group-related instantons.  Such a relationship is carried onward -- as the multifarious settings in which discrete energy interact in a Gliosis-based manner -- with less homotopically indical norm-states, is transferred into a perturbative shift -- as to the translation of the flow of the holonomic substrate, by which the nodes of space-time-fabric are brought through the arena of the netting of such said space-time-fabric, over time.  The Hilbert-related (volume-space-related) propagation of such a perturbative sifting of interconnected first-order point particles, that tend toward an inter-binding, by means of mini-stringular segmentation, is the general idea behind what cohomology is.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Heat And Gauge-Transformations

The overall process of both the creation of heat energy, along with the Ward-Caucy-related Fourier-based activity of the vibrational oscillations of heat energy -- in the form of both the creation of infrared photons in correlation with their vibrations, over time, as well as the Ward-Caucy-related Fourier-based activity of infrared photons in correlation with their vibrations over time -- works to involve a general genus of gauge-transformation, that helps to work to allow for a plausible tense of a Hilbert-related volume, instead of bearing a Minkowski-related volume, for those directly corresponding atoms, and, at a reverse-fractaled tense, for those directly corresponding molecules, that are to here be correlative to the general tense of such a so-eluded-to manner of space-time-based activity.  Furthermore -- those gauge-transformations that are most correlative to the dual activity of both the formation and the activity of infrared photons over time, acts in part, as that general genus of gauge-tranformation -- that works as part of the process by which the directly correlative orbifolds and orbifold eigensets, that are to here be most Yukawa to such a general tense of activity, -- may then be brought into a Ward-Caucy-related condition of then being more susceptible to bearing less than a purely holographic-based manner of spatial dimensionality.  This is partially due to the general tense of that "shimmering" of those correlative light-cone-gauge eigenstates -- that is to happen, when photons are in part, to scatter upon such eigenstates, in the process of what is here is to be related to the consequent formation of that form of electromagnetic energy, that is known of as infrared photons, or, in other words, of what is known of as heat energy.
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

Part 14 Of Session 12 Of Course 19 -- The Klein Bottle And Orbifold Differentiation

The torsional "orientifolds" that work to comprise that part of a worm-hole, that is just to the exterior of that general sector of its semi-anuulus-based section, works here in so as to form an integration of six different smoothly compiled two-dimensional surfaces, -- that come together in so as to form a torsional toroidal Minkowski Space, that is the equivalence of a heuristically majorized Hilbert Space (of a 12 spatial dimensional region of space).  This said integration of six general sets of two-dimensional flat space contours, works to act as a doubling-up of the initial dimensional compactification -- that exists from within what would exist in the Ward-Caucy-based bounds for the spatial dimensionality of an electron -- of which exists in what is known of as a d-field, and, a d-field exists in six spatial dimensions plus time (6*2=12).  I am here just referring to the bare minimum spatial dimensionality that is to exist for such fields in a minimum directly related Fourier-based differentiation.  So, when one takes the initial Laplacian-based condition of the 12-spatial dimensional Minkowski spatial contour of the ulterior Ward-Caucy boundaries that are of a worm-hole, and when we consider this as the divulging of a flat six spatial dimensional space that works to here complete its Mobiaty at both ends, in so as to form, in a sense, an arena of 12 spatial dimensions plus time -- to where the Lagrangian-based path of the said worm-hole will then work to form the equivalence, as well, of a heuristically majorized 10-dimensional field, -- that works to form those two extra sets of complex-roots, that work to pull (or to actually push), as an added Minkowski-based leveraging, in so as to work to project the propagation of phenomenology that moves relative to both the existence and the motion of electromagnetic energy -- to be "pulled" into the cross-product-based delineation of the respective given arbitrary contorsioning of space-time-fabric -- that is due to the wave-push of the Hamiltonian eigenindices of the so-stated worm-hole.  This acts as a sense of working to complete the second-side/second-edge of physical phenomenology, over the potential warping of space-time-fabric -- since the release of the spare energy from an electron is what works to form the holonomic substrate of electromagnetic energy.  This happens as is according to the Green Function via the Fujikawa Coupling.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Eight Of Session 12 Of Course 19 -- The Klein Bottle And Orbifold Differentiation

A worm-hole works to bear a set of orbifold eigensets, that differentiate in a Fourier-based manner in so  as to being a group-associated metrical-gauge-based Hamiltonian operator -- in so as to act, as well, as one overall Hamiltonian operand -- that behaves as one overall general genus of what may here be considered as the equivalece of a field-based transmitter, that also works to pull those phenomenology of a holonomic substrate that are to initially enter the depth of the semi-anuulus-based region of the said worm-hole, through a controrsioning or in other words throgh a bending of space-time-fabric, that works to translate the so-eluded-to Gaussian indices of the said entering holonomic substrate, in a kinematic manner, that pulls these said individually taken spaces through a mappable Lagrangian-based path, in a kinematic manner, into what would here tend to end-up being a completely different spatial region as to the destination-based volumed region where the so-stated holonomic substrate of entry is to end-up exiting the said worm-hole at.  This happens, in so as to make a projection of a Njenhuis tense of a Doubolt cohomological-based mappable tracing -- as to the physical mapping of the trace of one entity that is to then be transferred from one physical locality to another -- to happen, via what would mainly be due to the Fourier-based differentiation of a Minkowski-based bending of space, that is to here convey a directly corresponding Gaussian set of physical indices that are to here be translated from one spot to another -- in what would tend to be a difference of the equivalence of practically zero terrestrial-based time.  The spatial complexity of the Njenhuis tensorism of such a spatial contorsioning, would tend to involve two more sets of complex roots per eigenpulse of the self-same given arbitrary worm-hole, than the Real Reimmanian-based translation for a p-field would otherwise tend to bear, when this is taken under its directly corresponding Ward-Caucy-based conditions (this being that of the respective given worm-hole) -- which would here tend to make such a general state of a worm-hole to act as the equivalence of a heuristically majorized Hilbert Space.  To Be Continued!  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Gauge-Bosons And The Completion of the Second-Side/Second-Edge

The substringular multiplicit Ward-Caucy condition of Mobiaty, works to pull-in the multiplicit second-side/second-edge of the multiplicit topological stratum of the overall physical realm, mainly by both the Laplacian and the Fourier-based activity of gauge-bosons -- during the activity that is of the said gauge-bosons, that happens during each succeeding iteration of group-related instanton, particularly during each succeeding iteration of the multiplicit activity of BRST.  It is the light-cone-gauge eigenstates, that act as the relative multiplicit starting point of the activity that happens along the Rarita Structure, and, it is the gauge-boson eigenstates, that act as the relative multiplicit ending point of the activity that happens along the Rarita  Structure.  Even though homotopy tends to be maintained, during each succeeding iteration of group-related instanton -- the interconnection that exists in-between the multiplicit gauge-boson eigenstates and their correlative light-cone-gauge eigenstates, is functional by the activity of the "plucking" of the multiplicit light-cone-gauge by the said gauge-bosons.  Gauge-Bosons are E(6)XE(6) strings -- of which are of a heterotic substringular nature.  A maximum Minkowski or flat space, may have up to 26 spatial dimensions plus time.  Each set of universes (of the overall three sets of universes),  works to exhibit up to 32 spatial dimensions plus time.  The potential Mobiaty of space-time-fabric would be a holographic space -- that would work to contain up to 26 spatial dimensions plus time.  Yet, the so-stated plucking of the so-stated second-ordered light-cone-gauge bosons by their directly corresponding gauge-bosons, works to help at keeping the substringular fabric of each universe to remain in accordance of having the Ward-Caucy conditions of bearing a total of, instead, 32 spatial dimensions plus time.  So, it is the activity of the gauge-bosons -- in so as to have the said gauge-bosons act upon the multiplicit light-cone-gauge, in so as to work to form Schwinger-Indices -- that acts upon the multiplicit Rarita Structure, in such a manner in so as to complete the "second-side/second-edge" of the physical potential existence of Mobiaty of space-time-fabric, -- in so as to make the overall foundation of space-tim-fabric to be of a Hilbert or volume-based manner of construction, instead of being of a holographic Minkowski or flat-based manner.  It is this so-eluded-to covariant light-cone-gauge quantization, that acts in so as to make space-time-fabric work to bear both Minkowski-based characteristics and Hilbert-based characteristics, over time.
To Be Continued!  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Part Three of Session 8 of Course 19 -- The Klein Bottle and Orbifold Differentiaton

Let us say that one were to double supremumize a postulative sphere,  -- that worked to bear an initially added spatial parameter of dimensinoality, that would here be of a radial-axion-based manner.  Let us than say that one were to double supremumize a postulative sphere -- that worked to bear an initially added spatial parameter of dimensionalilty, that would here be of an orbital-axion-based manner.  Let us then say that one were to then double supremumize a postulative sphere -- that worked to bear an initially added spatial parameter of dimensionality, that would here be of a transversel-axion-based manner.  A supremum works to add three spatial dimensions to an extrapolated phenomenology.  So, a double supremumization works to add six spatial dimensions to an extrapolaed phenonology. Let us now consider a postulative integration of all three of theses ten dimensional spaces -- these spatial parameters of dimensionality, of which would here work to involve a Hodge-based adding of all of the resultant dimensional-based indices, as in the form of a compactification of all of the directoral-based topological sways that would here be necessary, in so as to work to form a potential extrapolation of an orbifold that would then be existent in a Fourier-based manner in 30 spatial dimensions plus time -- in any kinematic-based setting in which such a so-eluded-to extrapolation of an orbifold would then be moving through a discrete Lagrangian, through its here directly corresponding Hamiltonian operand, over the respective given arbitrary time period in which such an eluded-to extrapolation of a respective given arbitrary set of superstrings that operate in so as to perform one specific function would exist as such.  Now, let us say that a perturbative substringular force were to form a then resultant exterial tensoric topological sway -- that would then work to pull as a Minkowski-based Njenhuis wave-tug-wave-pull, that would cause a torsional-based rocking of the initially so-stated 30 spatial dimension-related extrapolated orbifold-based phenomenology. -- as the said orbifold that I have here denoted as potentially existent, would be moving in time and space, through a then resultant Njenhuis Hamiltonian operand that would work to bear a Doubolt cohomology -- that would then be spontaneously existent in the relatively proximal field that is of the directly corresponding Majorana-Weyl-based field, that would be directly related to the relatively locally cyclically permutative indices, over time. The then resultant Fourier-based covariant, codeterminable, and codifferentiable space -- that would directly appertain to the correlative Ward-Caucy conditions of the combined existence and motion of the so-eluded-to orbifold eigenset of this given arbitrary case -- that would then work to involve a 32 spatial parameter-based dimensionality, over the correlative successive series of group-related instantons, in which such a said orbifold eigenset would be functionable as I have here described.  This here eludes-to the condition -- that an individual set of parallel universes works to involve a realm of 32 spatial dimensions plus time.  (A spatial dimension is Not to be directly confused with a layer of reality or a parallel universe.)  This would here correspond to the condition -- that an individual set of parallel universes works to bear an overall Minkowski space of a total of 26 spatial dimensions plus time, plus, an additional 6 Njenhuis-based dimensions, of which works in so as to complete the  "second-side, second-edge" of the Mobiaty of space-time phenomenology.  This works to make space-time-fabric of more of a volumed space than of a flat space, as the fabric of space and time is completed in its Laplacian-based flow, over time.  To Be Continued!  Sincerely, Sam Roach.

Part Five of Session Seven of Course 19 -- The Klein Bottle and Orbifold Differentiation

A supremumization, taken eight times, of a majorized initially pointal-based reference frame, or -- if one were to integrate an initially pointal-based reference frame 26 times spatially, under a Laplacian-based set of conditions -- one would get what would be the equivalent of a maxed-out Minkowski space, or, a maxed-out flat space, that would here bear 26 spatial dimensions, when this is not including time.  If one were to spatially integrate an initially pointal-based reference frame, 32 times spatially, under a Laplacian-based set of conditions -- one would get a Hilbert space that would here be maxed-out for the directly corresponding Ward-Neumman boundary conditions, that would here appertain to the correlative spatial dimensions of one set of parallel universes.  Another way of looking at things, is that a supremumization -- taken three times, of an initially one-dimensional-based reference frame -- will work to form a ten spatial dimensional reference frame, of which, when majored, will form the twelve-spatial dimensional field that is often correlative to the spatial dimensionality of a worm-hole. I will continue with the suspense later!  To Be Continued!  Sam.

Part Four of Session Seven of Course 19 -- The Klein Bottle and Orbifold Differentiaion

A supremumization is when one integrates a physical space into three extra spatial dimensions.  So, if one were to take a supremumization of a supremumization of an initial six spatial dimension-based Minkowski Space -- one will then have a twelve dimensional-based Minkowski Space.  Such a just eluded-to twelve-dimensional Minkowski surface or flat-based surface may often be considered as a volume-based space or a Hilbert Space,  instead.  (A Minkowski Space is a flat-based space, and, a Hilbert Space is a volume-based space.)  So, if one were to be initially considering a ten-dimensional Hilbert Space -- that is subsequently double-integrated into two additional spatial dimensions, into what will then be a twelve-dimensional Hilbert Space -- then, what this will here amount to, is the generally taken Laplacian-based condition of having the extrapolation of a majorization of a ten-dimensional volume-based space into a twelve-dimensional volume-based space.  One can have a flat space that may have up to 26 spatial dimensions, plus time.  The condition as to whether or not one is dealing with the consideration of either a flat-space or a Minkowski-based space or a volume-space or a Hilbert-based space, is whether or not one is either to be able to or to not be able to treat the space-time-based fabric in which one is to go through, over time, as a contortable sheet that is not viably travelled through in a transversel-based manner otherwise, or, instead, if one is to treat the space-time-based fabric in which one is to go through, as actually being a viably travelled through operand -- that would here be traveled through in a transversel-based manner, respectively.  A volume-based space or a Minkowski Space is most associated with a worm-hole that would -- in this case -- bear all of its additive source of velocity to the condition of the bending of space-time-fabric.  Yet, if any of the additive source of the velocity at all that is caused by the activity  of traveling through a given arbitrary worm-hole is due to a respective given arbitrary tense of a tachyonic propulsion, then, the manner of describing the nature of the space that would here be traveled through, would be a twelve-dimensional volume-based space or a twelve-dimensional Hilbert space -- when this is not including the dimensionality due to time itself.

The Sixth Part of Session 16 of Course 18 -- The Ricci Scalar and Kaeler Differentiation

When there is a tachyonic-based perturbation, in general, of substringular phenomenology, this general tense or genus of perturbation of superstringular-based entities, is projected by superstrings of discrete energy permittivity that work to bear a Njenhuis-based supplemental torsioning of the respective given arbitrary general locus in which such a tense of perturbation is intiated -- to where the resultant Lagrangian of the here directly correlative superstrings of the said discrete energy permittivity, will bear a specific respective given arbitrary Rayleigh-based scattering, which will result in a relatively annharmonic re-delineation of the so-eluded-to discrete entities of holonomic substrate that are thus pulled from a Noether-based flow into a tachyonic-based flow  This is to where the effect that this will have upon the here relatively local Hilbert spatially arrangements, will act in so as to have attributed to it a primed Njenhuis normalcy -- when such a tense or genus of a Njenhuis relationship, will behave in the so-eluded-to general format of perturbative activity, relative to the norm-conditions of the here multiplicit relationship of the resultant varied Klein Bottle eigenbase of this general type of case.  I will continue with the suspense later!  To Be Continued! Sam Roach.

A Little Explanation As To the Morphologies

What I mean by the condition that Neilson-Kollosh ghosts bear a "hyperbolically toroidal" shape or morphology, is that the toroidal-based nature of the ghost anomalies that work to comprise any given arbitrary Neilson-Kolosh cohomological-based set of indices, tends to slope either hyperbolically inward -- in a converging genus of mappable tracing -- or, these often may slope hyperbollically outward -- in a diverging genus of mappable tracing, as such a format or genus of a set of cohomological-based indices, that work to comprise any respective given arbitrary Neilson-Kollosh ghost anomaly, that may be traced in a mappable manner, through any given arbitrary Lagrangian-based path -- that the directly corresponding graviton or gravitino, that such a case scenario eludes to -- as such a respective given arbitrary graviton or gravitino is being propagated through, over time.  So, if one is dealing specifically with the Lagrangian-based path of a graviton -- the respective directly corresponding ghost anomaly that works to form the correlative set of cohomological-based indices -- will be formed in so as to make a mappable tracing of simply a given arbitrary toroidal-based configuration, that is either hyperbolically converging or hyperbollically diverging, that is homotopically Hilbert or volume-spaced, with an annulus --  throughout that region in whih such a ghost anomaly is formed, by the physical memory of the mappable tracing of the projection of the trajectory of the directly corresponding graviton, of this given arbitrary case scenario.  Yet, if one is, instead, dealing with the Lagrangian-based path of a gravitino, the respective directly corresponding ghost anomaly that works to form the correlative set of cohomological-based indices -- will be formed, in so as to make a mappable tracing, that may be extrapolated as being the shape of the perimeter of a given arbitrary toroidal-based annulus of a configuration that is either hyperbolically Minkowski or flat-spaced, in either a relatively holomorphic-based converging manner or in a relatively holomorphic-based diverging manner -- throughout that region in which such a ghost anomaly is formed, by the physical memory of the mappable tracing of the projection of the trajectory of the directly corresponding gravitino of this given arbitrary case scenario.  The reason being -- that, any given arbitrary graviton works to bear more of a transversal-based angular Hamiltonian-based fractal of momentum in the substringular, whereas, any given arbitrary gravitino works to bear more of a radial-based Hamiltonian-based fractal of momentum in the substringular.  To Be Continued!  Sam.

Part Three of the Ninth Session of Course 18 -- the Ricci Scalar and the Kaeler Metric

When any given arbitrary unfrayed superstring of discrete energy permittivity that is moving in a Noether-based manner is pulled transverselly in a discrete kinetic flow -- the holonomic substrate of the so-stated topological entity will then here bear a wave-tug/wave-pull that is propagated to the scalar magnitude of the Planck-Length, through the Ward-Caucy-based coniaxial of the net Hamiltonian operand, that may be described of as a traversal of 3*10^(-35) of one meter -- in either the resultant directoral Minkowski-based planar re-delineation for a transversel distribution that is of a flat-spaced transfer, or, in a resultant directoral Hilbert-based volume-related re-delineation for a transversel distribution that is of a volumed space transfer.  If the transfer of the integrative index-based coordinates of any given arbitrary superstring that is propagated in a directoal wave-tug/wave-pull is of a Minkowski-based manner, then, this is indicative of the re-delineated superstring that is completely flush in the directly associated redistribution of the so-stated index-based coordinates of the here respective given arbitrary topological entity of holonomic substrate that has here adjusted in position from one instanton to the next.  Yet, if the said transfer is, instead, of a Hilbert-based nature, then, the here eluded-to directoral-based wave-tug/wave-pull will then here involve a certain degree of a torsioning of the core-field-density that is Gliossi to the so-eluded-to superstring -- of this specific example -- at the Poincaire level.

Orbifolds that Alter in their Gaussian-Basis of Format

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