Nature Of Lagrangian-Based Paths And Conservation Of Homotopic Residue

 When an accelerating mass-bearing cohesive set of discrete energy quanta, is here to be spatially transferred -- via a unitary Lagrangian-based path -- then, each correlative individually taken dimensional-related variable, that is here to work to help in describing the nature of the directly corresponding homotopic residue, that is here to tend to be conserved, will consequently tend to work to bear a unitary directoral. When an accelerating mass-bearing cohesive set of discrete energy quanta, is here to be spatially transferred -- via a binary Lagrangian-based path -- then, each correlative individually taken dimensional-related variable, that is here to work to help in describing the nature of the directly corresponding homotopic residue, that is here to tend to be conserved, will consequently tend to work to bear a binary directoral. When an accelerating mass-bearing cohesive set of discrete energy quanta, is here to be spatially transferred -- via a tertiary Lagrangian-based path -- then, each  correlative individually taken dimensional-related variable, that is here to work to help in describing the nature of the directly corresponding homotopic residue, that is here to tend to be conserved, will consequently tend to work bear a tertiary directoral; etc... . To Be Continued! Sincerely,  SAMUEL DAVID ROACH. (1989).

Tree-Based Directorals Versus Commutative-Trace-Based Directorals

 The mathematical description of a given arbitrary escalating Lagrangian, that is here to be of a Clifford Expansion — tends to work to bear a set of tree-based Directorals; whereas, the mathematical description of a given arbitrary escalating Lagrangian, that is here to be of a Euclidean Expansion — tends to work to bear a set of commutative-trace-based directorals, — in the process of working to describe the flow of the cohomology, that is here to be of the correlative cohesive set of discrete energy quanta, that is here to be exhibiting the said Lagrangian, that is thence to be escalating in its general scalar attribute. SAM ROACH.

External Yukawa Field And The Kahler-Metric

Let us initially consider an orbifold eigenset, that is here to be reverberating at a general proximal local region.  When the immediately external Yukawa field, is to alter in its directoral-related net scalar amplitude of angular momentum, over time, as this is here to be taken, when in terms of that  attribute of the Kahler-Metric, that is of the wave-tug that is to be applied upon the topological stratum of the here stated orbifold eigenset, in a Gliosis-related manner -- this will consequently often tend to cause the initially stated orbifold eigenset to perturbate out of the here mentioned inferred tense of a reverberation-related mode.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Tree-Amplitudes And Knotted Phenomenology

The higher that the order of genus of a Tree-Amplitude-related directoral is to be, for any given arbitrary Ward-Cauchy-related cotangent bundle of holonomic physical phenomenology, the more knotted that such a said respective Ward-Cauchy-related cotangent bundle of holonomic physical phenomenology will tend to be -- at its respective internal reference-frame.  Sincerely, Sam Roach.

Polarity Of Legendre Homology

Let us initially consider a tense of a discrete overall quantum of Legendre homology, that is here to be delineated by the generation of the Lagrangian-related activity of an electromagnetic source.  Next, let us say that the voltage (energy per charge) that is to be directly associated with the said electromagnetic source, is to be of a positive polarity. This will then mean -- that the directoral-related angular momentum of the earlier mentioned delineated Legendre homology, will be directed as a cross-product-related operation of kinetic energy, -- to where the kinetic energy that is here to be produced by the said electromagnetic source (in the form of voltage, or, energy per charge), will here be directed relatively outward.  However, -- if the voltage is to, instead, to be directly associated with a negative polarity, then, this will mean -- that the directoral-related angular momentum of the so-eluded-to Legendre homology, will then, in this ulterior case, be directed as a dot-product-related operation of kinetic energy, -- to where the kinetic energy that is here to be produced by the said electromagnetic source (in the form of voltage, or, energy per charge), will here be directed relatively inward.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Spinors And Dilatinos

Take the expression for the euclidean expansion, that is of any one given arbitrary Majorana-Weyl-Invariant-Spinor eigenstate -- that is of cotangent bundle R4.  This just mentioned expression -- of which is here to be in terms of its scalar amplitude, is here to be considered when this is coupled while from within the framework of its directoral-related conditions.  The respective externalized reference-frame, via which this said eigenstate that is spinning in a back-and-forth manner at an internal reference-frame -- is here to be, as well, propagating through a Lagrangian-based path in a kinematic manner, via a Fourier Transform as a Hamiltonian operator, in a transversal manner, over time.  Now -- couple the said expression for the euclidean expression of the said spinor, with both the brief time that it is propagating through as it is traveling (as is it is spinning) along the course of its said Lagrangian-based path, AND a pointal-related mass, AND the average angle that the here mentioned spinor is to be spinning in a back-and-forth manner through, as it is spinning via a central coniaxial.  At this point in derivation -- the just eluded-to metric-gauge-related pulsation per cubic directoral-based meter -- that is here to be resulted in, may be thought of as a dilatino.  The consideration of meter that I have mentioned here, is generally to be conveyed, via the usage of the correlative Hodge-based indices that are of any one respective given arbitrary case. Such so-eluded-to Hodge-Indices, are to directly correspond to the correlative litigee of directorals, that are here to be most applicable to the coherent Ward-Cauchy-related situation of such a general genus of a case.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Solution 8 Of Test 2 Of Course 20

From the time that any one given arbitrary photon is to be scattered, until it is re-quantized back into a beam of light -- such a so-eluded-to entropic photon, is here to toggle from being delineated at a Laplacian-based extrapolation, in an orthogonal manner from its initial directoral-related tense of holomorphicity, -- as one may trace such a delineation from the point of scattering up to the covariant positioning at which it is to ensue in so as to re-quantize back into a beam of light, to then toggle back into being delineated at a Laplacian-based extrapolation, that is here to then be able to be extrapolated as working to bear a tense of holomorphicity, --  that is in a general linear distribution from where the photon was to have been scattered, up to the covariant positioning at which it is to re-quantize as I have mentioned earlier, back to toggling back into the earlier mentioned general genus of orthogonation ( a tense of Ward-Polarization, that may be traced in an extrapolation from its space-related point of scattering up to where its is to be re-quantized), and so-on, -- until the here initially stated entropic photon, is to be brought back into the beam of light as a Yang-Mills-related topological phenomenon that is here to bear partially Yau-Exact singularities. (To where the said photon is to go back into being as a standard discrete quantum of electromagnetic energy over time.)
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

Stuff About Resultant Holomorphic Direction

Each superstring of discrete energy permittivity -- that works to comprise one given arbitrary orbifold eigenset, is to work to bear one potential tense of a directoral-based holomorphic tendency.  When all of these tendencies are to work upon each other -- this happens, in so as to "co-operate" as to then to be acting as a resultant directoral-based holomorphic tendency for the said overall orbifold eigenset.  The so-eluded-to resultant holomorphic direction of the given arbitrary orbifold eigenset, will be in the direction of the angular momentum of the so-stated eigenset, to where this phenomenology is to then to move through its resultant Hamiltonian operand -- via the correlative Lagrangian-based path.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Two Of Field Genus And Holomorphic Direction

In so long as there are no external anomalous forces that are here to be applied in a viable Yukawa manner to either an f-field, a d-field, or a p-field, -- an f-field will generally bear a high expectation value of working to bear its respective set of potential holomorphic directoral tendencies, a d-field will generally bear a high expectation value of working as well to bear its respective set of potential holomorphic directoral tendencies, and a p-field will generally bear a high expectation value of working as well to bear its respective set of potential holomorphic directoral tendencies.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Two Of Black-Hole "Blow-Torches"

When holonomic substrate from black-hole "blow-torches" exit the apex-like end of an individually taken black-hole, this antimatter is then acted upon, in so as to convert the effectual De-Sitter/Ante-De-Sitter gravitational directoralization that is of its associated Ricci Scalar, into an Ante-De-Sitter/De-Sitter gravitational directoralization that is of its associated Ricci Scalar -- at that general point in time.  Yet, in this case, the illumination of the described "blow-torch" is then to work to form an eminent tense of impedance, upon what may be described of metaphorically as a "jet-stream," to then to work to convert the given antimatter into matter.  Again, the cohomological binding of multiple "blow-torches" may often work to form a supernovae, which, when perturbated upon in a Dirac-like manner, may often work to form a Nebulae.  In either case, some phenomena that is frayed in a black-hole, is tugged-in by the consequent tremendous gravity -- while then being converted into an anti gravitational phenomenon, that is then "spit-out" of any given arbitrary said black-hole.  Disorganized material phenomena that is "spit-out" will then exit the wide end of a black-hole -- while disorganized anti-matter-related phenomena will, instead, exit the apex-like end of a black-hole.  In either case, such "blow-torches" often accumulate -- in so as to work to form supernovas, of which often work to form Nebulae, that redistribute material phenomena through the universe.  This is not the only way supernovas are formed, though.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Holomorphic Direction Of Orbifold Eigenset

Let us consider the tendency for the holomorphic direction, of any one given arbitrary discrete energy quantum, that is of one particular genus of such a discrete quantum of energy.  (P.S.  The following is a general theoretical condition, in so as to help at eventually being able to understand what one is to be working towards, when one is here to be considering an actual case scenario).  Let us next, consider that there is to be a relatively large Hodge-Index -- as to the number of those discrete quanta of energy, that are to here to be present, from within the Ward-Cauchy-based bounds of one respective given arbitrary orbifold eigenset -- of which are to each be of that same general genus of discrete energy quanta, that the respective initially mentioned discrete quantum of energy was of, that I had brought-up at the beginning of this given post.  The influence that is to then to be attributed towards the holomorphicity of the respective given arbitrary orbifold eigenset, that is of the general genus, that is of the initially so-eluded-to genus of discrete energy quanta that I had inferred at the beginning of this post, will then tend to be the resultant average holomorphic direction, that is to then to be attributed to the net mean Lagrangian path, that one is to be able to extrapolate, -- when one is given the overall differential geometry that is to here to be related to the initial Laplacian-based Ward-Cauchy conditions -- that are here to be in correlation to the differential geometry of the initial substringular conditions, via which motion of the discrete energy quanta of the said orbifold eigenset is to be Yukawa to, over time. This will then help one to be able to then have a better ability to extrapolate the ensuing directoral-based holomorphicity of such a case, of the here said given arbitrary orbifold eigenset, over the ensuing sequential series of group-related instantons. I will continue with the suspense later!  To Be Continued! Sincerely, Sam Roach.

Electrons And Holomorphic Direction

Let us initially consider an electron.  Furthermore, let us consider the mass-bearing superstrings of an electron, -- as such Calabi-Yau-based superstrings of discrete energy permittivity are to exist here, in so as to work to come together as part of the said electron, -- to where the electron, as a unit, is to act here as an orbifold eigenset.  Let us next consider an individual mass-bearing superstring of discrete energy permittivity, that works to help at forming the said electron, to where that electron of this case is here to act as an orbifold eigenset.  The Calabi-Yau field of such mass-bearing states, is to here to bear a proximal local shell-like toroidal-shaped cohomological-based surface, at the Poincare level to its external core-field-density.  The so-eluded-to Calabi-Yau eigenstate, that is here to act as a mass-bearing eigenindex, that is of the said electron, is to theoretically act in such a manner -- in so as to work to bear a tendency of tugging to bear its relatively forward-holomorphic direction in the mean Lagrangian path, that is to exist right in-between both the directoral-based delineation of the angular momentum that is in the direction of its edge, as well as also existing right in-between the directoral-based delineation of the angular momentum that is in the direction of its anuulus.  Next, consider the integration of all of the so-eluded-to mass-bearing superstrings of discrete energy permittivity, that are to theoretically comprise the "rest mass" of the so-stated electron.  Each of such Calabi-Yau-based strings is to tend to behave in such a way, to where these are to heuristically lean-in towards the multiplicit-based earlier mentioned mean Lagrangian path -- that lies in-between the multiplicit edge and the multiplicit anuulus of the so-eluded-to Gliosis-Sherk-Olive (GSO) toroidal-based cohomological-based field.  The resultant of such a tendency, is to then to work in part, to help influence, along with the main influences of its charge and its magnetic field in relation to the general protonic field that it is attracted to, -- the Ward-Cauchy-based conditions that are related to the general manner of the spin-orbital momentum of the said electron, over time.  I will discuss more later, -- the more prominent influences of charge upon the magnetic field of sub-atomic particles, -- which happens in so as to work more at helping at producing the spin-orbital momentum of an electron.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Cyclical Reverberations And Reference Frames, Part Two

Let us initially consider a given arbitrary orbifold eigenset, that works to be of a cyclical nature -- that works to reverberate via a relatively rectangular Lagrangian-based path, over time.  Let us say, once again, that such a cyclical reverberation is one that involves the tendency of working to bear a cyclical permutative tense -- to where, seeing that, over the course of each ensuing iteration of such a so-eluded-to reverberation, the relative respective Ward-Caucy-based angling of the said given arbitrary respective orbifold eigenset is mildly perturbative -- in so that the directly corresponding Stoke's-based depth that is here to be involved, will alter when in terms of the directoral-based tense of its correlative angular momentum-based indices, to where, at the so-eluded-to internal-based reference frame, the tense of such a cyclical permutative rectangular reverberation is mildly altered in its specific cohomological-based mappable tracing -- per each succeeding iteration of such a said general genus of this form of a reverberation.  Let us next say that the general motion of the spin-orbital-based momentum, that is to here be directly correlative to the wave-tug/wave-push of the Hamiltonian-based operation of the said orbifold eigenset, is to here be considered of as tending to go in the relative Njenhuis-to-forward-holomorphic directoral wave-based flow -- over the course of the correlative group-metric in which such a said orbifold eigenset is to be in the course of such a so-stated reverberation-based metrical eigenbase of a Fourier-related translation over time.  Next, let's say that -- from an external tense of a reference frame -- that the so-stated reverberating orbifold eigenset of such a case, is to, as well, be oscillating from being pushed initially into the relative norm-to-forward-holomorphic direction into then being pushed into the relative norm-to-reverse-holomorphic direction, over time -- to where such a so-eluded-to orbifold eigenset, from a given arbitrary external vantage-point, is to be oscillating in such a manner, as may be relatively considered of as oscillating in such a way that goes from moving relatively "up," to then moving relatively "downward" -- if the torsioning of the more planar-based kinematic context, that is of the reverberation of the said orbifold eigenset, is one that may be then considered of as to be said to be torquing to the relative "left"-related direction.
I will continue with the suspense later!  To Be Continued!  Samuel David Roach.

A Further Interim As To Session 2 Of Course 20 -- Calabi Manifolds Calabi Interactions

If the Ward-Caucy-based Yukawa Coupling, that is of one set of zero-norm-state-projections, that are to strike one superstring of discrete kinetic energy permittivity, in so as to work to form a photon via the Fujikawa Coupling -- is to strike the just mentioned superstring at one given arbitrary angle, as would here be subtended from in-between the correlative said set of zero-norm-state-projections and the correlative Fadeev-Popov-Trace eigenstate -- the directly corresponding angle, that is to here be delineated by the directly corresponding individually taken set of zero-norm-state-projections, that are to here strike the correlative counterstring of discrete kinetic energy permittivity, by which this is to result in forming the directly corresponding counterpart of the said photon, via the Fujikawa Coupling -- this will happen, to where this is to then be subtended by the same genus of a Ward-Caucy-based angle, from in-between the correlative said set of zero-norm-state-projections and the correlative core-field-density of the directly corresponding superstring, that was here initially mentioned as working to form the so-stated photon.  If the so-eluded-to angle of Gliosis-based strike, is to be either more acute or more obtuse than it should theoretically be, in so as to work to form the initially extrapolated tense of the holomorphic pulse -- that the soon forming photon and its counterpart were to have -- in order to not veer in its directoral-based propagation, then, the holomorphic direction of the soon propagated photon and its counterpart will contorsion, as I will soon explain later!

I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Cyclic Perturbations Of Noether Current

Let us initially consider an orbifold eigenset that goes from a tense of acceleration to a tense of deceleration, back to a tense of acceleration, and so on -- in such a manner to where the then apparent tendency of one going from a tense of acceleration to a tense of deceleration and back, is to be cyclical as well -- when this is taken in terms of the gradual process of going from an increase in the scalar amplitude of the velocity of the said arbitrary eigenset, into the gradual decrease in the scalar amplitude of the velocity of the said orbifold eigenset, and back.  So, the initial Ward-Caucy condition of the so-stated orbifold eigenset is in a state, to where the said eigenset is traveling at a respective given arbitrary rate.  The respective direction of the so-stated orbifold eigenset is through a constant unitary Lagrangian, via a Hamiltonian operand -- that works to bear no abrasion of tensoric-affiliated topological sway.  The  so-mentioned eigenset is to then accelerate relatively smoothly, up to a specific given arbitrary maximum velocity, while then decelerating relatively smoothly back down to the initially extrapolated velocity that works to bear its directoral-based translation -- as a disturbance in space-time-fabric that is being pushed ahead further and further through the so-stated progressive unitary Lagrangian.  As the so-stated cyclical-based perturbative-related tense of a Fourier differentiation, works to push the so-stated orbifold eigenset further and further along the same directoral-based Lagrangian -- both the Hodge-Indices of the holonomic substrate of the here given arbitrary retentive metrical-gauge-based Hamiltonian resultant -- that is successively indistinguishably different, and also the tense of the kinematic behavior of those eigenindices that work to comprise the so-eluded-to composite of the said resultant Hodge-Indices, is to here work to bear a constant succession of gauge-metrical cyclical operational functioning -- to where the chain of activities that is to here, be of the kinematic translation as to the qualitative functioning that works to form the cyclical tense of that behavior that is directly associated with the cyclical perturbation of the tense of the Majorana-Weyl-Covariance, that is of the so-stated orbifold eigenset, to where this is to repeat back-and-forth in this case, as if it were an eigenstate that is to repeat in a relatively deep Njenhuis quantum-associated "well."  (The relative "sides" of the orbifold egienset's flow is contained.)  As the tense of the said Majorana-Weyl-Covariance  is to fluctuate relatively smoothly, the correlative tense of the directly related Noether Current is to fluctuate relatively smoothly as well.  As this is happening, the tense of the related covariance is to then go form a relative loosening upon the eigenindices of its Hodge-Indices, into a relative tightening upon the eigenindices of its Hodge-Indices. I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

What A Hamiltonian Operation Is

Let's say that one were to have an orbifold eigenset, that consisted of multiple orbifolds.  Let us now say that the said orbifold eigenset were to be differentiating in a Fourier-based manner through a discrete Lagrangian.  Let us next consider each individual orbifold that were here to work to comprise the so-stated eigenset of orbifolds -- to be of a different respective genus of superstringular vibration at the Poincare level of the individual superstrings of discrete energy permittivity, that works to comprise the discrete energy quanta that are put together in so as to work to form the said orbifold eigenset.  Le us then call each individually taken genus of superstring that bears a different Gliosis-based oscillation from the others -- or, in other words, let us then call each of the individually taken orbifolds that work to comprise the so-stated orbifold eigenset, a different symbol.  Although the overall orbifold eigenset of such a case may here be considered as a Hamiltonian operator -- each individually taken orbifold that works to comprise the said operator, may be here termed of as an eigenmember of the so-stated Hamiltonian operator.  Next -- take the scalar amplitude/scalar magnitude-based Hodge-Index of each individually taken eigenmember that I have here eluded-to, and put this into a mathematical format by which it will be worked upon as an eigenbasis.  If the orbifold eigenset as a whole works to bear an even chirality amongst its constituent members, then, fill-in the "Jacobian eigenbasis" with 1s ("ones") -- in so as to treat this now as a determinant that may then be solved for.  Yet, if the orbifold eigenset as a whole works to bear an odd chirality amongst its constituent members, then, fill-in the "Jacobian eigebasis" with 0s (zeros) -- in so as to treat this now as a determinant that may then be solved for.  The resultant multiplets will then be the directoral-based scalar amplitude or scalar magnitude of the delineatory index of the correlative Hamiltonian operation.  I will continue with the suspense later!
To Be Continued!  Sincerely, Sam Roach.

Part Four of Session 12 of Course 18 -- The Ricci Scalar and the Kaeler Metric

In light of the last post that I put into the computer, when a non-tachyoinic-oriented orbifold is to bear a nature of a spin-orbital-based metrical index, the motion of the said orbifold is to only move in such a so-eluded-to spin-orbital-based manner, by the scalar amplitude that works to correspond to the distance of one Planck-Radii.  This is from whatever its initial locus of iteration is to be at, over the course of going from an initial iteration of group-related instanton -- to its immediately succeeding locus of iteration is to be at, over the course of its here given arbitrary second iteration of group-related instanton.  Such an eluded-to re-delineation is to happen through the Hamiltonian-based operand, in which the so-eluded-to set of superstrings that operate in so as to perform one specific function are to be re-positioned -- to where the so-stated re-distribution will here work to move in the Lagrangian of the said orbifold, as would here be in direct consideration of the wave-tug/wave-pull that the so-eluded-to directoral permittivity of the so-stated superstrings, that work to comrpise the said orbifold, are to pulled into.  This is to happen in the general direction of what would here work to appertain to the course of optimum rest or least resistance.  Likewise, if any cohomology that is not tachyonic, that is to be re-delineated in a transversal-based manner -- over the course of two given arbitrary respective succeeding iterations of group-related instantons, will be pulled in such a manner -- in so that the scalar amplitude, that would here directly appertain to the distance in which such a set of ghost-based indices is to be re-delineated, will be re-distributed by a magnitude of one Planck-Length.  This would here work to elude to the condition that the Hamiltonian operand, in which such a set of ghost-based indices will here be re-distributed by, over the course of the two so-stated succeeding iterations of group-related instantons, to where this will bear a wave-tug/wave-pull -- that will be brought through its correlative Lagrangian by a distance of the said scalar amount of a Planck-Length.  This will happen in the general direction of the directoral topological sway, that is in the manner of optimum rest or least resistance.  Also, as with an orbifold, any cohomology that is not tachyonic -- that is to be re-delineated in either a radial-based manner and/or in a spin-orbital-based manner, over the course of two given arbitrary succeeding respective iterations of group-related instantons, will be pulled in such a manner -- in so that the scalar amplitude that would here directly appertain to the distance in which such a set of ghost-based indices is to be re-delineated, will be re-distributed by a magnitude of one Planck-Radii, respectively, per each of such potential genre of delineation.  Again, this would here work to elude to the condition that the Hamiltonian operand, in which such a set of ghost-based indices will here be re-distributed by, over the course of the two so-stated succeeding iterations of group-relataed instantons, will bear a wave-tug/wave-pull that will be brought through its correlative Lagrangian, by a distance of the said scalar amount of a respective Planck-Radii, either radially and/or in a spin-orbital-based manner -- in the  general direction of the directoral topological sway, that is in the manner of optimum rest or least resistance.
I will continue with the suspense later! To Be Continued! Sincerely, Sam Roach.

Lorentz-Four-Contractions and Orbifolds

If a given arbitrary physical phenomenon moves through either a binary or a tritiary-based Lagrangian, in the process of traveling at such a velocity to where the said physical phenomena bears a Lorentz-Four-Contraction of two for either the two spatial dimensions that are appertaining to that eluded to motion that is going through a binary Lagrangian, or, for those three spatial dimensions that are appertaining to that eluded to motion that is going through a tritiary Lagrangian, then, these two or three respective given arbitrary spatial dimensions will be the ones, of the said physical phenomenon that has here been eluded to as moving as such, that will be contracted to the scalar amplitude of two in both respective given arbitrary cases.  This is given the conditions of this bilateral given arbitrary set of cases, in which the eluded to formats of physical scenario involve one or more additional spatial dimensions than those that are here moving, in each respective case, in such a manner in so that all of those spatial dimensions that are here directly involved with the directoral pull of each individual case of the kinematic flow of the two so-stated Lagrangian spatial delineations over time will thence be contracted to the same degree of scalar amplitude.  This is because the velocity of each of the spatial dimensions that are directly associated with each of the eluded to kinematic flow geni in both respective cases are moving at the same eluded to velocity -- to where the Lorentz-Four-Contractions of each of the just eluded to parametric-based spatial dimensions that are contracted are thus contracted to a scalar factor of two.  Such a general format of motion would then here involve a typically hermitian-based format of spatial curvature -- over that duration that would here involve the Hamiltonian operation of the eluded to physical phenomenon that is moving through either a binary or in a tritiary-based basis of Lagrangian-based space, in which the said genus of both individual respective Hamiltonian operands that are crossed during the process of the transversal motion of the said physical phenomenon over time is moving in a curvature that changes in either the same number of spatial derivatives or less than the number of dimensions that it is moving in in an operand-based tense over a sequential series of instanton, to where the then here present existence of Chern-Simmons singularities is minimal -- these just mentioned geni of singularities would only exist here if there is a metrical spur in the kinematic-based harmonics of the motion of the eluded to general format of physical phenomena.  To Be Continued!  Sam Roach.

About Electromagnetic Wavelengths

A photon that is propagating in a line that is straight -- when in multiconsideration of the condition of space-time-curvature -- bears both a spin-orbital momentum and an angular momentum that is operational during each succeeding propagation index of the said photon, as it travels in the so-stated straight manner in a vacuum.  Any photon and/or beam of photons that is traveling in an unperturbated manner through a vacuum over time moves in a manner that is straight -- when one considers the euclidean Ward-Caucy conditions of a propagated beam of electromagnetic indices that exists here as a quantized set of one or more photons that operate in so as to perform a given arbitrary function -- of the propagatorial delineations that work to allow for electromagnetic energy to behave as it does.  As a partial index of a beam of light, in this here given arbitrary scenario,the index acts as a photon that is pulled in a manner that is terrestrially straight over time at an even velocity (this photon, in this case, is transmitted linearly over time), the said photon -- although bearing no Lagrangian-based Chern-Simmons singularities due to the condition of here not being perturbated from its direct path -- by neither scattering, torsioning, nor a relatively circular wave-tug/wave-pull, does bear a partially hermitian tense of delineation.  This is due to the condition that the pulse of the individually so-stated photon -- per each static-based considered coniaxial settings of the said photon -- at each smoothly metrical locus to where the pulse of the said photon goes from increasing in the speed of its spin at certain even intervals, at the directly corresponding group instantons, in which both the coniaxial-based spin-orbital momentum and the coniaxial-based angular momentum at the directly corresponding instanton-based intervals, into altering in so as to be decreasing in the speed of its spin at certain even intervals at the directly corresponding group instantons.  This is to which both the coniaxial-based spin-orbital momentum and the coniaxial-based angular momentum at the directly corresponding instanton-based intervals forms a spurious condition of cetain respective elongated to decremented pulsations, while then doing a similar spin-orbital operation at an isometrically stable set of intervals -- yet, with the direction of the angular momentum bearing a directoral wave-tug/wave-pull that is then directed in the relatively reverse holomorphic direction of the here continued holomorphic directoral-pull of the so-stated photon.  The whole distance as to the even increase to decrease of static Hamiltonian thrust, that then bears the same even increase to decrease of static Hamiltonian thrust, yet, with the alteration of the angular momentum pull of the mentioned photon going from pushing in the direction of the photons permittivity into pushing in the direction of the photons impedance -- is the distance of the wavelength of whatever the wavelength of the given arbitrary photon is.  The wavelength of a beam of light is a measurement of the fluctuation of the electric field that is directly associated with a given arbitrary genus of electromagnetic energy.  So, if a form of electromagnetic energy was, for instance, 159nm, for one-fourth of this distance -- the photons that work to comprise the eluded to beam, that goes detectibely straight to our observation in a vacuum -- each partial of photonic basis, each of such photons, gradually -- in an even manner -- increase in their Hamiltonian-based thrust over the course of 3*10^8 iterations (yet over a set of group actions that each are comprised of very many group instantons), each of which happen over many actual instantons.  This increase in thrust bears no Lagrangian-based topological sway of the photons, and, this, as well, does not alter the so-stated condition of the photons hermicity.  Then, for the second quarter of this wavelength, the Hamiltonian-based thrust is gradually and evenly calmed by a factor of 3*10^8 -- in so as to go back to is most relaxed condition of spin-orbital momentum.  For the second half of the activity that the here given arbitrary photon works to complete its wavelength, the difference in the pulsation of the photons at the Poincaire level of their kinematic differentiation is only different, due to the direction of the angular momentum being pulled in the direction of the impedance of the photon, instead of the initial directoral-based angular momentum pull being directed in the direction of the permittivity of the just mentioned photon.  For this whole wavelength, the so-stated photon is moving, as a whole, in the relatively forward-holomorphic direction.  For any other electromagneitc wavelength, such a tendency is similar, but, the distance to complete such a cycle here would alter -- in proportion to the difference in so as to what the other given arbitary wavelength of the electromagnetic energy here is. The increase of Hamiltonian-based thrust in the pulsation of a photon forms infinite Chern-Simmons singularities, while, the decrease of Hamiltonian-based thrust in the pulsation of a photon forms infinitessimal Chern-Simmons singularities. To be Continued.
I will continue with the suspense later!  Sincerely, Samuel David Roach.

Inverse To Photon Formation

When a photon is converted back into a discrete unit of plain kinetic energy, the inverse of the Fujikawa Coupling happens via the inverse of the Green Function.  This is a given arbitrary example of a bosonic superstring converting back into a fermionic superstring.  So, this is a given arbitrary example of a closed string converting back into an open string.  In this case, the genus of norm-state projection that initializes the said format of transformation is a zero-norm-state projection that exists at the relatively forward-holomorphic directoral basis, and, the genus of norm-state projection that works at actually opening the initial closed superstring exists at the relatively reverse-holomorphic directoral basis.  So, here, the impedance of the inverse of such a format of Yakawa Coupling (here, this is an eigenmetric of the inverse of the Fujikawa Coupling) happens in the relatively holomorphic direction, while, the said coupling that is being discussed in this given sentence has permittivity that happens in the relative reverse-holomorphic direction.  This is the corralary of the Fujikawa Coupling.  This works to cause an initally vibrating hoop of discrete energy permittivity to be converted into a vibrating strand of discrete energy permittivity.  I will  continue with the suspense later!  Sincerely, Sam Roach.