Homology Into A Cohomology

A zero-norm-state-projection that acts as a group-attractor, that is coming from the reverse-norm-to-holomorphic side of an individually taken homology that is isotropically unstable yet harmonic in its parametric topological sway, -- if it is moving in a direction that is most symmetric with the holomorphic eigenmetric of the so-eluded-to topological sway of the discrete open-loop that is working to form the mentioned homology, will tend to cause a Yukawa Coupling -- that will work to close the said open-loop via the Green Function, in such a manner that is hermitian, such as in the Fujikawa Coupling, yet in this case such a proscribed tense of activity works to involve here the closing of an initially open-loop Ward-Cauchy-relateld phenomenology, instead of working to close an open substringular strand.  This will tend to work to help at converting the said homology into a cohomology.I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

More As to The Idea Behind Substringular Recycling

Mini-Stringular segmentation is a general genus of phenomenology -- that is constantly being fed both into and out of both superstrings, first-ordered point particles, norm-state-projections, along with such a general genus of phenomenology as well as also being fed into other Ward-Cauchy-related phenomenology.   Such a constant re-distribution of mini-stringular segmentation, is part of what works to recycle substringular ground-states to norm-states -- and vice-versa.  Mini-Stringular segmentation is both: what works to form the holonomic substrate of substringular fields, what works to form the "yarning" of first-ordered point particles, what works to form zero-point-energy, etc... .  As far as I can currently surmise, the smallest phenomenology that can be divied-out, is on the order of mini-stringular segmentation.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Recycling Of The Residue From Annharmonically Scattered Cohomologies

In the process of the Fourier-related translation of Gaussian Transforms, -- the Rayleigh scattering of GSO cohomological eigenstates that are formed on the relative multiplicit Real Reimmanian Plane, works to form a general tense of Ward-Cauchy-related residue, that is replenished by that general tense of Ward-Cauchy-related residue, that is formed by the Rayleigh scattering of Neilson-Kollosh cohomological eigenstates, that are, instead, to be formed off of the relative multiplicit Real Reimmanian Plane.  This happens in such a manner, to where such residues act, in so as to work to form a tense of a system of substringular or Ward-Cauchy-related recycling, over time -- in so as to help-out in the process of that general multiplicit freeing-up of room in the substringular, that is needed in order for each eigenstate of Hamiltonian operation, to be able to both persist and exist, as eigenindices of discrete energy that act in so as to allow for both the persistence and the existence of energy at all.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Gaussian Transformations Versus Kahler-Metric

I have often mentioned as to what Gaussian Transformations are, in leu of what it means to when a discrete quantum of energy is Gliosis to the Kahler-Metric.  Here is the difference between what each of these two ideas are, as I have tried to describe.  Gaussian Transformations refer to the condition of Hamiltonian operators of space -- relating to the existence of other Hamiltonian operators of space -- in so as to make room for the multiplicit Hamiltonian operators of space, so that spatial eigenstates may be able to freely move around enough, in order for spatial eigenstates to be able to both persist and exist over time.  Discrete quanta of energy being Gliosis to the Kahler-Metric, refers to that general activity that is to happen -- in order for those fractals of discrete energy to be re-attained by substringular eigenstates of energy, so that discrete energy may both persist and exist over time.  What I have just mentioned as the general "activity" of Gaussian Transformations is necessary, because space needs to often be "sturdied-up" in order for Hamiltonian operators of space to be able to viably relate to each other.  Furthermore, what I have just mentioned as the general activity of superstrings being Gliosis to the Kahler-Metric -- is necessary, because even though discrete energy is theoretically fully efficient, it actually is extremely close, yet not literally, 100 percent efficient.
I will continue with the suspense later!  To  Be Continued!  Sincerely, Samuel David Roach.

A Little More As To Homology Versus Cohomology

Substringular Ward-Cauchy-related physical memories, that are conical in their mappable-tracing -- tend to be of the nature of being homologies -- that generally tend to be made by open-strands of stringular phenomenology.  Whereas, substringular Ward-Cauchy-related physical memories, that are toroidal in their mappable-tracing -- tend to be of the nature of being cohomologies -- that generally tend to be made by closed-loops of stringular phenomenology.  Furthermore, substringular Ward-Cauchy-related physical memories, that are semi-toroidal in their mappable-tracing -- tend to be of the nature of being homologies -- that generally tend to be made by open-loops of stringular phenomenology. I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Examples Of Open Loop Phenomenology

Let us consider two different cases of Ward-Cauchy-based open-loop phenomenology, that exist in the sub stringular -- of which act in such a manner, that may be described of as a manner of being "hook strings."  Let us initially consider the first one that I had in mind.  There is the case of a sub stringular open-loop, that acts as an eigenindex of its own genus of Hamiltonian operation, that is isotropically stable.  This may be termed of as being a "1+1" string (not to be confused with a "2 dimensional" string).   It tends not to bear any significant topological-related torsioning across the "width" of its parametric dimensional symmetries.  There is, as well, the case of another sub stringular open-loop, that acts as an eigenindex of its own genus of Hamiltonian operation, that is isotropically unstable.  This may tend to be termed of as being a "2+1" string (not a 3 dimensional string).  This, on the other hand, tends to bear a significant topological-related torsioning across the "width" of its parametric dimensional symmetries.
I will continue with the suspense later!  To B Continued!  Sincerely, Samuel David Roach.

Homology Versus Cohomology

Here is the basic difference between what a homology is, versus what a cohomology is:
A homology is the physical memory as to the when, the where, and the how, that either an open substringular strand or an open substringular loop has differentiated, as a Hamiltonian eigenindex, over time.  A cohomology is the physical memory as to the when, the where, and the how, that a closed substringular loop has differentiated, as a Hamiltonian eigenindex, over time.  Such physical memories may be anywhere from being at a proximal locus, that is just external to the core-field-density of the superstring -- in other words, at the Ward-Cauchy-based field that is just external to the topological stratum of the substringular eigenindex, -- to being as a physical memory that may be extrapolated from the effect of such a respective strand or a loop, that has here to have just potentially differentiated through a Lagrangian that may be mapped-out, over a Fourier Transform that involves a sequential series of instantons.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Hamiltonian Wave-Tug Of Norm-State-Projections

Let us here consider either a Campbell, a Hausendorf, or a Campbell-Hausendorf norm-state-projection -- that is here to strike a zero-norm-state-projection, in a Gliosis-based manner, -- over the course of one relatively brief even gauged-metric.  Since the zero-norm-state-projection only involves both one first-order point particle at its relative norm-to-forward-holomorphic end, and one first-order point particle at its relative norm-to-reverse-holomrphic end, -- whereas both Campbell, Hausendorf, and Campbell-Hausendorf norm-state-projections, always tend to work to involve a greater Hodge-Index of first-order point particles at at least one of their two segmentation-related ends --- the respective norm-state-projection that is not eminent as a zero-norm-state-projection, will tend to bear a dominant Hamiltonian wave-tug upon the said respective zero-norm-state-projection.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Gravity Waves And Holomorphicity Of Impact

When one is to be considering the general angle, by which any one given arbitrary respective photon is to strike the externalized core-field-density of the correlative light-cone-gauge eigenstate -- that it is to come into contact with, in a Gliosis-based manner -- to where if the directly corresponding superstring and its directly corresponding counter string are then to be positioned at the relative left to the extrapolated positioning that one were to have, if one is to take the vantage-point of the norm-to-holomorphic positioning of the said photon -- in the direction in which the eminent scattering is to be made upon that general proximal locus, -- then, the consequently formed Schwinger-Indices that are thence to be made will then tend to have a higher expectation value in so as to be of a harmonic vibration.  Yet, if one is to be considering the general angle, by which any one given arbitrary respective photon is to strike the externalized core-field-density of the correlative light-cone-gauge eigenstate -- that it is to come into contact with, in a Gliosis-based manner -- to where if the directly corresponding superstring and its directly corresponding counter string are then to be positioned at the relative right to the extrapolated positioning that one were to have, if one is to take the vantage-point of the norm-to-holomorphic positioning of the said photon -- in the direction in which the eminent scattering is to be made upon that general locus, -- then, the consequently formed Schwinger-Indices that are thence to be made will then tend to have a higher expectation value of being of an annharmonic vibration.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Harmonics Of Gravity Waves

In the general case, as to when electromagnetic energy is to scatter by striking mass-bearing discrete energy -- when this is taken outside of a vacuum -- those harmonic gravity waves that are thence formed by the consequent quantization of the correlative Schwinger-Indices, that are thence expelled by the correlative light-cone-gauge eigenstate, will have the tendency of often moving in the direction of working to form the general phenomenology of sound.  Furthermore -- in the general case, as to when electromagnetic energy is to scatter by striking mass-bearing discrete energy -- when this is taken outside of a vacuum -- those annharmonic gravity waves that are thence formed by the consequent  quantization of the correlative Schwinger-Indices, that are thence expelled by the correlative light-cone-gauge eigenstate, will have the tendency of often moving in the direction of working to form the general phenomenology of heat.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Angle Of Strike Of Photons And Genre Of Schwinger-Indices

When any one given arbitrary photon is to strike the externalized core-field-density of any one respective light-cone-gauge eigenstate, that is of the correlative discrete energy  that the so-eluded-to discrete electromagnetic energy quantum is to make a Gliosis contact, with at potentially different covariant-related angles over time, -- this will then work to allow for the consequent potential variety of Schwinger-Indices that are here to potentially be formed by the so-inferred scattering of light, -- that is here to occur when a photon strikes another discrete quantum in a relatively direct manner.  Such a variety of potential angleings, works here to form the possibility of many different complex roots that may be formed, in the process of the consequent initial metrical and Lagrangian-based Chern-Simons singularities that may be formed by the result of the said photon being here in the process of directly hitting the externalized core-field-density, that is of one respective light-cone-gauge eigenstate -- as the just mentioned eigenstate is to here to be in the process of vibrating via the sub-Fourier process of gauge-bosons behaving in so as to act in so as to "pluck" the correlative second-order light-cone-gauge eigenstates, that are here to work to make-up the here mentioned overall first-ordered light-cone-gauge eigenstate, that the said photon is to strike in a strongly Yukawa-based manner.  The coupling of such so-eluded-to Chern-Simons couplings, in the form of the so-inferred Schwinger-Indices acting in so as to be quantizing in so as to form that general genus of holonomic substrate, that may be thought of as actual gravity waves, -- to where this tends to form a vast array of wave-based gravitational effects, that are then to tend to be made most Yukawa at that region that is most proximal local to those substringular neighborhoods -- by which the directly corresponding Rarita Structure eigenstates are to be most able to incorporate the attribution-based  effects of these said gravity wave eigensets or gravity waves.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Some More As To Schwinger-Indices And Gravity Waves

After the general Fourier-related activity of gauge-bosons -- acting in so as to "pluck" the correlative second-order light-cone-gauge eigenstates of one respective discrete quantum of energy, in a manner that is metaphorically like a harp being played -- to where this is to form Schwinger-Indices, that are thence to be propagated outward from the here directly corresponding locus of the correlative discrete quantum of energy, -- the consequent Schwinger-Indices that are thence formed, are initially formed as a fractal of what are commonly thought of as gravity waves.  Once enough of such a general genus of Schwinger-Indices are to become eigen -- via the here consequent quantization of the so-eluded-to vibrations that are here to be propagated along the proximal local Hamiltonian operand-related eigenstates that are here of the Rarita Structure -- this happens to where the consequently formed eigenstate of holonomic substrate that are to literally act, in so as to be effectual as a metrical-gauge-related eigenstate of what we would normally think of as actual gravity waves, are thence to be formed.  Since gravity waves are a set of Schwinger-Indices-related eigenindices, that come together in a quantific manner -- in so as to operate in order to perform one specific function in space and time, -- gravity waves behave as to the multiplicit vibrations along the Rarita Structure, as orbifold eigensets are to behave as those directly corresponding discrete quantum of energy that work to comprise any said given arbitrary orbifold eigenset.  Once that enough of any one specific set of Scwhinger-Indices that are formed, in so as to act as a fractal of gravity waves, are to be quantized enough, in order to perform one specific viable Ward-Cauchy-based function in time and space, -- the consequently formed gravity waves are vibrations or wave-like phenomenology, that are simultaneously propagated -- in a manner that is relatively outward and perpendicular to the proximal locus region that such individualy taken gravity waves are to be traveling through -- in the form of one relatively symmetric or one relatively assymetric homotopic gravitational-based Hamiltonian operator, that is pulled through the correlative Hamiltonian operand that it is being transferred through, as such gravity waves are to consequently to be delineated along its directly corresponding Lagrangian-based path.  Such gravity wave-based eigensets, (what are most commonly thought of as the individually taken gravity waves themselves), are extremely smaller in diameter than a wavelength of light, although such gravity wave eigensets are extremely larger than the diameter of one discrete increment of a quantum of energy.  Such gravity waves tend to have a diameter that is on the order of 10^(-18) of a meter to 10^(-21) of a meter.This would then make gravity wave eigensets, or, to keep it simple, gravity waves, -- to be basically logarithmically in-between the size of a discrete quantum of energy and the size of any respective given arbitrary wavelength of electromagnetic energy, as such a quantization of vibrations along the Rarita Structure, is made Yukawa to discrete energy--  over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David.

Course 20, Session 10 -- Part One

Light and all other forms of electromagnetic energy, tend to travel in multiple beams of energy, that are interconnected -- via a process known of as quantization.  Any electromagnetic energy that is here to be propagated, is to be transferred through space and time, in discrete bundles of photons, -- of which are here to be delineated upon their environment, in the form of one or more beams of energy, over the course of the general duration of time (and in the path of least time).  Different types of electromagnetic energy exist in different beam-related bundle sizes, of which work to help in causing the general condition of the many different sizes of wavelengths of electromagnetic energy -- that are here to exist as differentiating in a kinematic-related manner, over the multiplicit sequential series of group-related instantons, that are to be happening in realm of the light energy and the light matter that exist in physical space and time.  Such so-eluded-to variations in the genre of the different sizes and types of wavelengths of electromagnetic energy that are to exist in the multiverse, helps to form the individually taken operations that each specific genus of electromagnetic energy is to form -- as such electromagnetic energy is to work to influence its environment in an interdependent manner, as such said energy is to be Yukawa to other energy in the realm of space and time.  All motion exists relative to both the existence and the velocity of light, over time. Photons exist in p-fields, and photons, when individually taken, are the discrete increments of electromagnetic energy.  All light and all other forms of electromagnetic energy, exist in integer-related packets of one or more photons.  Therefore, this happens in such a manner, to where all motion exists relative to both the existence and the velocity of the general genus of the most important generic type of p-field, -- to where all motion exists relative to light.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Photons And Rham Cohomology

Let us initially consider a given arbitrary photon -- that is moving transversally via a unitary Lagrangian-based path, -- in so as to work to form a Rham cohomology, over an evenly gauged Hamiltonian metric.  Such a photon may be said to be basically just generating cohomology in such a case (as opposed to degenerating cohomology).  Next, let us say that the said photon is to, all of the sudden, be scattered upon a phenomenology of holonomic substrate -- that such a photon is to eminently become Yukawa towards, in a Gliosis-related manner, -- at an instance of time.  Once the said photon has been scattered -- the consequently entropic photon is to then to briefly be just degenerating cohomology, as it is in the consequent operation of its perturbated Fourier Transform (as opposed to generating cohomology).  As such a so-stated photon is here to have then to have acted as an entropic eigenstate that is, over one relatively transient gauged-metric, to have gone from its prior condition of just generating cohomology -- into a state of Ward-Cauchy-based conditions, to where it is instead to be just degenerating cohomology, -- the photon of such a given arbitrary case scenario, that has just become entropic, is to now be moving along in such a manner -- to where it is to then to be working to form a Doubolt cohomology, -- in so long as the so-stated photon is in the process of scurrying via  the process of radiative scattering.  Once the said photon is to go back into quantizing with other light, -- then, the said photon will tend to return to going back into the tendency of basically  just  generating cohomology, via the Hamiltonian processes of a consequently formed Rham cohomology -- that will be aptly utilized instead, in such a case.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Perturbative Cohomological Eigenstates

Besides the more obvious general reason as to why an initially Rham-based cohological eigenstate, is to be perturbated into the ensuing general tense of a cohomological stratum, that is known of as a Doubolt cohomology, -- as to when a Rham cohomology is to scatter upon another cohomology, in such a manner that the initially mentioned Rham cohomology is to then to tend to become, instead, of the said Doubolt-related nature, -- there is as well to be one other epifany-related additional general alterior reason -- as to why an initial Rham cohomology is to eventually become of a Doubolt nature, to where this is because of the eventual spontaneous proximal local presence of certain entities, which may be as both group-attractors and/or the proximal local presence of certain entities, which may be as ghost-inhibitors, -- to where both of such just mentioned general categories of what would generally be as the nature of being Cevita-related Hamiltonian operators, are here to have an eminent tendency of, via the innate Hamiltonian operation of the activity of their respective Fourier Transforms, to helping at causing a peturbative effect upon both the pulsation and/or the path-based flow of the so inferred orbifold eigenset, that  was to initially be functioning as a Hamiltonian operator that was here to be undergoing a Fourier Transform -- via the mappable-tracing of the initially mentioned Rham cohomology, that is here to be extrapolated as to then of becoming of a Doubolt cohomology, over an evenly gauged  Hamiltonian operation.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Dual-State Metrical Coupling

Let us initially consider two different orbifold eigensets -- of which are each traveling here through a discrete Lagrangian, to where both of the so-inferred Fourier-related Lagrangian-based settings, that are here to be in the process of being propagated -- are hermitian in a Lagrangian-based manner, even though both of the said cohomologies are here to be eminently Chern-Simons when this is taken in a metrical-based manner, -- over an evenly gauged Hamiltonian operation.  Let us next say, that the two distinct substringular pulsations, that are here to have been being made by both of the individually taken orbifold eigensets, are here to bear a potential tense of being made  Ward-Supplemental to each other when in a metrical-related manner -- if both of the said eigensets were to strike each other at a certain angle -- over the course of the mentioned evenly gauaged Hamiltonian operation.  Let's next say that such a so-eluded-to Gliosisi-related contact was to happen -- in so as to then to work to cause both of the said orbifold eigensets to then to be hermitian in both a Lagrangian-based manner, as well as in a metrical-based manner too, in this particular case.  Such a coupling would often then tend to form a Rham-related cohomological eigenstate of dual-state eigenindices, -- of which would, as well,  to tend here to then be in the process of generating more cohomology than it is then to be degenerating.
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.

Part Two As To Coupled Cohomologies

Let's initially take into consideration two different distinct orbifold eigensets, to where both of these said eigensets are here to be undergoing their respective Fourier Transforms in a manner, that is both covariant, codifferentiable, and codeterminable -- over an evenly gauged Hamiltonian operation.  Both of these said respective orbifold eigensets, are here to bear two individually taken Rham cohomologies -- as well as the condition that these orbifold eigensets are here to be undergoing their respective tenses of the general processes of a Majorana-Weyl-Invariant-Mode.  Next, let us say here, that there is to soon be the eminent presence of a group-attractor, that is here to be Yukawa to both of the said orbifold-related phenomena.  These orbifold eigensets are here to be proximal local, as well as to here to be consistently of the same layer of reality.  The earlier mentioned group-attractor is here to bring about a certain Cevita interaction upon the two said eigensets, by drawing both of the initially eminent Rham cohomologies out of their respective tenses of Majorana-Weyl-Invariance -- over a transient span of a sequential series of group-related instantons.  Consequently, both of the earlier mentioned Rham cohomologies, will soon alter in so as to then to become of the nature of two initially distinct Doubolt cohomologies.  After an ensuing relatively brief number of instantons after the so-inferred Rayleigh-related cohomological perturbation, the two spurious respective Doubolt cohomologies will then often be of the nature -- in so as to potentially tend to couple into one overall cohomology.  If the activity of such a coupling, is to bring about a Reimman scattering of  cohomological eigenindices -- that are to tug the two initially adjacent Chern-Simons cohomologies into a tense of to then to work in such a manner, in so as to become of one Rham-based cohomological holonomic substrate, then, the resultant Wess-Zumino interaction will then often tend to work to form a dual state of metrical-gauge-related Hamiltonian operators -- that work here to form one overall tense of a Majorana-Weyl-Invariant-Mode. 
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

Coupled Cohomologies

Sometimes, when two Doubolt cohomologies are to couple into one overall tense of a topological stratum, in so as to work to produce a certain given arbitrary Wess-Zumino interaction -- the resultant holonomic substrate of cohomology, will then work to become of a Rham-related nature.  Often, such a resultant respective Rham cohomology, will work to bear a relatively high scalar amplitude of Majorana-Weyl-Invariance.  When this is to occur for a set of orbifold eigensets that are of a Calabi-Yau nature, -- such eigenindices of the just implied general genus of Majorana-Weyl-Invariant-Mode, will often tend to then generate as much cohomology as it is to degenerate, -- over an evenly gauged Hamiltonian-related metric.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.