Neutrinos -- Frequency -- Holomorphic Gauge-Metric

 When the gauge-metric of a neutrino-related frequency, is to reverse in its holomorphic direction of pulsation, this may often tend to work to encode, for a reversal in the holomorphic direction, of the angular momentum, of a directly corresponding respective Hamiltonian Operator. SINCERELY, SAMUEL.(1989).

Incursion Of Sporadic Inverted Homotopic Transfer Upon Cohomology

 The incursion of a sporadic tense of inverted homotopic transfer-related gauge-metric eigenstates, upon a given arbitrary cohomology-related setting, may often tend to have the capacity, of working to facilitate the induced proximal local presence, of at least some sort of neighboring entropy. SAM ROACH. 

Riemann-Casimir-Invariant-Coupling

 When Ward-Cauchy-Related eigenstates are to bind, in so as to help facilitate the net homotopic inter-webbing of the multiplicity of superstring-related phenomenology in the cosmos, I call this general operation, the Riemann-Casimir-Invariant-Coupling. (The  R-C-C gauge-metric). SAM ROACH.

The Discrete Re-Distribution Of A Gauged-Action

 The actual physical motion of the discrete re-distribution of a gauged-action, may often tend to be thought of here, as being an example, of a particular general genus, of a gauge-metric eigenstate. TO BE CONTINUED! SAMUEL ROACH. 

Lagrangian Operational Indices -- Gauge-Metric Eigenstates

 Lagrangian operational indices of re-distributed pressurized vacuum -- as taken at the Ward-Cauchy-Related level -- often tend to act as gauge-metric eigenstates. TO BE CONTINUED! SAMUEL. 

Two Different Propagating Convergent Covariant Inversely Isometric Hamiltonian Operators -- Dolbeault/De Rham Cohomology

 When two different propagating convergent covariant inversely isometric Hamiltonian Operators, of which are here to each work to bear a different rate of escalation-related spatial transference, as these inferred systems of energy are here to work to bear a Noether-Based projection of transversal/radial trajectory, over time, to where such inferred "teams" of converging energy, are here to also work to bear the general physical condition, in which these convergent "teams" of energy, are here to bear a relatively Nijenhuis nature, in regards to one another, in the projection of the directoral-based wave-tug of their correlative topological sway, of their kinematic coni-axial eigen metric, when taken over their directly associated Fourier-Related-Progression, that it may often tend to be the case, that as these two different cohesive sets of energy, when these are here to intersect, may often convert their inferred initial Dolbeault cohomology, that these had started out here to be expressing, into a spontaneously formed De Rham cohomology, over the course of an organized correlative spatial translation of cohomological deformation, as taken over the course of a correlative perturbation of gauge-metric-based permittivity. Sam Roach.

Gauged-Action -- Gauge-Metric Eigenstate/Metric-Gauge Eigenstate

 The Lagrangian-Based phenomenology, that is most viably associated, with the gauged-action of the kinematic tense, of a spatially propagating physical entity, that is here to be of an energy-related topological manifold, is hereby to be eminently corresponding, to the general concept, as to what a gauge-metric eigenstate happens to be working to assist at describing. Whereas; The holonomic-based phenomenology, that is most viably associated, with the gauged-action of the kinematic tense, of a spatially propagating entity, that is here to be of an energy-related topological manifold, is hereby to be eminently corresponding, to the general concept, as to what a metric-gauge eigenstate happens to be working to assist at describing. I WIIL CONTINUE WITH THE SUSPENSE LATER! SAM ROACH.

A Curious Mathematical Thought I Would Like To Run By You

 The following is a mathematical stipulation, that I have recently thought of. Please let me know if you think that this makes an adequate amount of sense or not.:

I potentially derived, that:

[(I*PI*(The del of the Ricci Flow)] = [(-PI^2)*(the sine of (e^(Ricci Flow)))]. 

If this is accurately the case, this seems to tell me, that:

The holonomic stratum, that works to eminently help, at allowing for the functionality of the I*PI(Del) Action, may often tend to be proportional to, [(-PI^2)*(the sine of (e^(Ricci Flow)))]; And:

The Lagrangian-Related stratum, that works to eminently help, at allowing for the functionality of the I*PI(Del) Action, often tends to be proportional to, [(I*PI^2)*(the sine of (e^(Ricci Flow)))].

Therefore; It follows, that:

The general restraining "force," that may be directly associated, with the reductional operation, of the general phenomenology of metric-gauge-related pulsation, may often tend to be proportional to:

[(-1)/(the sine of (e^(Ricci Flow)))]; Whereas, 

The general restraining "force," that may be directly associated, with the reductional operation, of the general phenomenology of gauge-metric-related pulsation, may often tend to be proportional to:

[(i)/(the sine of (e^(Ricci Flow)))].

I WILL CONTINUE WITH THE SUSPENSE LATER! TO BE CONTINUED! SAM ROACH.

Net Lagrangian-Based Singularity

 When a given arbitrary Noether-Based mass-bearing cohesive set of discrete energy quanta, is to undergo a net Lagrangian-Based Chern-Simons singularity, to where it is here to be exhibiting an alteration in more derivatives of motion, than the number of spatial dimensions that it is here to be traveling through, then, such an inferred "team" of mass-bearing energy, is here to have a relatively high likely-hood, at the moment at which such a said mass-bearing set of energy, is to be passing through the general locus of such a stated singularity, to be working to bear a spur in the gauge-metric-related motion, of its directly corresponding i*PI(del) Action. TO BE CONTINUED WITH THE SUSPENSE LATER! SINCERELY, SAM ROACH.

Metric-Gauge/Gauge-Metric

 The holonomic interaction of a gauged-action, may often be analogous in its relationship, with the herein proximal local metric-gauge-related eigenstate, thus implied. Furthermore; -- The potentially covariant kinematic-related interaction of a gauged-action, may often be analogous in its relationship, with the herein proximal local gauge-metric-related eigenstate, thus implied. TO BE CONTINUED! SAMUEL.

Scalar-Related Expressions

Particularly when one is here to be dealing with the transference of energy, that is here to be directly corresponding with the Fourier-related translation of a phenomenology, that is of a Noether Flow -- one may then call the correlative directorial axes, that are here to be centered around a Hamiltonian operator as a phenomenon of wave-tug, that is here to act as an extrapolated entity of a tense of holonomic substrate -- when this centralized set of holonomic-related directorials, may then act as a function as to here to be tugged along the path in which the said Hamiltonian Operator is to be going in, in so as to act as the source of what may here be called a genus of a particular case of a metric-gauge eigenstate.  Furthermore -- when one is here to be dealing with the actual motion of the  transference of a set of one or more discrete quanta of either energy and/or zero-point energy, via a Fourier-related translation of a phenomenology that is of a Noether Flow -- one may then call the  correlative directorial axes, that are here to be centered around the Lagrangian, -- as a phenomenon of wave-tug, that is here to act as an extrapolated entity of a tense of motion -- when this so-eluded-to set of motion-related directorials may then act as a function of here, to be tugged along the path of the said actual motion or  Lagrangian of such a set of one or more discrete quanta of energy, -- in so as to then to be acting as one general genus of what may be termed of here as being a particular case of a gauge-metric eigenstate.  Such a tense of either "metric-gauge" or "gauge-metric,"  -- when one is here to be taking the directorial flow of a phenomenology -- without mathematically working to consider the correlative variables that would otherwise be included,  such phenomenology, when of Noether Flow,  may be termed of as being an example of a scalar euclidean expression.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Concisely -- Lagrangian Versus Hamiltonian Operator

The Lagrangian is the gauge-metric of a state or system of energy, whereas -- the Hamiltonian operator is the metric-gauge of a state or system of energy.  Therefore -- the Lagrangian is the actual motion of a state or system of energy, whereas -- the Hamiltonian operator is the actual holonomic substrate (the actual substirngular physical entity) of a state or system of energy.
To Be Continued!  Sam Roach.

Some Stuff As To Dimensional Contraction And Orbifold Eigensets

When one superstring of discrete energy permittivity that is of one given arbitrary orbifold eigenset, is to either comapctify or to decompactify by a specific number of spatial dimensions, at a specific instance of time -- then all of the superstrings of discrete energy permittivity, that work to comprise the said orbifold eigenset, will then tend to respectively compactly/decompactify by that same said specific number of spatial dimensions, at that said specific instance of time.  Therefore, if one specific superstring of discrete energy permittivity, that is of one given arbitrary orbifold eigenset, at right before an iteration of BRST, is to vibrate annharmonically by a specific number of spatial dimensions, in a holomorphic manner, at that so-eluded-to proscribed iteration of gauge-metric -- then all of the superstrings of discrete energy permittivity that work to comprise the said orbifold eigenset, will then tend to vibrate annharmonically by that same specific number of spatial dimensions, in a holomorphic manner, at that so-eluded-to proscribed iteration of gauge-metric.  Furthermore -- if one specific superstring of discrete energy permittivity that is of one given arbitrary orbifold eigenset, during the Regge Action, is to vibrate annharmonically in a specific number of spatial dimensions, in an antiholomorphic manner, at that so-eluded-to proscribed iteration of gauge-metric -- then all of the superstrings of discrete energy permittivity, that work to comprise the said orbifold eigenset, will then tend to vibrate annharmonically by that same specific number of spatial dimensions, in an antiholomorphic manner, at that so-eluded-to proscribed iteration of gauge-metric.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Metric-Gauge or Gauge-Metric

To make things clearer, when one is to discuss what may be termed of here as a Hamiltonian operator, which in a given case, is in terms of a tense of a metric-gauge -- then, one is here referring to a holonomic substrate-based phenomenology,  of which may be considered as a quantum-based phenomenology of scalar magnitude -- of which may be measured here, when in terms of the Hodge-based index of the discrete number of discrete quantum units of such physical entities of iteration, that are to here be participating in such a respective event, of any of such given arbitrary associations of the like.  Yet, when one is to, instead, be discussing, what may be termed of here as a Hamiltonian operator, which in this given case, is in terms of a tense of a gauge-metric -- then, one is here referring, instead, to a scalar amplitude-based phenomenology, of which may be considered as a quantum-based scalar as to the amount of interaction that is to be taking place here -- in any of such given arbitrary associations of the like.  So, whether or not one is referring to a Hamiltonian operator as a substringular eigenmember of a particular holonomic substrate, Or, if one is, instead, referring to a Hamiltonian operator as a scalar degree or a scalar amplitude of a particular quantum-based event -- this is based upon whether or not one is to then be referring to the said respective given arbitrary Hamiltonian operator as of either being of the general genus of being either of a metric-gauge conditionality (as a holonomic substrate that is acting upon its substringular environment), or, as  being of the general genus of being of a gauge-metric conditionality (as a discrete amplitude of a substringular-based activity).
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part Five of Session Three of Course 19 -- the Klein Bottle and Orbifold Differentiation

As to the specific how and the when that the specific kinematic activity, that is of any given arbitrary Klein Bottle eigenstate, is to wobble -- over the course of any respective given arbitrary iteration of group-related instanton, in which such a so-stated eigenstate is undergoing an iteration of one group-metrical course of the Kaeler Metric -- is dependent, in part, upon the multivarious external factors, that work to effect the environment of the internal Ward-Caucy conditions that are of the Fourier Translation of such a substringular composition.  This multivarious interconnection of external factors, that come together in so as to work to effect the kinematic activity of the said Klein Bottle eigenstate -- in a tightly-bound extrapolatable gauge-metric, that is involved with any one specific respective given arbitrary instanton in which such a Klein Bottle is here working in so as to provide the adequate substringular environment, so that the directly corresponding discrete quanta of energy that enter such a so-eluded-to composition may be able to re-attain the condition of working to bear their fractals of discrete energy -- so that there may be a continued existence of discrete energy or energy period -- is, in part, dependent upon both the holonomic-substrate-based existence and the Fourier-based activity of those substringular eigenmembers of the proximal local substringular region, when such a consideration, as well, works to include the consideration of those relatively loosely constructed Wilson Lines that work to form the framework of the holonomic substrate of the so-mentioned Klein Bottle of such a case, itself.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part Five of the Second Session of Course 18

After the phenomenology of each of the respective predominant layers of reality -- one from each respective set of parallel universes -- moves into what may be termed of as the Main Heterotic Stringular phenomenology, it goes into the region of the center of just where the adjacent world-tubes of the adjacent set of parallel universes are at, while then moving in the norm-to-forward-holomorphic -- for forward-time-bearing-momenta eigenstates, -- while yet then simultaneously moving norm-to-reverse-holomorphically, for backward-time-bearing-momenta eigenstates -- into the adjacent set of parallel universes' world-tubes.  Such an (N-1) activity for forward-time-bearing-momenta eigenstates, and, such an (N+1) activity for backward-time-bearing-momenta eigenstates, then iterates, as likewise, one more time.  Then, there are two consecutive (N+1) of such activities for the forward-time-bearing-momenta eigenstates, of which acomapany two consecutive (N-1) of such activities for the backward-time-bearing-momenta eigenstates.  This happens in so as to bring the relatively-thick-amorphous-shaft-shape-like phenomenologies of the respective predominant layer of reality -- one for each respective set of parallel universes -- back to the world-tube general cross-section, where each of their respective Bases of Light will soon reiterate at.  Then, the three respective layers of reality -- one per set of parallel universes -- will cycle here once, along the Ultimon, in so as to re-reach their respective cross-sectional locants as to where their individually taken Basis of Light will reiterate.  At the end of the fifth so-eluded-to H Bar gauge-metric of the generally unnoticed overall gauge-metric of Ultimon Flow, the predominant Basis of Light of each set of parallel universe will majorize at the "interior" world-tube-section of the general overall world-tube eigenlocuss -- to where its directly corresponding Basis of Light is to temporarily station at -- one "mer" of such a Basis of which is stationed at the forward-time-bearing-momenta general world-tube eigenlocus, and one "mer" of such a Basis of which is stationed at the backward-time-bearing-momenta general world-tube eigenlocus.  These two "mers" are interconnected by mini-string via the substringular encoders.  At this point, the ~.283 of one H Bar duration, that is directly associated with the "space-hole," will then begin.  I will continue with the suspense later!  To be continued!  Sam.

The importance of gauge-metric

Phenomena has to move to exist.  Gauge-Metric is the topological Laplacian Poincaire Ward conditions that integrate through the Fourier Conditions of substringular multiplicit group metrics that must exist in order for superstrings to have the ability to move through space, and, therefore, be the energy that is necessary for reality to exist. Simply, a gauge-metric is a duration that happens in less than a discrete unit of time.  We notice time when the corresponding superstrings are basically at a standstill.  The integration of a successive series of group instantons (codifferentiable discrete units of time) works to form the flow of motion that acts -- via those holonomic substrates that move to display the corresponding inter-kinematics of such energy -- in such a manner in so as to form that energy that makes up space-time-fabric.  Superstrings are the discrete units of energy permittivity. Permittivity is the ability of phenomena to continue to move through space. If discrete units of energy could not move, energy would cease to exist. Without energy, there would be no light, nor would there be any mass. When superstrings circle the Ultimon many, many times, these phenomena (superstrings) lose some of their permittivity. The process that causes superstrings to regain the permittivity that these need in order to remain energy so that energy may exist is known as a Gaussian-Transformation, which is usually a gauge-transformation. Simultaneously, Gaussian Tranformations help Fadeev-Popov-Trace eigenstates to regain the discrete impedance that these need in order for energy to exist at all, too.  Energy impedance is the steadying of energy permittitvity that is necessary in order for energy to not resonate and then shatter. The initial situation is that gauge-transformations eventually lead to entropy. Yet, there is a way of limiting gauge-transformations to those that just allow for substringular permittivity without allowing for excess entropy. Entropy is essential for at least the change of physical states. I will say no more of this. The reason that energy started and still persists comes down to the existence of the Higgs Action. The Higgs Action is the main operator that allows for Gaussian Transformations.

Part Two Of Genus-Bases oF Chern-Simmons Indices

The reverse-holomorphism of the previously mentioned singularities would thus be -infinity,
-infinity^2, -infinity^3, and -infinity^4, -0+, -0+^2, -0+^3, and -0+^4 -- respecitively.  This is based on both the singularities that here refer to a hermitian case and also those singularities that here refer to a non-hermitian case. 
When singularities are based on spuriousness, each truncated jerk in the accelleration/decelleration of the related vibrations of the said trace fors a 0+ based singularity (if holomorphic and in one normal coniaxial framework).  If the related holomorphism is reversed with the initial conditions of what here works to define a positive directoralization, then, the singularity is based on 0- instead of 0+.  If more axials vibrate than that which allow for a condition of hermicity, then, for each added covariance, multiply the truncation-based singularity by 0+ -- for positive holomorphicity, or 0- -- for negative holomorphicity.  This is for one eigenmetric of truncated anharmonic sway.  Ellongated jerks involve the  same concept, yet here involving a multiple of singularity of infinity+ -- for positive holomorphicity, or infinity- -- for negative holomorphicity.  Indiscrete scalars may be multiplied by the values of singularity when there is a given set of conditions of an additional lack of hermicity.  For instance, if a trace similar to what I have mentioned is different on account of changes in all 32 spatial dimensions that are inter-twined in one given set of parallel universes that this situation would here refer to -- and also, if during a set of iterations of instantons that correspond to the directly related Fourier Transformation, the trace of a kinematically projected superstring bears an anharmonic sway that is ellongated during a gauge-metric that is part of the overall group metric in which the mentioned trace is vibrating, then, the superstring, in the course of kinematically traversing the said trace, will bear a singularity of infinity^31*infinity -- or, infinity^32.  Yet, if the mentioned trace that here changes in all 32 spatial dimensions bears an anharmonics that is briefly truncated in a gauge-metric that happens during the same overall group metric in which the said trace is vibrating, then, the trace will here bear a singularity of infinty^31*(0+) -- or, infinity^30.  In both cases, the Chern-Simmons index will bear a genus of 30.  (32-2=30.)  As another example, if the same type of trace that changes in all 32 spatial dimensions of its set of parallel universes is truncated in what may be here described arbitrarily as the negative direction, then the overall singularity that it will bear will be infinity^31*(0-) = infinity^(-30).  As one last example for the day, if the said just mentioned trace bears an ellongated anharmonic sway in the "negative" direction during a gauge-metric that exists within the locus of the extrapolated vibration of the said trace, then, its corresponding singularity at the junction of the change in its dimensionality will be infinity^31*(-infinity) = infinity^(-32).  That's all for now.  I will continue with the suspense later!  Sincerely, Sam.

Some More About BRST

The Bette Action and the Polyakov Action happen during the same general metric, per instanton.
Both the Bette Action and the Polyakov Action happen during the BRST portion of instanton.
The Bette Action works to help allow for superstrings to be orientable.  If a superstring is neither orierntable during both the Bette Action and the Regge Action -- when in pertainance to any given arbitrary superstring over the course of one particular instanton -- then, the superstring will be tachyonic over the course of the ensuing instanton.
The Polyakov Action works to reverse contract superstrings to the inverse extent that the corresponding superstrings are Lorentz-Four-Contracted during BRST.
Right after BRST, if a given arbitrary superstring is to undergo the Kaeler-Metric during the inter-related instanton, the related superstring re-contracts as it falls into the corresponding Klein Bottle eigenstate that it is to enter during the gauge-metric that is here related to a partial activity of a corresponding Gaussian Transformation.
If the prior mentioned superstring is not to undergo the Kaeler-Metric over the course of the corelative instanton, then, the said superstring simply goes into the Regge Action right after the corresponding metric of BRST.
If a superstring is to go thru the Kaeler-Metric, then, the Regge Action happens for half of the duration that it would otherwise take to do so.
If the prior said superstring is to undergo the Kaeler-Metric, then, the said superstring will go thru the given eigenmetric from the moment that it leaves BRST to the moment that it goes into the Regge Action for half of the duration of metric that it would normally take to go thru the Regge Action.
The Polyakov Action works to methodically convert superstrings into a relative assortment of point commutators.
The Regge Action organizes both the result of the Polyakov Action and the result of the Bette Acton so that the related superstrings may be facilitated to go thru the rest of Ultimon Flow over the course of what is here to be the cause of the ensuing iteration of kinematic flow in so that the next instanton may happen.
Gotta Run!  I will continue with the suspense later!  Sincerley, Samuel David Roach.

Whether Something is Fourier or Laplacian Based

Whether Something is Fourier or Laplacian Based


                 
A Fourier Transformation is time based, while a Laplacian Transformation is not time-based. Discrete units of time are not the smallest metrics, though. Duration that is smaller than a discrete unit of time is known as a gauge-metric. So, even though a gauge-metric involves kinematic activity that occurs during the course of either an instanton or during the course of Ultimon Flow that is not during an instanton, such activity is considered to be -- in a sense -- a transpiring that is to happen over a Laplacian Transformation, since such activity happens within a discrete unit of time. Fourier Transformations always involve at least two or more instantons -- no matter how you fractor the associated transformation. In Newtonian mechanics, a Laplacian Transformation may involve many instantons that, even together, considering the scenario, are relatively non-time-oriented. So, for the most part, what is considered Fourier (time-oriented) or what is considered Laplacian (non-time-oriented) is relative to the scenario that one is considering. Yet, non the less, any differentiation that happens within an instanton, is, in a real sense, of the nature of a Laplacian Transformation. So, even though gauge-metrics are of sub-time, understanding their activity is quintessential to understanding the relativistic mechanics that underline the activity of the light-cone-gauge. Whithout the light-cone-gauge, E(6)XE(6) strings would be unable to form Schwinger Indices. Without Schwinger Indices, the Rarita Structure would not vibrate -- causing gravity to not take effect via the Ricci Scalar. Without gravity, everything would fly apart and there would be nothing.