The Ricci Flow Always Tends To Be Negative, For Forward-Moving Time

 The Ricci Flow of a forward-time moving Noether-Based Hamiltonian Operator, will always tend to be of a negative scalar magnitude. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. (1989).

Alteration In Escalation Of Euclidean Expansion -- Metric Spur -- Formation Of A Set Of Metric-Based Chern-Simons Singularities

 When the rate of the escalation of the Euclidean Expansion of the spatially kinetic transference, that is of the Fourier-Related-Progression, of a given arbitrary Noether-Based mass-bearing cohesive set of discrete energy quanta, is to alter in its scalar magnitude, this general kinematic process, may often tend to be eminently associated, with the formation of a metric spur, in the dimensional-related pulsation, that is here to tend to be eminently correlative, to an alteration in the scalar amplitude of the net wave-tug, that is here to be corroborative to the transversal "drive," of the directly corresponding net angular momentum, that is here to be primarily associated, with the general characteristic, of the Lagrangian-Based motion, that is of such a Noether-Based mass-bearing cohesive Hamiltonian Operator. Such an inferred general tense of a metric spur, may thereby often tend to be directly associated, with the corroborative formation, of a set of one or more correlative respective metric-based Chern-Simons singularities. SAMUEL ROACH. (1989).

Covariant Attribute Of (1/(e^(Del(Ricci Flow))))

 The greater that the scalar magnitude is to be, as to the interdependent Ward-Cauchy-related attribute of: (1/(e^(del(Ricci Flow)))), -- from among two different interdependent covariant mass-bearing cohesive sets of discrete energy quanta, over a discrete increment of time, -- the greater that the relativistic interdependent covariant pulsation will consequently tend to be, in lieu of the interaction that is here to occur, from among these two different stated cohesive sets of discrete energy quanta, over such an inferred discrete increment of time. I will continue with the suspense later! To Be Continued! Sam Roach.

Del Of The Ricci Flow And Metric-Gauge-Related Pulsation

Let us initially consider a covariant relationship, that is here to exist between two different orbifold eigensets. Let us think, more specifically, about the relationship between the Del of the Ricci Flow, and the directly related resultant covariant metric-gauge-related pulsation -- that is here to exist (or "co-exist"), between (or among) the given arbitrary field, -- that is here to help at working to link the interaction, that is here to occur between the two different but interdependent inferred cohesive sets of discrete energy quanta, that are to be considered in this particular case scenario. :

When the Del of the covariant Ricci Flow is to be of a positive fractional value, that is here to be relatively closer to "0," then, the resultant metric-gauge-related pulsation will consequentially tend to be of a larger scalar magnitude/amplitude -- than if the correlative Del of the covariant Ricci Flow were, instead, to bear a positive fractional value, that would otherwise be relatively closer to "1."

Furthermore; when the Del of the covariant Ricci Flow is to be of a negative fractional value, that is here to be relatively closer to "-1," then, the resultant metric-gauge-related pulsation will consequently tend to be of a larger scalar magnitude/amplitude -- than if the correlative Del of the covariant Ricci Flow were, instead, to bear a negative fractional value, that would otherwise be relatively closer to "0."

To Be Continued! Sincerely, Samuel David Roach.

Scalar Amplitude Of The Kinematic Translation Of Correlative Chern-Simons Invariants

The higher that the scalar amplitude of that correlative tense of physical magnetism is to be, that is here to be directly associated with the physical charge of any one given arbitrary Noether-based mass-bearing orbifold eigenset, over time, -- the greater that the directly corresponding scalar amplitude will then tend to be, of the correlative rate that is of the kinematic translation of those correlative Chern-Simons Invariants, that are here to be most directly associated with the externalized radial/(transversal) transfer of such a said given arbitrary Noether-based mass-bearing orbifold eigenset, over an implied correlative evenly-gauged Hamiltonian eigenmetric. To Be Continued! Sam Roach.

Rate Of iPI(del) Action

Let's initially consider a mass-bearing orbifold eigenset, -- that is thus, in part, comprised of mass-bearing superstrings of discrete energy permittivity.  As the here proximal local Polyakov Action is to either be increased or decreased in its scalar amplitude (magnitude), then, the directly affiliated Lorentz-Four-Contraction, is to here be respectively either to be decreased or increased.  This is because the Polyakov Action acts here, in so as to be an inverse operation -- of what is known of as the Lorentz-Four-Contraction.  For instance -- as such a said general tendency, such as the Polyakov Action, is to be increased (This is a case in which the correlative mass-bearing orbifold eigenset, is here to be slowed down), there is then to be an increase in the number of partition-based discrepancies, that are here to exist in those superstrings of discrete energy permittivity, that are here to exist in the directly corresponding orbifold eigenset, that would here be expressed to be of a correlative nature.  Consequently -- as a tendency such as the Polyakov Action, is to increase in its rate, -- then, the correlative rate -- as to an increase in the so-eluded-to Hodge-Index, that is here to be as of the number of partition-based discrepancies -- that are here to exist in those individually taken superstrings of discrete energy permittivity, that are here to work to comprise such an orbifold eigenset, will then tend to be increased in its scalar amplitude.  This increase here, will then tend to be inversely proportional -- to what will here be a decrease in the number of mass-bearing superstrings of discrete energy permittivity, that are here to work to comprise the said orbifold eigenset.  This would then work to mean, that there will here tend to be an increase in the rate of the directly correlative iPI(del) Action -- that is here to be proximal local to those mass-bearing superstrings of discrete energy permittivity, that are here to work to comprise the initially implied mass-bearing orbifold eigenset.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.