The Externalized Topological Structure, Of A Recursively Smooth Homotopic Curvature

 The externalized topological structure, of a recursively smooth homotopic curvature, may often tend to work to exhibit the display, of diffeomorphic characteristics. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. 

The More Yau-Exact That A Hamiltonian Operator Expresses Itself As

 The more Yau-Exact that a Noether-Based Hamiltonian Operator expresses itself as, the greater the tendency, that its directly associated generated homotopic residue, will spontaneously become  homogeneously distributed, in a piecewise continuous manner, over an ensuing duration of viable relativistic time. I WILL CONTINUE WITH THE SUSPENSE LATER! SINCERELY, SAMUEL.

Homogeneous Distribution Of Homotopy

Noether-Based homotopy often tends to be homogeneous in its correlative distribution, when that Hamiltonian Operator, of which is here to be working to express the stated given arbitrary homotopy, is Slater in its directional translation. TO BE CONTINUED! SINCERELY, SAMUEL ROACH. (1989).

The Underlying Sub-Tension Of The Ricci Flow

 When the underlying sub-tension of the of the Ricci Flow is supplemental in its projection, the Ricci Flow may be said to be smooth, to where the directly associated Ricci Curvature may then be said to be flat. I WILL CONTINUE WITH THE SUSPENSE LATER! SINCERELY, SAMUEL DAVID ROACH. 

The Ricci Flow, "In A Nutshell"

 Here is the brief development of a synapsis, as to what I perceive the Ricci Flow to be. Please bear with me:

A Hamiltonian Operator -- as the "Thing" of energy -- is to be tugged through space, via its Lagrangian (to where, such a stated "Lagrangian," is the "Motion" of such a respective tense of energy). As the Hamiltonian Operator is tugged through its Lagrangian, over time, its eminent core-field-density, is to interact with its immediately externalized field, to where such an inferred tense of an interaction, works to form the general phenomenology of "cohomology." The interaction of such cohomology, with the respective proximal  local gravitational force, (the interaction of the said cohomology, with that gravity, which is at the kinematically progressive kinetic locus, of which the said cohomology is here to be propagating through), works to form a flow, of which may be described of here, as being the "Ricci Flow." SAM.

Perturbative Gravitational Forces Counterbalancing -- Yau-Exact Conditions

 When perturbative gravitational forces counterbalance each other, this tends to work to allow for Yau-Exact conditions, of which works to allow for those correlative Noether-Based Hamiltonian Operators, that are here to be proximal local to the presence of such an inferred non-perturbative gravitational field, to tend to be of a Calabi-Yau nature. Hamiltonian Operators that work to exhibit a Calabi-Yau nature, may be said to display the general tense, of a Calabi-Yau Manifold. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH.(PHS1989).

When Perturbative Gravitational Forces Counterbalance Each Other

 When perturbative gravitational forces counterbalance each other, this tends to work to allow for a flat Ricci Curvature, of which tends to work to allow for a smooth Ricci Flow. SAMUEL ROACH. 

Gravitational Warp -- Perturbative Ricci Flow

 When a Ward-Cauchy-Related cohomology-based topological structure, that is here to be proximal local, to the core-field-density, of a directly corresponding kinematically propagated Hamiltonian Operator in time and space, is thence to be spatially transferred through a region in space and time, in which the gravitational force is here to be of a warped nature, this general characteristic, will thereby tend to spontaneously work, to induce the consequential physical attribute, to where the earlier stated Hamiltonian Operator, will thereupon tend to work to exhibit a perturbative Ricci Flow, from within the Ward-Neumann bounds, of such an earlier inferred region of gravitational warping. TO BE CONTINUED! SAMUEL ROACH. 

Diffeomorphic Field Incurred Upon By A Cevita Action

 When a diffeomorphic field is incurred upon by a Cevita Action, this may often have the capability, of tending to be able to alter the said diffeomorphic field, into a heteromorphic field. SAM ROACH.

Heteromorphic Field Incurred Upon By A Wess-Zumino Action

 When a heteromorphic field is incurred upon by a Wess-Zumino Action, this may often have the capability, of tending to alter the said heteromorphic field, into a diffeomorphic field. SAM ROACH.

A Homogeneous/Heterogeneous Kinetic Disturbance Of Space

 A homogeneous kinetic disturbance of space-time-fabric, has the general tendency, of working to form, a harmonic tense of energy. Whereas; A heterogeneous kinetic disturbance of space-time-fabric, has the general tendency, of working to form, an anharmonic tense of energy. TO BE CONTINUED! SAM. 

Abrupt Alteration In The Viscosity Of Space-Time-Fabric Traveled Through

 When there is to be an abrupt alteration, in the viscosity of space-time-fabric, of which a given arbitrary Hamiltonian Operator is here to be traveling through, this will often tend to spontaneously work to cause, the consequential formation, of a set of one or more Lagrangian-Based Chern-Simons singularities.

Perturbative Alteration In Field Intensity -- Lagrangian-Based Chern-Simons Singularities

 When there is to be a perturbative alteration in the field intensity, that is here to be incurred upon the Lagrangian-Based motion, of a given arbitrary Hamiltonian Operator, this will often tend to spontaneously work to cause, the consequential formation, of a set of one or more Lagrangian-Based Chern-Simons singularities. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. (1989).

Spurious Dimensional Gauging -- Metric-Related Chern-Simons Singularities

 When the dimensional gauging of a Hamiltonian Operator becomes spurious, it will spontaneously tend to consequentially work to bear a correlative set of metric-related Chern-Simons singularities. SAM.

Spurious Dimensional Gauging

 When the dimensional gauging of a Hamiltonian Operator becomes spurious, its pulsation will tend to become spurious. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. (1989).

A Vibrating Hamiltonian Operator, That Works To Express A Recursively Smooth Ricci Flow

 A vibrating Hamiltonian Operator, that works to express a recursively smooth Ricci Flow, often tends to work to exhibit the general characteristics, of a Majorana-Weyl-Invariant Spinor. SAM ROACH. 

Spinning Yau-Exact Gauge-Invariant Superstrings

 Spinning Yau-Exact gauge-invariant Noether-Based mass-bearing superstrings of discrete energy permittivity, tend to work to bear a recursively smooth Ricci Flow. SINCERELY, SAM ROACH.

Yau-Exact Gauge-Invariant Superstrings Of Discrete Energy Permittivity

 Yau-Exact gauge-invariant Noether-Based mass-bearing superstrings of discrete energy permittivity, tend to work to express a De Rham cohomology. TO BE CONTINUED! SINCERELY, SAMUEL ROACH.

Gauge-Invariant Hamiltonian Operator -- No Anti Holomorphic Kahler Conditions Exhibited

 A gauge-invariant Hamiltonian Operator, does not tend to exhibit the display of any anti holomorphic Kahler conditions. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. (1989). 

Recursively Recurrent Tense Of Anti Holomorphic Kahler Conditions

 When a given arbitrary Hamiltonian Operator, is "stuck" within an infinite well of energy, it will often tend to work to exhibit, a recursively recurrent tense, of anti holomorphic Kahler conditions. SAM.

Harmonic Isotropically Stable Lagrangian -- No Lagrangian-Based Chern-Simons Singularities

 A given arbitrary mass-bearing Noether-Based Hamiltonian Operator, that is in the process of working to bear a harmonic isotropically stable Lagrangian, often tends to work to bear no proximal local Lagrangian-Based Chern-Simons singularities. SAM ROACH.

Isotropically Stable Anharmonic Vibrating Hamiltonian Operator -- Chern-Simons-Related Spur In Its Correlative Motion

 When a given arbitrary isotropically stable Noether-based mass-bearing Hamiltonian Operator, is to vibrate in an anharmonic manner, over time, such a mentioned Hamiltonian Operator, will often tend to have a greater tendency, of working to bear one or more Chern-Simons-Related spurs, in the projected path of its correlative Lagrangian-Based motion, than an otherwise analogous anharmonic vibrating Noether-Based mass-bearing Hamiltonian Operator, that is not isotropically stable. TO BE CONTINUED! SINCERELY, SAMUEL ROACH. 

Isotropically Stable Hamiltonian Operator -- Smooth Externalized Cohomology-Related Mappable Topology

 A given arbitrary isotropically stable Noether-Based mass-bearing Hamiltonian Operator, may often tend to work to bear a smooth externalized cohomology-related mappable-topology. SAMUEL ROACH. 

Recursively Smooth Rotational-Based Ricci Flow

 A recursively smooth rotational-based Ricci flow, will tend to work to bear a greater scalar amplitude of permeability, than an analogous recursively smooth Ricci Flow, that is Not rotational-based. SAM.

Electromagnetic Energy Interacting With Mass-Bearing Light-Cone-Gauge Eigenstates

 When electromagnetic energy is to interact with a Noether-Based mass-bearing light-cone-gauge eigenstate, in a Glosses-Related manner, this will often tend to work to form a perturbation, in the distributional delineation, of the said light-cone-gauge eigenstate. SAMUEL DAVID ROACH.

Noether-Based Mass-Bearing Light-Cone-Gauge Eigenstates That Are Distributed Adjacently

 Noether-Based mass-bearing light-cone-gauge eigenstates that are distributed adjacently, often tend to be gauged asymmetrically. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. 

Perturbation Of Cohomology -- Often Associated With An Increased State Of Entropy

 When a given arbitrary Noether-Based Hamiltonian Operator, of which is here to be initially exhibiting the display of a De Rham cohomology, is to spontaneously alter, into exhibiting the display of a Dolbeault cohomology, this will often tend to be directly associated, with an increased state of entropy. SAM.

Spinning Isotropically Stable Hamiltonian Operator

 A given arbitrary symmetrically spinning isotropically stable mass-bearing Noether-Based Hamiltonian Operator, will often tend to work to bear a harmonic charge. TO BE CONTINUED! SAM ROACH.

Spurious Recursively Rotating Mass-Bearing Hamiltonian Operator -- Entropic Charge

 A kinematically spurious recursively rotating mass-bearing Noether-Based Hamiltonian Operator, will have the general tendency, of working to exhibit the display, of the general tense, of entropic charge. SAM.

Relatively "Pronounced" Clifford Expansion -- Increased Asymptotic Nature Of Correlative Hyperbolic Slope

 A Clifford Expansion may be said to be relatively "pronounced," when the projection of the directly associated hyperbolic slope, which is here to be eminently correlative to such a said Expansion, is to increase in the scalar amplitude of its asymptotic nature. TO BE CONTINUED! SAM ROACH.

Kinematically Stable Hamiltonian Operator -- Greater Net Polyakov Action

 The more kinematically stable that a given arbitrary Hamiltonian Operator is to be, the greater that the directly associated net Polyakov Action eigenstate will consequently tend to be. SAMUEL ROACH.

Polyakov Action -- Applicable Order Of Slater Equation

 The greater that the scalar amplitude of a given arbitrary eigenstate of the Polyakov Action happens to be, the higher of an order of the Slater Equation, of which is here to be applicable to a mathematical description, of such a Polyakov Action-Related eigenstate. TO BE CONTINUED! SINCERELY, SAM.

Clifford Expansion -- Applicable Order Of Slater Equation

 The more pronounced that a given arbitrary Clifford Expansion happens to be, the higher of an order of the Slater Equation, which is here to be applicable to a mathematical description, of such an expansion. 

Stronger Polyakov Action -- More Pronounced Clifford Expansion

 The stronger that the Polyakov Action happens to be, the more pronounced that its directly associated Clifford Expansion will thereby tend to be exhibited as. SAMUEL DAVID ROACH. (1989).

When A Light-Cone-Gauge Eigenstate Is Transversally Perturbative

 When a light-cone-gauge eigenstate is transversally perturbative, it will often tend to have a spurious Lagrangian. 

When A Light-Cone-Gauge Eigenstate Is Radially Perturbative

 When a light-cone-gauge eigenstate is radially perturbative, it will often tend to have a spurious pulsation. 

Light-Cone-Gauge Eigenstates -- Lagrangian-Based Chern-Simons Singularities

 When the wave-tug of the light-cone-gauge eigenstate of a discrete quantum of energy, is to work to bear a spurious perturbation in its direction, this will often tend to result, in the covariant proximal local presence, of a Lagrangian-Based Chern-Simons singularity. TO BE CONTINUED! SAM ROACH.

Light-Cone-Gauge Eigenstates -- Chern-Simons Singularities

 When the wave-tug of a light-cone-gauge eigenstate, is to work to bear a spurious perturbation in its corroborative scalar amplitude, the directly associated discrete quantum of energy, of which such a stated light-cone-gauge eigenstate is to be proximal local to, will often tend to consequently work to bear, a spontaneously resultant metric-based Chern-Simons singularity, at the eminently pivotal locus, at which such a stated spurious perturbation, is thence to occur. TO BE CONTINUED! SINCERELY, SAM ROACH.

Gauge-Invariant Hamiltonian Operator -- Flat Ricci Curvature

 A gauge-invariant Hamiltonian Operator, may often tend to be eminently associated, with the proximal local presence, of a flat Ricci Curvature. I WILL CONTINUE WITH THE SUSPENSE LATER! SAM.

"Locked-In" Light-Cone-Gauge Eigenstate

 A gauge-invariant light-cone-gauge eigenstate, may potentially be described of, as working to bear a "locked-in" gauge-action.  A light-cone-gauge eigenstate, that may potentially be described of, as working to bear a "locked-in" gauge-action, will often work to bear the general tendency, of having an isotropic tense of stability. A light-cone-gauge eigenstate, that is here to work to bear a gauge-action, that is here to have an isotropic tense of stability, will often work to exhibit the display, of a smooth Ricci Flow. Therefore; A gauge-invariant light-cone-gauge eigenstate, of which is here to work to bear a "locked-in" gauge-action, will often, at times, tend to work to exhibit the display, of a smooth Ricci Flow.(1989). SAMUEL ROACH. 

A Hamiltonian Operator That Is Gauged In A Hermitian Manner

A Hamiltonian Operator that is gauged in a hermitian manner, will often tend to work to bear a smooth Ricci Flow.'TILL NEXT TIME! TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH.  

A Spuriously Gauged Hamiltonian Operator

 A spuriously gauged Hamiltonian Operator, will tend to lack a smooth Ricci Flow. SAM ROACH.

Smooth Ricci Flow

 When a given arbitrary Noether-Based Hamiltonian Operator is isotropically stable, its directly associated Ricci Flow will have a tendency of working to bear an eminent hermitian nature. SAMUEL ROACH,

Alterations In Covariant Cohomological Deformation -- Perturbation In Proximal Local Gravitational Force

 When there is to be an alteration in the flow of the covariant cohomological deformation, of a given arbitrary Hamiltonian Operator, this will often tend to be indicative, of a perturbation in the proximal local gravitational force. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. (1989).

About What The Ricci Flow Is

 Individually taken superstrings, act as the "thing" of energy; Whereas the Lagrangian, is the motion of such inferred "things" of energy. As individually taken superstrings, are to be moving through space and time, the interaction of such said strings, with the field, that is here to be directly external to these stated superstrings, works to form a phenomenology, that may be thought of here, as being the general topological stratum of COHOMOLOGY. The interaction of such COHOMOLOGY, with the general force of gravity, works to form the flow of a tense of deformation, which may be thought of, as being, what may here be called, the RICCI FLOW. SAMUEL DAVID ROACH. (PHS 1989). -- Hello, Genesis House!

Typical Heuristic Values For Typical Ricci Flow

 As I have described of before; The heuristic scalar magnitude of the Ricci Flow, for a Noether-Based Yau-Exact discrete quantum of energy, is typically a negative two. Yet; The reductional heuristic scalar magnitude of the Ricci Flow, for the general conditions of a Noether-Based discrete quantum of energy, is typically -1.945910149. All forward-time-moving Yau-Exact discrete quanta of energy, are of a Noether-Based nature. Yet; Not all Noether-Based discrete quanta of energy are Yau-Exact. This is since, not all discrete energy quanta are Ricci Flat. Yet; The vast physical conditions, in which there is to be either the general presence of either a flat Ricci Curvature, and/or, when it is often to otherwise follow, that the general presence of what basically amounts to the physical conditions of a Yau-Exact nature, is here to be so eminently effectual, that the consequential relatively "invasive" prevalence of the general mannerisms of Yau-Exact physical conditions, is a key factor, at influencing the general state, as to what the typical scalar magnitude of the Ricci Flow, happens to be exhibited as. SAMUEL DAVID ROACH. 

Recursively Inverting Clifford Expansion

 At times; When the Laplacian-Based projection, of the cohomological mappable-tracing of a Clifford Expansion, is to recursively invert in its concavity -- as taken in a piecewise continuous manner -- this may often have the general tendency, of potentially being indicative of a tense of helicity, as exhibited by the respective Laplacian-Based projected trajectory, that is of that inferred cohomological-based pattern, of which is here to be physically exhibiting the inferred display of a mappable torsion, that is here to be incurred upon that proximal local space-time-fabric, in which such a cohomological mappable-tracing, is here to be existent from within. SAM ROACH. 

Slater Relation -- Clifford Expansion

 When one is to take the Slater relation of that hyperbolic-related tangential divergence, that may often be eminently associated with a given arbitrary first-order Clifford Expansion, one may often consequently derive from this, the respective directly associated second-order Clifford Expansion. SAM ROACH.

The Ricci Flow, When The Hamiltonian Operator Is Yau-Exact

 When a Noether-Based forward-time moving Hamiltonian Operator is of a Yau-Exact nature, it will tend to have a Ricci Flow, that will heuristically have a scalar magnitude of a negative 2. SAMUEL ROACH.

Positive Ricci Flow Indicative Of Backward-Moving Time-Based Phenomenology

 A positive Ricci Flow, is indicative of a backward-time moving phenomenonology. SAM ROACH. 

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).