Showing posts with label homotopy. Show all posts
Showing posts with label homotopy. Show all posts

Tuesday, September 15, 2026

The Metaphorical "Body" Of The Substringular

 The Rarita Structure, is metaphorically like the water of the substringular.

Superstrings of discrete energy permittivity, are metaphorically like the flesh of the substringular.

Light-Cone-Gauge Eigenstates, are metaphorically like the blood of the substringular.

The gauge-bosons, are metaphorically like the nerve tissue of the substringlar.

Fadeev-Popov-Trace eigenstates, are metaphorically like the electrolytes of the substringular.

The Ultimon, is metaphorically like the body of the substringular.

The Schwinger-Related Vibrations, are metaphorically like the ATP and the ADP of the substringular.

The Fourier-Related-Progression, is metaphorically like the bodily motion of the substrngular.

Homotopic Transfer, is metaphorically like the body-related flexibility of the substringular.

Homotopic Restraint, is metaphorically like the bodily strain of the substringlar.

Black-Holes, are metaphorically like the cancer cells of the substringular.

& the E(8)XE(8) superstring-related-oscillation-based-mode, is metaphorically like the soul of the substringular.

(Co)Homology-Based Topological Manifolds, are metaphorically like the cells of the substringular. 

Neutrinos encode for the forces of nature, by the multiplicity of acting upon the region, proximal adjutant to the light-cone-gauge, in so as to help facilitate the initiation of the gauge-bosons’ induction, as to metaphorically pluck the stated light-cone-gauge (eigenstates) like a harp, in so as to facilitate the formation of kinematically propagated Schwinger-Related vibrational oscillations, that are to flow, as previously spontaneously induced, to interact with the panoply, of the multiplicity of physical phenomenology, in so as to facilitate the formation, of the forces of nature. 

Neutrinos, are metaphorically like the genetic material of the substringular. 

The “spatial frequency” as coupled with the angular frequency, in the substringular, is metaphorically analogous, in a way, to the general concept of thought frequency. 

EDITORIAL: By the way: Let’s work at learning from each other. I’ve gotta work at that too! Surviving as a human race, is more important, than who’s right and who’s wrong!

When homotopic expansion is kept under restraint, by the withholding force of action, of a kinetic tense of discrete energy permittivity, that this type of a case, may at times, be eminently corroborative, to the likings of a viable genus, of the exemplification, of a Fourier-Related-Progression. 

A homotopic expansion, that is inverse Euclidean, is to tend to bear a transversal inverse contortion, of its topological concavity, in the general process, of its eminently corroborative contortion-based symmetry. Whereas; A homotopic expansion, that is inverse Clifford, is to tend to bear a radial inverse contortion, of its topological concavity, in the general process, of its eminently corroborative contortion-based symmetry. When the particular Euler characterization, of the homotopic expansion, is to be reduced by a genus of Lagrangian-Based exemplification, in so as to thereby tend to work to bear a complex tensor-based physical attribute, to the bending of the eminently corroborative phenomenology, that this particular situation, will thereby tend to be one, in which the topological concavity is to invert.

Euclidean/Clifford Homotopic expansions, that are inextricably heuristic in nature, often tend to be light energy/light matter-based. Whereas; Euclidean/Clifford Homotopic expansions, that are inextricably inverse in nature, often tend to be dark energy/dark matter-based. 




Tuesday, March 7, 2023

Homotopy Of Frequencies

 Two different kinematically flowing covariant, homeomorphic frequencies, often tend to bear an eminent  tense of homotopy, when in terms of their directly associated Fourier-Related-Progression.SAM ROACH.

A highly succinct, gauge-invariant, kinetically transferred, Kahler Hamiltonian Operator, that is proximal local, to a viably incurred, anti gravitational field, may often tend to work to exhibit, a venue of relatively strong,  Kahler-Based physical attributes, that may be described of, as being eminently related, to a general genus, of what may be termed of, as being extremal metrics.  

A kinetically impelled, Yau-Exact, Kahler Hamiltonian Operator, that works to bear a Euclidean-Based Expansion, that is here to be in sync, with its eminently associated Clifford-Based Expansion, may often tend to work to exhibit, a hermitian-related tense of acceleration.  

A kinetically transferred, Calabi-Yau field, when under the proximal local influence, of an anti gravitational force, that works to attenuate, the general covariant physical incursion, of an otherwise more applicable tense, of Gravitational Topological Variance, may, at times, tend to increase the potential probability, in which the implicit, eminently associated, kinematically propagated, Calabi-Yau Manifold, in question, may thereunto have an enhanced capability, of thereby spontaneously exhibiting, the general likings, of a covariant, diffeomorphic Kahler-Based field, as taken over a proscribed duration of time.  

A Modification Of My Understanding Of The DNA Molecule:

In a reverse-fractal metaphorical manner; The projected trajectory, of the heuristic unraveling, of a DNA molecule, works to involve an analogous dual characterization, that may be considered, in a way, to be akin, to working to exhibit the form of a Dolbeault cohomology, while yet spontaneously working to exhibit, the behavior of a P-Adic cohomology. Whereas -- In a reverse-fractal metaphorical manner; The projected trajectory, of the heuristic bringing together, of two different eminently associated strands of a corroborative DNA molecule, works to involve an analogous dual characterization, that may be considered, in a way, to be akin, to working to exhibit the form of a Dolbeault cohomology, while yet spontaneously working to exhibit, the behavior of an Etale cohomology, 

The stronger the Slater-Based Incursion is to be, the greater that the spontaneous covariant escalation of Cohomological Generation, consequently tends to be. Also; The stronger the Poincaré-Based Incursion is to be, the greater that the spontaneous covariant escalation of Cohomological De-generation, consequently tends to be. 

The more succinct that the corroborative Fourier-Related-Progression is to be, for an eminently associated, kinetically transferred Kahler Topological Manifold, the more likely that such an implicit Kahler Hamiltonian topological entity, that is here to behave as a team of mass-bearing discrete energy eigenstates, may often tend to be potentially capable of thereby working to potentially achieve, a consequentially resultant enhanced ability, of being facilitated into spontaneously escalating in its Lagrangian-Based Expansion, over a proscribed duration, in what will tend to be physically demonstrative here, as working to exhibit a relatively hermitian set of conditions. 

The more resolute that the corroborative Fourier-Related-Progression is to be, for an eminently associated, kinetically transferred Kahler Topological Manifold, the stronger that its directly related inertial-based pulsation may often tend to be, to where external forces may thereby find it relatively more difficult, to be able to impede the continued motion, of the stated Manifold.  

The more conformal invariant, that a given arbitrary, kinematically propagated Fadeev-Popov Trace eigenstate, is to be exhibited as working to express, the more steady-state, that the eminently associated, implicit discrete energy quantum, may often thereby tend to work to be demonstrative as being; To where, the more likely, that the  mentioned implicit discrete energy quantum, may thereby have the general tendency, of working to express a viable tense of corroborative gauge-invariance, to where such a stated eminently associated discrete quantum of energy, may thereby often tend to bear an enhanced tendency, of exhibiting the general Ward-Cauchy-Related physical feature, of a viable tense, of corroborative isotropic stability.  

A pulsating frequency, that works to bear, a corroborative dimensional-related wave-tug, may often tend to spontaneously work to exhibit, a resolute tense, of an eminently associated Fourier-Related-Progression. Whereas; A pulsating frequency, that works to bear, a corroborative durational-related wave-tug, may often tend to spontaneously work to exhibit, a succinct tense, of an eminently associated Fourier-Related-Progression. 

When a given arbitrary Kähler Hamiltonian Topological Manifold, of which is here to be imparted upon, by an eminently associated Slater-Based Incursion, is thence to spontaneously work to bear a corroborative angular frequency, that is here to be symmetrically magnified, in a respectively recursive manner, over a proscribed duration of time, it may often tend to consequently follow, that the earlier stated Kahler Hamiltonian Topological Manifold, will thereby often become spontaneously transversely accelerated, in a respectively probable proportionality, that is here to be eminently in covariant corroboration, with the implicit pseudo description, of the Slater Induced wave amplification, of which is here to be in regards to the eminently associated escalating Lagrangian-Based Expansion, that is here to be kinematically propagated, in what will generally tend to be expressed of as, in both a wave-based manner, And, in a particle-based manner. 

Harmonically re-calibrating Chern-Simons Invariant gauge-actions, tend to couple the i*PI(del) Action with angular frequency, working to produce the stuff of charge. 



Thursday, January 19, 2023

When A Yau-Exact Calabi-Yau Manifold Is Kahler

 When a Yau-Exact Calabi-Yau Manifold, is to work to bear a recursive physically attributable spatial translation, of its covariant proximal local homotopic metric-related characteristics, in a piecewise continuous manner, as taken over a directly corresponding Fourier-Related-Progression, this will often tend to be indicative of the proximal local presence, of a topological manifold, of which is here to be expressing the general quality, of exhibiting the display of a tense of the Kahler-Metric. SAM.(1989). 

Monday, January 16, 2023

Homeomorphic Field That Is Also Homotopic

 A given arbitrary Noether-Based homeomorphic gauge-invariant set, of two different highly Kahler Hamiltonian Operators, of which are here to be kinematically morphologically interdependent, as taken at the Poincare level, to the Gliosis-Based Riemann surface, that is of their so-eluded-to relatively smooth externalized Gaussian core-field-density, may often be construed of here, as being a dual homotopic state, of a kinetically driven pair of geometrically symmetrical covariant interchanging energy eigenstates. SAMUEL DAVID ROACH.

Sunday, January 15, 2023

Cassimer Invariance -- Noether-Flow

 Since Casimir Invariance may potentially be thought of, as being the perpetual tendency of substringular  phenomenology, interchanging eigenstates, to maintain homotopy per instanton, it can thereby be theoretically surmised, that the multiplicity of Casimir Invariance, may often have a viable influence, upon the multitude of symmetrisms, of that net general physical condition of Ward-Cauchy-Related Gaussian geometric ordering, that is often thought of, as being Noether-Flow. SAMUEL DAVID ROACH. 

Topological Contortion-Based Symmetrism

 In many potential genre of the word, the term, homotopy, may often be thought of as being:

(Interactive) Topological Contortion-Based Symmetrism. LATER ON! SAMUEL ROACH.

Friday, January 13, 2023

Incursion Of Heat Upon The Cohomology Of A Hamiltonian Operator

 The incursion of heat, upon the topological manifold, of the cohomology of a Noether-Based mass-bearing Hamiltonian Operator, may often tend to work to produce Chern-Simons-Related spurs, as taken at the Poincare level, to the net world-sheet of the stated Hamiltonian Operator, when this is here to be considered, as being induced into existence at a region, which is proximal local to the general region of the said incursion, when this is taken along the topological surface of the homotopy-related structure. SAMUEL ROACH. 

Hermitian World-Sheet -- Smooth Homotopy

 When the mappable-tracing, as taken along the topological surface of a given arbitrary world-sheet, is hermitian, then it may be said, that the directly associated cohomology, is here to tend to bear a smooth homotopy. I WILL CONTINUE WITH THE SUSPENSE LATER! TO BE CONTINUED! SAM.

Wednesday, January 4, 2023

Anharmonic Divergent Tense Of Homotopy

 Tesla Energy tends to express an anharmonic divergent tense of homotopy. SAMUEL ROACH.

Saturday, November 19, 2022

Inter-Binding(s) Between Linked Cohomology-Related World-Sheets

 When the inter-binding(s) between linked cohomology-related world-sheets is (are) hermitian, the inferred net flow of curvature, of which is here to interdependently exist from amongst the proximal local presence of such world-sheets, is thence to often tend to work to bear a relatively smooth homotopy. SAMUEL ROACH. 

Sunday, October 9, 2022

Hermitian Homotopy -- Deeper Pulsation Of Majorana-Weyl-Invariant-Mode

 The more hermitian that the homotopy of a net Majorana-Weyl-Invariant-Mode is to be, the deeper of a pulsation that its directly associated Hamiltonian Operator will tend to display. SINCERELY, SAMUEL. 

Hermitian Homotopy Of Net Majorana-Weyl-Invariant-Mode

 The more hermitian that the homotopy of a net Majorana-Weyl-Invariant-Mode is to be, the stronger of a resonant vibration that its directly associated Hamiltonian Operator will therefore tend to exhibit. SAM.

Thursday, October 6, 2022

Cevita Action; Working To Facilitate, An Anharmonic Perturbation Of The Homotopic Translation, Of A Respective Set, Of Light-Cone-Gauge Eigenstates

A Yukawa-Based incursion, of a given arbitrary exemplification of an eigenstate, of the Cevita Action, may often have the capacity, of being able to work to facilitate, an anharmonic perturbation, of the general homotopic translation, that was here to be inherently expressed, by a respective set, of an initially quantized group, of integrable light-cone-gauge eigenstates, of which are here to be considered, as working to help comprise, the discrete energy-related phenomenology, of a given arbitrary beam of electromagnetic energy, that is here to have been eluded-to, as being in the process of ensuing, in so as to have just been spontaneously scattered, by an externally viable Ward-Cauchy-Related source. SINCERELY, SAMUEL ROACH.

Wednesday, October 5, 2022

Perturbation Out Of Homotopy

 When the isomorphic symmetry of the holonomic metric, of an initially homotopic set of discrete energy, is brought into a perturbative state, this will often tend to incur the general physical condition, to where such a mentioned respective set of discrete energy quanta, is thence to often tend to ensue, in so as to spontaneously be brought out of such a general physical condition of homotopy. SAMUEL ROACH.

Friday, September 30, 2022

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).

Sunday, January 5, 2020

Some Stuff As To Space-Time-Fabric

Mini-Stringular Segmentation works to form those general fields, -- by which discrete energy and norm-state-projection-related commutation, are thence to be able to be held together, via what may be termed of here as being the general substringular condition of "homotopy." In-Between the countless eigenstates of mini-stringular segmentation, that are here to be existent in the substringular, -- there is the multiplicit proximal local presence, of what I term of here, as being the phenomenology of "pressurized vacuum."  The overall arena, by which the substringular is here to be exhibited by discrete energy -- over the course of the sequential series of the countless iterations of those instants, of what I term of as being the generally noticed durations of Ultimon Flow, there tends to generally  be the condition, by which such an arena is here to be filled by the summation of both the overall scalar magnitude of mini-stringular segmentation, Plus, the overall scalar magnitude of that pressurized vacuum, that is here to exist in-between the strand-like eigenstates of the said mini-stringular segmentation. I will continue with the suspense later! To Be Continued! Samuel David Roach.

Sunday, December 29, 2019

Mini-Stringular Segmentation And Second-Order Point Particles

In regards to my particular model of string theory, what works to form the intrinsic binding of the multiplicit homotopic inter-connections of Ward-Cauchy-based fields, that are here to exist in the substringular, is the the kinematic presence of what I term of as being "mini-stringular segmentation."  Mini-Stringular segmentation, is what tends to bind the vast array of substringular fields together, -- and this is comprised of here by what I term of as being tiny "beads" of second-order point particles, that are here to be held together by what I term of as being the kinematic presence of "sub-mini-string."  These just mentioned second-order point particles may be thought of as being balled-up third-order point particles, that are here to tend to be subtended, in a relatively invariant manner at an internal reference-frame,  from within the general Ward-Neumman bounds of these said second-order point particles.  Consequently; as the kinematic disturbances in space, that are of the wave-related vibrational oscillations of mini-stringular segmentation, -- is to become codifferentiable with its environment in a kinematic manner, to where this is thence to work to form the general tense of that multiplicit perturbation in time and space, that is here to work to allow for the general covariance of the wave-based interaction of such inferred superstringular fields, those second-order point particles are consequently to tend to bear a relative tense of conformal invariance at an internal reference-frame, even as the so-eluded-to external reference-frame that is here to be of the mini-stringular segmentation itself, is here to bear a relative tense of a continual covariant wave-related perturbation.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Wednesday, August 29, 2018

Homotopy And First-Order Point Particles

A basic idea behind the concept of homotopy, is -- that every first-order point particle has at least a certain amount of mini-stringular segmentation extending from it -- at all times in which it is unfrayed.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Tuesday, August 28, 2018

The Light-Cone-Gauge And Homotopy

In so long as there is no fraying involved in the directly pertinent substringular fabric of which I am about to describe, -- whenever  any given arbitrary first-order light-cone-gauge eigenstate is to act, in so as to be in the process of retying its second-order eigenstates -- this of which happens as the general genus of the homology that is of the directly corresponding superstring of discrete energy permittivity, is to either go from being of a Legendre homology into a symplectic homology, or, vice-versa -- then, such a general genus of a Ward-Cauchy-related activity, is to happen with a maintenance of homotopy in the process of such a perturbative interaction.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Tuesday, February 6, 2018

Inter-Connective Mini-Stringular Segmentation

What I am about to talk about first, is most related to substringular impedance -- so read carefully -- and  "hold onto your hats!"  The higher that the scalar amplitude of the Polyakov Action eigenstate is, the more mini-stringular segmentation that there will tend to be -- that is fed into the proximal locus of the directly corresponding first-order light-cone-gauge eigenstate.  The more mini-stringular segmentation that there will be, that is fed into the proximal locus of the directly corresponding first-order light-cone-gauge eigenstate -- the more mini-stringular segmentation that there will tend to be, that is fed into the correlative proximal local second-order light-cone-gauge eigenstates, that are here to have worked to comprise the earlier mentioned first-order light-cone-gauge eigenstate.  This relative insurgence of mini-stringular segmentation, will then tend to work at causing a relative insurgence of impedance-based interconenctive mini-stringular eigenindices -- of which will then tend to work to cause a relative increase in the scalar amplitude of the proximal local impedance-based covariant field eigenindices -- that will then tend to be proximal at the here relatively adjacent substringular neighborhood.  Here is an example, in so as to work to elaborate at what I mean by this.  Mini-Stringular segmentation is what works to inter-connect Ward-Cauchy-based substringular phenomenology, as well as the condition that mini-stringular segmentation is what works to form both substringular fields and the general basis of homotopy.  Such said segmentation is what works to hold the unfrayed quanta of energy in the space-time-continuum together, per each successive iteration of group-related instanton.  The more of a "Hodge-Index" that one is to relatively bear, as to the scalar magnitude of the degree of the mini-stringular segmentation, that is then to be present -- the more likely that there is to be a higher scalar magnitude as to both the number of mini-stringular inter-connections, as well as the number of inter-connective field eigenindices -- that may exist here, to be utilized in so as to then to work to bear a Yukawa Coupling with that general stratum, that is here to be most directly associated with such an increase in mini-stringular segmentation.  Thence -- when the Lorentz-Four-Contraction that is most directly associated with a phenomenon is low, and its consequent Polyakov Action, is then to be high -- then, its consequent light-cone-gauge eigenstate, and thus the directly corresponding wave-related tense of substringular impedance, will then tend to bear a higher stability of homotopic residue.  This will then tend to be the inverse as to what will happen to the correlative discrete quantum of energy permittivity.  This will then tend to, instead, to work to decrease the field-interconnection-based eigenindices, in so as to work to bear a lower stability of homotopic residue  -- that would otherwise work for superstrings of discrete energy permittivity.  "Superstrings," in my model, may be generally typified as being superstrings of discrete energy permittivity.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.