Thursday, January 12, 2023

The Homotopy Duality Paradox

 Here is a paradox that I have thought about, that I would like to share with my readers here:

Let us initially consider two different world-sheets of cohomology-related holonomy. Let us now say, that these two different respectively considered world-sheets, are, in at least some manner or another, to inter-bind, in a cohomology-related manner, at some Laplacian-Related particular region, in time and space. Let us next say, that one of these two stated world-sheets, is primordially of five physical spatial dimensions, whereas, the other of the two stated world-sheets, is instead, primordially of six physical spatial dimensions. Let us next say, that there is some sort of a tense of homotopic convergence, of which is here to help work to facilitate, at least some sort of a connection, between these two different and distinct inferred of, cohomology-path-based topological manifolds, of potentially traceable propagated holonomic curvature-related structure. Next; Let us say that there were here to be, two different sets of two propagational Ricci-Based flows of cohomology-related deformation, that are here to be distributed in delineation, both along and through, the general proximal local region, at which these two different individually taken sets of inferred homotopic curvatures are to inter-bind, in so as to work to bear a potential case scenario of homotopy, when this is in terms of the desirable continuous flow of space-time curvature, from the propagational Transform of Fourier-Related-Progression of one of these two said world-sheets, to the other. Let us now consider, when each of the individually taken sets of cohomology-related flow, are to become eminently Gliosis to one another, at the Poincare level to their core-field-density, that the inferred consequential collision of vibrational oscillation, will thereupon tend to result, in a net generative flow of cohomology-related deformation, of which is here to be tugged into the "arena," of only one of the two individually taken earlier mentioned world-sheets. Let us say, that one of these two net gauged flows of cohomology-related deformation, is to be tugged into the respective world-sheet eluded-to earlier, that is of five spatial dimensions plus time. Whereas; The other of these two net gauged flows of cohomology-related deformation, is to be tugged into the respective world-sheet eluded-to earlier, that is of six spatial dimensions plus time. Let us next say, now, that the mentioned net flow, that is to be tugged into the field of cotangent bundle R5, at the point of crossing the inferred boundary, that is here to be indistinguishably interconnecting the two stated world-sheets, is to be changing in its sixth  spatial-related derivative. Also; The mentioned net flow, that is to be tugged into the field of cotangent bundle R6, at the point of crossing the inferred boundary, that is here to be indistinguishably interconnecting the two stated world-sheets, is also to be changing in its sixth spatial-related derivative. The cohomology-related flow of the two, as such, that is to be net transferred into the world-sheet of R5, will tend to have a Chern-Simons-Related spur, at the regional locus of the general interconnection, that is here to be between the two earlier stated "meshing" world-sheets; Yet -- The cohomology-related flow of the two, as such, that is to be transferred into the world-sheet of R6, will tend to be hermitian, at the regional locus of the general interconnection, that is here to be between the two earlier stated "meshing" world-sheets. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. (PHS1989).

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