All world-sheets have either a jointal flow, a smooth-curved-based flow, or, a combination of having both a jointal flow and a smooth-curved-based flow -- when taken along the topological mapping of the Lagrangian tracing of the respective world-sheets that here may be in question. All cohomology must then have either a jointal flow, a smooth-curved-based flow, or, a combination of both a jointal flow and a smooth-curved-based flow. There are two basic types of Real Reimmanian cohomology that are to be considered here. There is a general format of cohomology that may be named of as a Rham-based cohomology. And, there is also a general format of cohomology that may be named of as a Doubolt-based cohomology. A cohomology that is of a Rham-based genus of cohomology is traceable in mapping through the Lagrangian of the trajectory of its projection, in a manner that has a tendency of bearing a relatively straight delneation -- in so long as no exterialized Hamiltonian operation does not pull the directly corresponding mapped-out ghost anomaly-based trace of the correlative world-sheets away from a relatively linear projection over time. Yet, more intrinsically, a Rham-based cohomology is a cohomology that is traceable, as a holonomic substrate, as a hermitian delineation of the physical mapping of the prior motion and existence of superstrings that have just moved within a relatively Real Reimmanian-based region -- over any given arbitrary scope of time in which such a residue of the projection of the trajectory of such directly affiliated superstrings have just transiently moved from within a region that may be deemed of as being within what may be thought of as a relative Real Reimmanian plane. Such a cohomology is considered Real and not Njenhuis as well, on account of the conditionality that the formation of those ghost anomaly-based indices that work to form the directly associated ghost anomalies -- that are here the physical memory of both the motion and the existence of superstrings -- are formed over the metrical course of the iterations and reiterations of the eluded to associated superstrings that are being mapped-out, from one positioning of these superstrings during one group instanton to the next positioning of these superstrings during each succeeding group instanton. This happens during the course of being mapped-out as a traceable memory of the time-oriented conditions of such superstrings, as these have kinematically differentiated during the generally noticed durations of Ultimon Flow. So, even if a given arbitrary superstring is pulled out of the condition of having a relatively straight delineation, as is often the case, if the affiliated ghost-based pattern is hermitian over both the mapped-out translation of the Lagrangian, and, is also hermitian over the directly associated group metric of the said superstring over time, then, such a resulting ghost anomaly-based pattern is said to be of a Rham-based genus. The tendency of the inertia of a physical entity that is hermitian is to move in a relatively straight delineation. So, this is why a Rham-based cohomology is considered to have a basis of tending to move in a relatively linear projection. So, a Doubolt cohomology -- since it is not hermitian -- tends to move in a more jointal topological-based sway, as the directly associated ghosts that work to form the correlative cohomology are here pulled out of hermicity by either a Lagrangian-based spike, and/or, are pulled out of hermitcity by a metrical-based spike. This works to show the condition that the formation of singularities in either the Lagrangian-based projection of ghost anomalies and/or the formation of singularities in the metrical-based projection of ghost anomlies.indicates a Chern-Simmons genus that has a tendency of veering off of a relatively linear-based path. I will continue with the suspense later! To Be Continued!
Sincerely, Samuel David Roach.
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