Hello. My name is Samuel David Roach. I will provide part of an expaination for the person who provided the given topic of discussion.
A singularity in space is a spot where the limits of a wave pattern that is being considered do not mathematically exist and/or are not discrete between two or more loci that are being considered in a related scenario. For instance, if the third derivative of a general wave pattern changes between two loci in space that are distributed in space in a Lagrangian manner and under a Laplacian consideration, then the limits of curvature that exist in-between the two given loci will either not exist and/or will not be discrete in-between the given loci. Here, the point at which the limits of curvature are definitely made indiscrete is the particular locus where the third dirivative of curvature in the given wave pattern is altered or perturbated. Now, consider the given wave pattern to differentiate under time constraints that are kinematic and thus involve a Fourier Transformation. The given singularity as a specific entity would then more than likely differentiate in terms of its specific locus, even though the general wave pattern that we are considering would still have a limit of curvature that would not exist and/or not be discrete in-between two sections of the harmonics of the vibrating wave. In this case, the locus of the singularity in terms of Laplacian Transformation would remain relatively conformally invariant, yet the locus of the singularity in terms of Fourier Transformation may or may not bear a locus that space-wise will bear a tense of conformal invariance. Since the third-derivative of curvature here will change at the static location under the given Laplacian conditions, or at the covariant location under the given Fourier conditions, the spot where the curvature will change in its third derivative will be either a static or a kinematic singularity. Since the general curvature described bears a change in its third derivative, the curve itself will either exist in a multiplicit Minkowski Space or in a Hilbert Space, since such a change in the limits of curvature involves a Lagrangian that either implies holograpic volume or involves a distribution that actually happens over a volume in space. A differentiation that is not time oriented involves Laplacian conditions. A differentiation that is time oriented involves Fourier conditions. A singularity does not mean that zero or infinity are actually things -- it means that the flow of a wave pattern that is either static, harmonically oscillating, anharmonically oscillating, or is partially harmonically and partially anharmonically oscillating has a curvature that bears limits in-between two or more of its loci at one or more locations that alter abruptly relative to the general flow of the associated general wave pattern that is involved in a particular scenario. If such an abrupt change is smooth in all of the derivatives equal to the number of dimensions that a given wave pattern is in, then the associated singularity is described as hermitian. Yet, is such an abrupt change is not smooth in all of the derivativates equal to the number of dimensions that a given wave pattern is in, then the associated singularity is described as Chern-Simmons. If a singularity is not Chern-Simmons although the singularity is altered to where over a described covariant metric the singularity differentiates off of the Real Reimmanian plane, then the given singularity is not Yau-Exact. Yet, a hermitian singularity that is not perturbative (does not kinematically over a metric relocalize off of the Real Reimmanian plane under a limited Fourier set of conditions or over a condition of relative Laplacian Transformation that actually involves a very limited framework of time), then the singularity that is involved here is considered to be Yau-Exact.
Such a topic relates to whether or not something is Chern-Simmons, Yau-Exact, or partially Yau-Exact. If the curve formed by the trajectory of a superstring changes in any more direvatives than the number of dimensions that it exists in, then, the trajectory is said to bear one form or another of a Chern-Simmons genus. When the flow of the trajectory of a curvature of a superstring is not smooth in its kinematic translation over time, then the said trajectory is said to be spurious. A spurious trajectory that is still hermitian is said to be partially Yau-Exact. The more spurious and/or non-hermitian a trajectory, the more anharmonic is its translation over space. It takes anharmonic motion to form certain forms of perturbation that work to allow for certain necessary changes -- such as anharmonic Schwinger-Indices work to indirectly, through the Rarita Structure, allow for the Wick Action so that Gaussian Translations may subsequently forf.
Thank you for your time.
Sincerely, Samuel David Roach
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