Non-Euclidean-based Traces

Substringular phenomena tends to move in such a manner in so that it leaves physical traces as to where it just was before it reached a different spot. Such physical traces are known of as ghost anomalies. Such ghosts may move in either form a euclidean-based mapping or a euler-based tracing. The tracing may be either proportional to its immediate surroundings, or, the expansion of the mapping as may be derived by a Laplacian-based tracing of the ghost-like delineations that here may be Clifford in nature. These just mentioned ghosts form a Laplacian-basis as to how one may work to determine where certain substringular phenomena were, and, from such knowledge, such a mapping may work to help determine -- through non-euclidean math -- where such substringular phenomena will be in the future. So, the activity that forms such traces happens over Fourier-based Transformations, yet, the actual mapping of such traces often involves a timeless determination that involves relative "snapshots" of what would here exist in such a manner in so as to work to determine the physical evidence as to where, what, and how certain substringular phenomena had moved over the directly prior period in which it had moved in so as to form such relatively stagnant traces. Such ghosts may be Rham or Doubolt in terms of their covariant cohomology. Often, though, the topological-based framework of certain ghost anomalies may be kinematic -- causing the basis of such a framework to instead bear the need to be mapped over a tracing that here involves a Fourier-based Transformation through an onset of redistributional extrapolation. Sincerely, Sam Roach.