As To The Configurations of World-Sheets

If a given arbitrary world-sheet is of a toroidal-shaped-nature, then, the physical ends of the Ward-Neumman boudaries of those ghost anomalies that work to trace the mapped-out extrapolation as to the trajectory of the projection of the directly corresponding superstrings -- that worked to form the so-stated ghost anomalies -- via the physical evidence of the directly corresponding world-sheets, bear cap-like permutations that act as critical cusps that are due to the just-eluded-to cyclic permutation of those cross-sections of the so-stated external format of first-ordered point particles that bear a chirality, which is relative to the other of such so-stated critical cusps, that may be either symmetrically fashioned or assymetrically fashioned -- in relation to the directly corresponding trivially isomorphic alterior end caps of that toroidal-based pointal-construction of the mentioned ghost-based configuration -- that bears a mappable tracing that is shaped like a "doughnut" that bears a central anuulus that contains a non-time-oriented Lagrangian that is Gliossi to the so-stated pointal configuration of the world-sheet, which is relatively hermitian in unitary flow, as one were to map the coniaxions that work to indicate the relative vacuum that would here be at the Poincaire level of the center of the so-stated world-sheet.  If the so-stated end caps in this case are symmetrically arranged, any given arbitrary superstring that may be potentially caught in the said anuulus -- during any given arbitrary group metric in which the said ghost anomaly configuration is not yet annharmonically scattered -- will propagate out of the Ward-Neumman bounds of the so-eluded-to ghost-based configuration, in a forward-holomorphic-based directoral flow of the given topological sway.  If one of the so-stated end caps is arranged symmetrically, with its so-eluded-to counterpart, yet, the other end Lagrangian-based mapping of end caps is arranged antisymmetrically with its counterpart, then, the chirality of the so-stated Lagrangian will bear Chern-Simmons singularities.  Also, with the past format of scenario, over time, such a situation will work to form metrical-based singularities -- with the kinematic flow of its external-based enviorenment.  This metrical dissonance would then work to pull any given arbitrary superstring that is within the region of the so-stated anuulus of the toroidal-based world-sheet configuration in the reverse-holomorpohic directoral flow of topological sway.  If two or more of such sets of end caps is annharmonic -- in terms of the non-time-oriented mapping of the chirality of their counterpart -- as taken via a trivially isomorphic extrapolation, then, any given superstring caught within this genus of construction will rebound between the end caps per iteration.  Yet, this is given the general space-time-curvature-based considerations. So, ironically yet logically enough, if the end caps of this general format of scenario are only harmonically chiral, via the extrapolation of a Wilson-based linearity, then, the so-stated rebounding of superstrings that would be caught-up in a configuration such as this would rebound in a manner that would work to reattain fractals of discrete energy permittivity in superstrings. Hint: the Schotky Construction and the Klein Bottle.  I will continue with the suspense later!  To Be Continued.  Sam Roach.