The First Part of an Aside to Course 16

When a superstring reiterates through a trajectory, the given superstring that was just mentioned works to form a ghost anomaly -- that acts as the physical memory of the just eluded to world-sheet.  (A world-sheet is a discrete trajectory of a superstring.)  When either a one-dimensional superstring of discrete energy permittivity, or, when a two-dimensional superstring of discrete energy permittivity, forms a world-sheet -- there is often an annulus formed from within the Ward-Neumman bounds of the ghost anomaly that acts as the physical memory of the just eluded to world-sheet.  At the substringular level, the just mentioned genus of annulus is here an oriface or "hole" where there are no first-ordered point particles present -- at any given arbitrary iteration of group instanton, that works to directly correspond to the said condition of there being an annulus -- from within the Ward-Neumman bounds of the Hamiltonian operand of the projection of the trajectory of any given arbitrary superstring of discrete energy permittivity -- that would work to form such a said annulus over the course of the kinematic activity of such a given arbitrary superstring.  An annulus here is an empty projection that works to bear no first-ordered point particles that would otherwise contain such eluded to first-ordered point particles.  World-Sheet projection that bears both a Lagrangian-based smoothness and a metrical-based smoothness over time is said to bear a Yau-Exact genus of Real cohomology.  A Yau-Exact genus of Real cohomology does not in and of itself bear any directly corresponding Chern-Simmons singularities, when considering this from within the premises of its Ward-Neumman bounds, from within either the Lagrangian-based and/or from within the metrical-based kinematic orientation that works to directly affiliate with any given arbitrary ghost anomaly, of which corresponds to the trajectory of the motion of the corresponding superstrings of discrete energy permittivity that may be considered here as forming the eluded to projection over time.  A Yau-Exact genus of a Real cohomology tends to kinematically differentiate within the Ward-Caucy bounds, over time, in such a manner that bears a harmonic oscillation during the directly corresponding sequential series of iterations of group instanton -- in which the correlative superstrings of discrete energy permittivity that I have here eluded to are differentially associating as having the said Yau-Exact condition of a Real-based cohomology.  The directly associated Fadeev-Popov-Trace eigenstates that would here thus correlate to the said superstrings of discrete energy permittivity -- of which act as the corresponding discrete units of energy impedance -- would thus act accordingly as physical phenomena that bear a Yau-Exact genus of Real cohomology.  The difference in operational function that exists between a discrete unit of energy permittivity and a discrete unit of energy impedance is that the respective superstrings work to pull the discrete energy in the general manner of the relative holomorphic directoral topological-based sway, while the respective Fadeev-Popov-Trace eigenstates work to hold the discrete energy, in a homotopic manner,  back enough to keep the said energy from resonating.   Superstrings act as discrete units ofenergy permittivity, while, Fadeev-Popov-Trace eigenstates act as discrete units of energy impedance.  I will continue with the suspense later! Sam Roach.