Tachyonic Motion And Homotopic Residue

Tachyonic activities -- meaning here, quantum leaps that are not Noether, -- work to compensate for the condition of electromagnetic energy to not be gaining nor losing partition-based discrepancies, per instanton, while such phenomenology is in the process of acting as electromagnetic energy.  The idea of homotopic residue, works to refer to the resultant of the exchange of the holonomic substate of the said homotopic residue, -- whereas, the Betti number refers to the condition of either the compactification (positive Betti number) or the decompactification (negative Betti number) of the cohomological generation or cohomological degeneration of a superstring.  When there is a discharge of cohomological eigenstates -- this often results in either the compactification or the decompactification of spatial dimensionality.  A superstring's dimensionality -- if of a cohological-related tense -- will tend to compactify during right before BRST, -- whereas, such a said superstring will tend to decompactify during the ensuing Regge Action.  Sincerely, Samuel David Roach.