Recent discussions attributed fermion mass to an analogue of Weyl curvature which occurred by hypothesis when closed, spin
strings swept out closed world tubes. A new degree of freedom and corresponding curvature class were attributed to “second order tubes” that were swept out by initially introduced closed tubes, etc. Curvature classes were associated by hypothesis with composite masses
where d
enoted a mass-less spin
field and where a
and
respectively denoted an LH quark and an RH anti-lepton that were characterized by opposite I
3 values and shared a common generation. The resulting model accounted for known quark masses and predicted a new quark of mass 30 GeV/c
2. The composite masses
form a symmetry, the preservation of which is equivalent to the conservation of electrical charge and string scale. SUGRA interactions that preserve the proposed symmetry can therefore be precisely defined. In this context, gauge transformations that establish the proposed curvature classes also associate with a second realization of the originally generated symmetry, the preservation of which is equivalent to the conservation of string length and of the curvature
from which the postulated model generates admissible increments of large scale expansion. The latter symmetry is associated by hypothesis with the large scale structure of the observable universe, thereby motivating a theoretical approximation of the total number of galaxies. This result parallels the approximation that is indicated by observation.