  The Superspinorial Dual-covariant Field Theory (SSFT) developed in papers [1,
2] is treated in terms of Riemannian coordinates (RC) [7, 8] in space of the N
dimensions unified manifold (UM). Metric tensor of UM (grand metric, GM) is
built on the split metric matrices (SM) [1] which are a proportion of the
Cartan's affinors (an extended analog of Dirac's matrices) of his Theory of
Spinors [3] as explicated in [2]. Transition to RC based on consideration of
geodesics is described. A principal property of an orthogonal RC frame (ORC)
utilized in the present paper is constancy of the rotation matrix A of the
Riemannian space of UM, while transformation matrix B of the dual
superspinorial state vector field (DSV) varies together with Cartan's affinors
according to the dynamical law of SSFT derived in [2]. The spinorial genesis of
notion of the orthogonality as aspect of irreducible SSFT is pointed out in the
present paper. The main outcome of resorting to an orthogonal RC frame (ORC) is
explication of the conformal dynamic invariance of metric i.e. constancy of
ratio between components of GM in ORC frame. This leads to possibility of
reduction of algebraic equations of SSFT for the SM [2] to equation for GM
determinant where GM signature plays a role of N discrete parameters
non-specified in advance.
