NSk--Einstein establishes the local metric apparatus of the NSk/ψ program in the weak-field regime. The module does not construct a complete gravitational field theory; its role is to receive local geometric data together with the upstream weak-field package and to transform them into a coherent Einsteinian description comprising local time, the metric component g00, the spacetime interval, time dilation, and gravitational redshift. In the pure part, the module organises the relation between the family of geometric backgrounds g(θν) and the local relativistic apparatus, separating the deformation parameter of the background from local time. In the core part, it derives the local weak-field metric readout, the Newtonian consistency condition, and a package of results concerning geodesics, weak-field curvature, and local signal propagation. The module thus provides a theorem-level bridge between the geometric upstream of the program and downstream relativistic and spinorial modules, while leaving the gravitational source on the side of NSk--Gravity.
Nowak et al. (Sat,) studied this question.
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