When various pattern analysis methods are applied to study the Universe, this leads to considering the four interactive forces of Nature as emerging blueprints, and the fundamental constants as numerical primitives. Starting from two basic premises, the principles of interdependence and of asymptotic congruence, and using a statistical pattern recognition paradigm based on Bayes' law and the central limit theorem, Einstein's global field equation is generalized to incorporate a factor that takes into account the probability of presence of a given matter-energy density and better reflects its interconnected role with space-time curvature. One key feature of the resulting metric is that it postulates the existence of an intrinsic physical constant , a star-specific proper length that scales measurements in its surroundings. In this context, a weighted Newton's law of gravitation emerges from the slowly convergent process of massive object formation and the errors of convergence toward this Gaussian representation can be assimilated to three residual interactions that share common similarities with the Coulomb's law, the weak and strong forces. It is also shown that the archetype static model is algebraically equivalent to an asymmetric metric that describes a massive body dragging its associated space-time, inducing rotation and expansion. Furthermore, the whole paradigm highlights some basic relationships between many physical constants and the star proper length.